Episode 20.10: Matt and Martin


Nice show today, although my mic was still messed up. I’m starting to wonder if I simply function as a damping field for all of the studio’s electronics. My light even went out about a minute before the show. Ah, well. Apart from that, I enjoyed our first caller, a Christian with whom we had a fruitful discussion, in which Matt made himself understood as to why personal testimonials about life-changing results are still no measure by which we can conclude anything about the truth of Christianity’s supernatural claims.

Also, here’s the Presuppositionalism Panel Discussion video that Matt talked about participating in.

Comments

  1. Tom Horwat says

    Haha, loved Martins comment about so called atheists saying “No no, you’re atheisting wrong”. He’s absolutely right, theonly condition to being an atheist is to not believe in God. That’s it.

  2. King Lam says

    I miss the opening theme music that you used to have when you were doing the show at public access.

  3. says

    oddly, the first caller seems to think that a story that he has only second-hand knowledge of, from someone he never established as credible, should be convincing to other people as a third-hand story, especially when the caller himself is no more than another link in a chain of anonymous storytellers.

    as he finally unwound his story he sounded indistinguishable from, and no more compelling than, a preacher reciting a parable from scripture.

  4. Simon Hosking says

    I had a conversation with a friend of mine who is a Baptist Minister. He gave me a fascinating story involving an exorcism with multiple witnesses.

    It was a cool story, but as usual, there is no way to attribute the cause to Jesus. Many years ago I witnessed an exorcism with WAY more evidence than this Minister’s story. Only problem was the exorcism I witnessed was done in the name of Allah.

    It can’t be that both Jesus and Allah are doing exorcisms, but it could be that neither are.

    I don’t know how these exorcisms worked. I have a few hypotheses involving the power of the group, hypnosis and trance states but ultimately I just don’t know.

    I wish the first caller would get to the same conclusion. He doesn’t know why – accept it.

    (love the show btw.)

  5. says

    Regarding the first caller’s questions about how many peoples’ stories it’d take to be able to rationally conclude that their asserted cause is true,

    Suppose there was a virus that causes the infected to really enjoy football, and causes them to believe that this personality change was due to being abducted and reprogrammed by aliens (and not the virus).

    What we’d have is a bunch of people who have these experiences, and consistently state that they were abducted by aliens. It doesn’t matter how many people this happens to… that never becomes true. Their asserted “cause” is incorrect.

    When it comes to conversion stores with real people, we frequently have consistent psychological factors that can cause consistently asserted wrong causes. If we’re talking about America, we have:

    1) People living in a predominantly Christian society, with that messaging permeating through everything.
    2) The tendency of humans to anthropomorphize almost anything.
    3) The tendency to be superstitious, doing a lot of false pattern-matching.

    Under those conditions I’d expect to find people having life-altering experiences, attributing it to some invisible universe-controlling mind, based on flimsy weak correlations. The caller seems to deny that it’s possible for there to be a *different* common cause for these anecdotes.

    That’s why I don’t find his position compelling.

  6. Athywren - not the moon you're looking for says

    I’m in agreement with Martin re “regressive left.” It’s a meaningless phrase. The only thing it communicates is “I don’t like you or what you’re saying.” The only examples I’ve seen to date are left wing people who have the nerve to be angry, left wing people who comment without a full understanding of the facts, and people screaming on multiple platforms about how they’re being silenced by the regressive left, which, upon investigation, tends to come down to “I was criticised by (a) student(s).” The only use I’ve found for it is as a reason to doubt the rationality or honesty of the person bringing it up. It’s basically just the latest synonym for “left wing wrongthinker.”

  7. Athywren - not the moon you're looking for says

    Err… just for clarity, I’m saying I agree with what Martin said in the show – not saying that his stance and mine are necessarily equivalent on it. I’m sure there’s some degree of disagreement, just ’cause humans.

  8. Monocle Smile says

    Yeah, “regressive left” is like “make America great again.” Asking questions for clarification gets a string of crass non sequiturs in response. The same crowd says shit like “pussification of America.”

  9. says

    Yeah, as I said, it’s a dogwhistle from the kinds of people who dislike the fact that they’re suddenly living in an age where marginalized people have a voice of their own, and advocates to back them up. “Regressive” has entered the Lexicon Hysteriana simply because it’s the opposite of “progressive,” and it’s just flamebait. Because if you take the position that words have actual meanings (yeah, crazy, right?), if the “regressive left” were really regressive, it would have to be advocating a position that was a step backwards from progressivism. And in the context in which the right — including the crowd I’ve taken to calling the Donald Trump Atheists — is currently using it, they’re essentially suggesting that “being a raging, bigoted asshole to [insert minority or marginalized group here]” is a progressive stance, and that those who condemn such bigotry are taking the regressive stance. It’s part and parcel of the same reactionary mentality that causes otherwise intelligent people to shriek “Witch hunt!” and “Thought police!” when they really mean “I have received criticism.” And sadly, the fact that high-profile intellectuals like Dawkins have taken up this habit makes a certain class of cretin feel they’ve gotten validation.

  10. adamah says

    A point not mentioned to the 1st caller (Dave) is that the Bible is like a box of Whitman’s chocolate samplers, where one only needs to keep eating/reading to find a scripture that fits the desired outcome….

    E.g. many Xians will claim their material success in life (or turnarounds from drug abuse, etc) to be evidence of their being blessed by God, hence serving for them as concrete evidence of God’s existence.

    (And as another caller pointed out, nevermind that Jesus said to give all of one’s wealth to the poor to attain salvation, or that Xians would be persecuted and killed in Jesus’ name: that kind of thinking is not aligned with the quite-older ‘prosperity gospel’).

    On the other hand, those individuals ungoing misfortune (e.g. illness, death of family members, poverty, etc) will point to THAT as proof of God’s existence, claiming to be undergoing a test by God and pointing to the biblical example of Job.

    So win, lose, or draw, God is always given the credit. It’s a “can’t lose” proposition.

  11. EnlightenmentLiberal says

    To Jasper of Maine.

    Regarding the first caller’s questions about how many peoples’ stories it’d take to be able to rationally conclude that their asserted cause is true,

    Regarding the same issue. My take is: That’s not a question with an easy answer. It’s not simply a matter of numbers. Rather, we have to examine all of the plausible explanations, and see how well the (hypothetical) fact of a multitude of personal testimony fits each of the plausible explanations.

    Right now, we have a very large multitude of people who do testify that they talk with Jesus, or something. I’m not convinced. Rather, alternative hypotheses explain their testimony far better than their purported explanation “I actually talked with Jesus”. More of the same is not going to convince me. It’s going to take qualitatively different personal testimony. At the very least, it’s going to take testimony that very clearly does not fit the standard atheist alternative explanations.

  12. corwyn says

    @16:

    their purported explanation “I actually talked with Jesus”.

    That isn’t an explanation, but rather an assertion.

    Wanna see me make it disappear?
    “Can you use your phone to record the next time you talk with Jesus? Thanks.”
    Poof.

  13. noexitlovenow says

    Hamish is asking about the “regressive left”? Yeah, he is probably a poe.

    Regarding this term, there are those that have embraced the insult, but it adds nothing. You still need to argue about specific actions and/or policies in specific contexts.

  14. Joe E Dangerously says

    So my understanding of what the “regressive left” is, is something racists, sexists, and other bigots say to try to deflect away from their bigotry. The meme is more or less “it stops the conversation.” It’s pretty much used interchangeably with “SJW” and things like that. In other words, if you’re supportive of feminism or social justice you’re “regressive” because you don’t regard all points of view as equally valid. Well, you know what? Guilty as charged. I don’t consider racism, sexism, homophobia, transphobia, and other bigotry to be on the same level as real discourse. I think it was originally meant to describe Muslim apologists on the left, which is a problem, but it’s just completely lost its meaning by now. I don’t consider MRA talking points on the same level as serious discussions about women’s issues, for example, so the MRAs (Misogynistic Rape Apologists) label me “regressive” because I dismiss them as jackasses. Same with racists. If you use the term “Zionist” for example, I won’t take you seriously. That’s not regressive, that’s being sick of hearing bullshit xenophobia in the guise of a real conversation. But in the minds of bigots it’s simply a disagreement.

    Now since I know a lot of the viewers/listeners of TAE think like this, let me just cut this off at the pass. I don’t give a shit if you don’t think Superman is awesome or you liked Man of Steel or you don’t love Italian food. Those are opinions and they’re fine. If you think Batman is cooler than Superman, fine. If you don’t love The Sopranos, fine. If you don’t like Nintendo, fine. Those are all simple differences of opinion and though I might disagree with you I’m not offended by your opinions because they’re just opinions. But when you start to get into “feminism is a joke in the western world” territory that’s when your opinions become something else. Those views have real consequences. When you say “businesses should be able to refuse to serve black people if they want to” you’re talking about a scenario where certain people are being oppressed and advocating for that. When you say “if women are paid less it’s their own fault” you’re helping to strengthen a status quo that has detrimental effects on actual people. That’s not a difference of opinion. That’s bigotry. And no, those points of view are not valid and they are most certainly not on equal footing. You can go ahead and say Marvel’s superheroes are better than DC’s and I’ll disagree with you. That’s okay. But when you say the Holocaust didn’t happen and the Jews are orchestrating a giant conspiracy that fuels hate and hurts real people. That is not okay.

    (By the way, I’ve been having trouble logging in lately. That’s why I’m not logged in right now. I even saved the login on my system but every time I try it’s a “Bad Gateway” so I don’t know if anyone else is having this issue but just in case I thought I should mention it.)

  15. Dustin says

    The first caller should take in my euphoric feeling too.. In my room was feeling depressed, listening to music and then a euphoric feeling came over me… After a little and Happy as a kid in a candy store I thought, “sooo this is what theist feel when they experience a god”. An all knowing god knew i was going to be skeptical about it. So if it was a god it only pushed me farther away. But of course anyone wanting it to be true can find a way to rationalize this as my fault.

  16. amca says

    A response from Christians that I’ve heard regarding the “give all your money to the poor” story is that the instruction was specific to that person and not generalisable.

  17. says

    @Martin Wagner (and the rest of the AXP folks)

    Well this is cool, I found you all! Heh heh… OK, serious face. I know it didn’t come up in this episode, but I have a question regarding the fine-tuning argument (which I’ve heard hailed as one of the best arguments for a creator even though I find it one of the worst). In a nutshell, the claim as I recall is that the universe is so fine-tuned that if you tweak this or that parameter you’ll get a universe that cannot support life yada yada and I’ve seen “calculations” claiming the odds on a universe that can support life are one in something like 10^200 or some other silly number. While I’ve heard the counter that it’s possible in a multiverse scenario that there could be infinite universes and we happen to be in one that is suitable for life therefore here we are, I don’t recall personally hearing enough about the flaws in the attempts at calculating the probabilities. More specifically, the faults that the probability attempts fail to do something very important for them to be valid… they fail to remove impossible scenarios.

    Take for example a lottery where you pick six balls out of forty-five (assuming balls numbered 1 through 45). When doing the calculations you not only have to remove any combinations where you have duplicate numbers but you also have to remove all numbers less than one or greater than forty-five. This is where the fine-tuning argument fails most gloriously imo. Because we only have one set of parameters for universes that we actually know can happen, any variance to the parameters of the universe (weak force, strong force, gravity, speed of light, etc.) cannot be demonstrated to be viable. It’s possible, for example, that energy and matter will always “behave” the same way in any spawned universe simply because those are the properties of matter and energy. The speed of light could potentially always be exactly the same in any universe without variance. Even if you can plug varying numbers into calculations to hypothesize what could happen we have no examples at all of any different values being valid. It’s impossible, therefore, to determine if any changes are creating impossible scenarios that need to be eliminated from probability calculations and it is also possible that any other universes that may exist follow the exact same “laws” as ours.

    Now, I’m fairly certain that I’m not the first person in our or any other universe to think of it from this perspective, I simply don’t recall seeing it looked at this way, the failure of fine-tuning to be able to rule out impossible scenarios because they cannot demonstrate any other scenarios are possible. You, however, I’m sure have heard a lot more than I have, so I thought I’d toss this out there for… well, for whatever. 🙂 Hopefully this gets read. That would be cool.

  18. Kenny De Metter says

    I feel that I have to address the point about ‘regressive left’.
    It’s certainly true that the term is being misused

    However, the original usage of the word comes from Maajid Nawaz, who used it to describe people who call claim to be liberals, but who cannot bring themselves to condemn anti-liberal views and actions when they come from Muslims, and infact speak out against anyone who does want to address those points.

    For example, someone who dismisses violence towards women or gays specifically if it’s Muslims doing the violence, because they feel that speaking out against it would offend Muslims.

    The idea behind it being ‘regressive’ is that rather than progressing liberalism, it actually ‘regresses’ it, because,minorities within minorities ( for ex : gays in the Islamic world ) are not given the freedom they deserve.

    Essentially, this divides the ‘liberals’ into 2 strategic choices :
    1) Do you first try to address the problems in your home countries, even though they are less worse then those in other countries ?
    2) Do you first try to address the problems where they are the worst, even though your own country still has some problems ?

    I don’t know what the answer is. I just know there are decent individuals which I like on both sides, and I would just like it if they stopped attacking each other and worked together instead.

  19. says

    I had an amazing “religious” moment yesterday. I was driving home and saw a moving van with a religious verse on it (basically paraphrased as “love him because he loves you” or the like) and right as I saw that “Highway to Hell” started on the radio.

    I couldn’t help but marvel at how such a coincidence could be misinterpreted as more than that (when you consider how many times I’ve heard “Highway to Hell” and not seen that van…).

  20. Athywren - not the moon you're looking for says

    @Kenny De Metter

    However, the original usage of the word comes from Maajid Nawaz, who used it to describe people who call claim to be liberals, but who cannot bring themselves to condemn anti-liberal views and actions when they come from Muslims, and infact speak out against anyone who does want to address those points.
    For example, someone who dismisses violence towards women or gays specifically if it’s Muslims doing the violence, because they feel that speaking out against it would offend Muslims.

    So, essentially, imaginary people and/or Islamists who, much like the right of the rest of the world, appropriate left-wing language in order to attempt to shut down progressive activism? There’s already a word for them; it’s just ‘regressive.’

    Essentially, this divides the ‘liberals’ into 2 strategic choices :
    1) Do you first try to address the problems in your home countries, even though they are less worse then those in other countries ?
    2) Do you first try to address the problems where they are the worst, even though your own country still has some problems ?
    I don’t know what the answer is. I just know there are decent individuals which I like on both sides, and I would just like it if they stopped attacking each other and worked together instead.

    The answer’s fairly simple, really:

    1) Address the problems in your home countries.
    2) Support those who are addressing problems in their home countries.

    That way you get to address issues in both places (there are more than two places, but let’s just say that ‘here’ is one place, and ‘not here’ is the other place for now) without barging into other people’s spaces and saying, “this would all be fixed by taking your hijabs off,” without any consideration for their priorities, or how complex their issues might actually prove to be.

  21. kudlak says

    Grumpy Santa,
    Ever notice that there’s a whole highway to Hell, but only a “Stairway To Heaven”?

  22. kudlak says

    Grumpy Santa,
    Also, concerning fine tuning, a common assertion of creationists is that there could only be one person playing the lottery, with only one ticket, once. God supposedly did it in one shot, so they’re tied to the notion that the singularity only ever had one chance to get it right. It may be that there was a near infinite “attempts” to expand which all failed, and/or a similar number of tries that did expand to some degree before the right combination of things resulted in a stable universe. In relation to your lottery analogy their way of seeing the chances of winning are like looking at the odds of an individual playing once with a single set of numbers vs the odds of a particular draw being won by somebody with a ticket, … potentially.

  23. Kenny De Metter says

    @Athywren : there are people who are liberals in most regards, except when they are dealing with Islam.
    For example, they would correctly stand up against censorship when right wing Christians groups are doing it, but who stay silent when Islamists are pushing for censorship, or even encourage censorship because it ‘might offend Muslims’.

    It’s not entirely fair to just call them right-wing, as they are infact liberals in most cases. And I’m certain they consider themselves to be liberals/left

    I like your answer: ‘Support those who are addressing problems in their home countries’ .

  24. EnlightenmentLiberal says

    So, essentially, imaginary people and/or Islamists who, much like the right of the rest of the world, appropriate left-wing language in order to attempt to shut down progressive activism? There’s already a word for them; it’s just ‘regressive.’

    I will not go so far to support Sam Harris, who is a dipshit. However, there is a real phenomenon of “leftists” who subscribe to extreme versions of white guilt, guilt over colonialism, and radical cultural relativism, who actually do fit that profile. You can attack both sides just fine without endorsing either side.

  25. Peter Golinski says

    I’ve watched many videos now where Matt starts talking about rational arguments and logic. He did it again in this video. By the way he talks, he appears to use Term Logic aka Aristotelian logic (he mentioned Aristotelian syllogisms in this video) and I’ve also seen him use modal logic type arguments elsewhere at times. So what I want to know is:

    Which logic(s)/deductive system(s) does he claim to use?

    What is his justification that the one(s) he uses is/are the “correct” one(s) to argue with here?

    The reason I ask, is because the choice of logic system has a massive impact on which true statements may be produced by a rational argument, so the one you choose to use is very important. For example, I do advanced recreational mathematics: when I do maths, I use First-Order Predicate Calculus with a compatible deductive system. The reason why I use this logic is the same as why most Christians are Christians and Muslims are Muslims- because it is the one I was told to use and was indoctrinated into it (in fact I was never given a choice and not even told about the other options). However, I may have hypothetically been taught/indoctrinated in the constructivist school of thought and use intuitionistic logic. The theorems which result from the same axioms from using these two different logics are often different- ie: what one mathematician would consider true using one logic is not what another does using the other (first order predicate calculus allows theorems that intuitionistic logic doesn’t).
    The same applies to philosophical arguments– the logic that you use often results in different truths. Eg. If you use classic logic v’s intuitionist logic v’s any of the multitude of logics out there, you may get very different “true” statements even though you have argued correctly with respect to the logic/deductive system used.

  26. ironchops says

    I find the term “regressive-left” as an oxymoron. It’s almost like saying “right-left”. Why isn’t there a moderate party?

  27. says

    Hamish coming in with the question about “regressive” does seem a bit odd. IIRC, he was pegged as a JW, and I’m not aware of there being much meme cross over between the anti-Muslim pseudo-liberal neo-cons and that sect. He does claim to be “researching atheism”, and thanks to Sam Harris’ popular use of the term, Hamish is probably bound to discover it.

  28. NYC atheist says

    @31
    Hamish is Church of Scotland, which is a branch of Calvinism. I think you’re thinking of John from London, who is a JW.

  29. NYC atheist says

    @33
    You’re right, it’s the Free Kirk, not CoS. Neil Carter asked him on the episode he was on. Thank you.

  30. says

    Shelley Segal’s intro song segment from “Saved” will be on this week’s show and all future episodes. Youtube robots came looking for our copyright permission, we gave them old people’s medicine, and now we are good to go, at least until the next robot apocalypse. Enjoy in the meantime!

  31. says

    I would recommend getting to know the term “Regressive Left”, because it’s going to come up, and it’s not simple. Majid Nawaz and his book with Sam Harris are a good source. The problem some on the left have is, they want to allow for cultures to express themselves based on their traditions. Sometimes this means allowing for something that would be wrong in that leftist’s home culture. It becomes regressive when you allow for something that is harmful regardless of culture or time period, like not allowing women to go to school, or harsh penalties for minor crimes.

    TAE deals with this by considering what is right based on reason and logic. That’s “progressive” to me. Reason and logic don’t bother with Right and Left. I agree with Martin, the term is abused, used to shut down discourse. But you deal with that by having a definition that is meaningful, then showing that you don’t fit the definition.

  32. Monocle Smile says

    @wolfeyJ
    You provided two specifics, but I would very much like to see some citations about these “regressions” actually taking place in the US. I keep hearing this “regressive left” bullshit from fellow Americans talking about our own country, but they use it to mean all sorts of nonsense.

  33. Robert,+not+Bob says

    Regarding the presupposition discussion: how does presupposition differ from “belief by faith”? It IS belief by faith (evidence be damned). It’s what belief by faith means! Someone ought to point that out.

  34. Monocle Smile says

    @Peter
    I find it rather silly for you to say you were “indoctrinated” into one version of recreational mathematics. I take it you were an adult when first exposed, and there was nobody psychologically or physically browbeating you into doing math.
    The logic systems we devise were developed and refined based on empirical inquiry. Hence the GIGO principle. The same goes with math…it was developed by spotting patterns in collections of data.

    Eg. If you use classic logic v’s intuitionist logic v’s any of the multitude of logics out there, you may get very different “true” statements even though you have argued correctly with respect to the logic/deductive system used

    Like I said…if you get away from the castles in the air and actually put these systems to the test, we can see which are functional. For example, Aristotle once “reasoned” his way into deducing that women have fewer teeth than men. One look in his wife’s mouth would have demonstrated otherwise.
    Furthermore, “intuitionist logic” doesn’t make any goddamn sense.

  35. Walter says

    Can someone please clarify something for me ? what the caller @40:08 referring too ? When he mentioned how the scribes who wrote the Bible screwed up. What screw up exactly ? I would bring up and use this argument but i am not familiar with aforementioned. Or maybe it’s just because it’s 1:15 am lol.

  36. peter golinski says

    @ Monocle Smile:

    When taught maths, I was brought up in the classical logic tradition, as I’m willing to guess were you. This tradition is universal (as far as I know) among primary/high school education institutions. I was never told that there were drastically different alternatives: even when I was at uni doing maths for engineering I was never told that other logics besides predicate calculus were used by some mathematicians. It was only after doing advanced maths recreationally that I learned of the many different schools of thought/philosophical views regarding maths and how some of these require/use different logic. (By “advanced maths” I mean the deeper, low level philosophical maths such a meta-maths and foundational maths; not the advanced higher level maths like calculus, linear algebra, tensors, etc. that engineers are taught.)
    I was of course taught that there are many different theories, some which have contradicting theorems, eg: Euclidean v’s Non-Euclidean Geometry, but this is deeper than that. This is not at the level of which theory you are working in, but at the level of proof/logic. In fact, the vast majority of the population aren’t aware that the in many respects maths is quite arbitrary, but not only maths- so is rational thinking in general, because the rules of logic/deductive system are a personal choice in that you can choose what formal system you use to “reason rationally”.

    To give some guide as to how I was “indoctrinated”, way, way before I was an adult, here are some instances of me being introduced to logic and proofs : (I’m now mid-40’s so these events were a long time ago.)
    In grade 3 (8 years old), I can remember being shown, in a very informal way, that you can prove results in maths. For example, I specifically remember my teacher demonstrating to us that an odd plus an odd will always make an even. At this stage the logic used is not itself explicitly taught, but you are absorbing it in the background along with the method proof.
    In grade 6 (11 years), we were introduced to programming in BASIC– this (at the time) was an imperative, unstructured programming language. It has explicit logic statements such as if..then, etc. [As-an-aside, interestingly at my school we were first introduced to programming in grade 4 with the Logo language on commodore64’s– which is functional, not imperative– and hence is way cooler!]
    In grade 7 (12 years), we studied classical geometry, ie: Euclidean Geometry, using a primary school version of some of the simpler proofs of some of the theorems found in the Elements (The Elements is the very book that Euclid wrote thousands of years ago, collating together the most important known proofs of results of Geometry and other bits of maths known at the time in a systematic way). This introduced my class to formal classical logic and proofs, although by todays standard these proofs are not really very rigorous nor formal.
    At some grade in primary school I was told that the prime numbers were infinite (can’t remember exactly when, but i guess is was before year 6 because by that stage I had already learned about primes and factors, lowest common multiples, etc), but i cannot remember if it was just taught as a fact or if it was proven (I’m guessing we were almost certainly just told it as fact). However, this “fact” is very significant result, because the standard proof of the infinity of prime numbers, as you probably know, uses a proof by contradiction and proofs by contradiction are something that constructionist mathematicians using intuitionist logic reject.
    Throughout all of high school (which in my home state of Australia 30 years ago years was grades 8 to 12), the vast majority of theorems that we were taught we proved to some degree– very few are stated just as facts. This includes algebra results in junior through to calculus in senior. All proofs used traditional logic and proof methods.
    Also, in junior high school we proved that the the square root of 2 is irrational, this is another famous ancient proof that uses proof by contradiction– and thus this proof is rejected by some mathematicians (I don’t know if it can be proven any other way either- so the fact itself may not be true for them)
    At uni first year (17 years) I studied first-order predicate calculus and deduction in its own right. All maths taught in engineering (eg: advanced calculus, matrices, etc) was taught with the assumption that this is only way to do it.
    I became an “adult” (ie: 18 years old here in Australia not 21 as USA) at the end of 2nd year uni– at which stage,I had already seen/read 100’s of proofs using predicate calculus. I was well an truly immersed into this way of thinking.

    Now, the most important point about this is that: By the time we are adults, the majority of us are trained by the schooling system how to “think” in a rational way (ie. use a particular type of logic/deduction system) when doing maths, and we instinctively use that form of reasoning outside of maths in other areas- such as philosophy and in everyday life. That’s called “indoctrination”.

    In my case I was at least 21, before I formally read of other logics such as intuitionistic logics, and later on others such as paraconsistent, etc. (but I’m not really interested in them and don’t seek them out on purpose, cause I’m not a recreational logician, but a recreational mathematician). However, most people are never experience any other logic besides the traditional logic which they are taught in primary/high-school.

    [By-the-way: I’ve noticed that in the presuppositionalism discussion, one of them (Daniel?) has what looks to be slides for a lecture projected on the wall behind him. He seems to be preparing for a lecture on Modal Logic. So at least he should be aware that there many different logics around. Hence, I’m now wondering: Which logic he uses in a formal argument about the supernatural, and more importnatly, what is his justification for using it?]

  37. Monocle Smile says

    @peter
    No offense, but I nearly fell asleep reading that post. You seem to have ignored the important portions of mine.

  38. CompulsoryAccount7746, Sky Captain says

    Taking as granted that there are equally viable systems of logic with different outcomes…
     
    @Peter Golinski #30:

    The reason why I use this logic is the same as why most Christians are Christians and Muslims are Muslims- because it is the one I was told to use and was indoctrinated into it (in fact I was never given a choice and not even told about the other options).

     
    @Peter Golinski #42:

    However, most people never experience any other logic besides the traditional logic which they are taught in primary/high-school.

    So… atheists and Christians and Muslims are generally using the same logic. (You’re not saying they’re raised speaking incompatible languages with separate truths.) If discussion shifts to a sophisticated theology that exploits esoteric logics, parties would need to do so in synch or undermine the shift.
     
    I should expect proofs of god to be written in whatever style the author thinks can be coaxed into an apparent true outcome. Whether they did so correctly would be the disagreement.
     
     

    I’m now wondering: Which logic he uses in a formal argument about the supernatural, and more importantly, what is his justification for using it?

    Which formal argument? Are you expecting Matt to use a single system to counter ALL theistic proposals, based solely on being in the supernatural genre?

  39. CompulsoryAccount7746, Sky Captain says

    @Peter Golinski:
    It’s been a while since I heard him say it, but I think Matt’s stance on debating logical proofs is along the lines of what Monocle Smile said: castles in the air vs empiricism.

  40. peter golinski says

    @Monocle Smile #44

    Well, from my perspective I did respond to the most important point, and I crafted my response so that it would be very clear and detailed. But since you’ve brought it up I’ll go through the rest of your post:

    You said: “The logic systems we devise were developed and refined based on empirical inquiry. Hence the GIGO principle. The same goes with math…it was developed by spotting patterns in collections of data.”

    Ok, so you’re an empiricist. Well, for me it is obvious that simple maths, esp. arithmetic, originally developed has as abstraction from empirical observation of “things” in the real world- eg: when you add 2 apples + 2 apples you get 4 apples. However, the problem that I have with the full empirical view point is that there are many types of maths that have been developed that have absolutely no evidence that they describe real world interactions that were observed/known about at the time that they were invented. An example is Chess: show me in the real world (outside of a chess set) a collection of items that relate to each other in the same fashion as a the pieces of a chess set and board. Another example are the infinities (in case you didn’t know, in maths there are many infinities- actually an infinity of infinities- where each is “larger” is a sense than those created before it)- show me a collection of things in the real world which has aleph2 members (aleph2 is an infinity “larger” than the set of real numbers). Indeed, there are many instances throughout history where mathematicians have created branches of maths which at the time didn’t relate nor describe any known real-world interaction, but years (sometimes many, many decades later) it is found that they describe some newly discovered physical observation (this happens *alot* in physics). For these branches of mathematics, it is almost the exact opposite of empiricism: ie, the observation comes after the abstraction. If you show me just these two examples, out of the possible millions I could also give, then I’ll consider you right– until then I’ll continue with in my non-empirical view.

    You said: “Like I said…if you get away from the castles in the air and actually put these systems to the test, we can see which are functional.”

    Now, by saying this you’ve just clearly demonstrated that you didn’t comprehend at all the main query of my original post; because what you’ve just said, is more or less what I was originally asking of Matt to acknowledge, ie. Why does he think that the logic(s)/deductive system(s) he uses is/are appropriate for debating about the supernatural? Or if you like, How does he justify that they’re “functional” (your word) when debating about the supernatural? When/how has he “put them to the test” (again, your words)?
    Repeatedly I’ve seen Matt say that to people thigns like (these are paraphrased- I can’t remember exact words he’s used): “the best thing you can do is read a book on logic”, or “the laws of logic are absolute and god needs to be compatible with them”, but I’ve never actually seen him explicitly and very clearly say precisely which logic he’s talking about nor his justification that this logic is appropriate. I have sometimes heard him mention Aristotelean syllogisms (which would be Term logic aka. Aristotelian Logic) and also list the “laws of thought” commonly associated with Plato and others. But I would be very surprised if this is truly all he means, because these are very ancient logics which are outdated and considered primitive by modern logicians (actually the laws of thought can barely be considered a logic). Without wanting to put words in his mouth, I would suggest that he’s possibly really referring to modern predicate logic, which is well rooted in these ancient logics. Coincidently, predicate logic is also what the vast majority of mathematicians use (usually only first-order, some advocate second-order: second-order is more “powerful” in a certain sense), it is also what I use: but I freely admit I only use it because I was brought up believing that it is the only thing to use: I’ve never justified to myself that I should use it. (It’s too late for me to change now anyhow- I would have to unlearn so much that I would be constantly confused which theorems I currently know are still valid within the new logical framework)

    Lastly you said: ” Furthermore, “intuitionist logic” doesn’t make any goddamn sense.”

    Hmm, Have you just made a spectacle of your ignorance here? Have you actually read anything about intuitionist logic?
    Many very well respected logicians/mathematicians/philosophers of the previous century encouraged and promoted it. Do you think that they didn’t/couldn’t understand it? For most people, it certainly does “make sense” when they study it; they might not agree with it from a philosophical point of view, but they will certainly concur that it can be understood and it is a logic. Maybe the fact that it doesn’t make “any goddamn sense” to you says more about you and your abilities than it does about the logic.

    [PS: I just reread my previous post and noticed a slight mistake: I meant to say that I turned 18 at the after the end of my first year of uni]

  41. corwyn says

    @42:

    we were introduced to programming in BASIC– this (at the time) was an imperative, unstructured programming language. It has explicit logic statements such as if..then, etc

    If you think that the *procedural* if-then-else statements in BASIC are explicit logic statements, then perhaps you should revisit what logic is.

  42. CompulsoryAccount7746, Sky Captain says

    @peter golinski #47:

    there are many types of maths that have been developed that have absolutely no evidence that they describe real world interactions that were observed/known about at the time that they were invented. An example is Chess: show me in the real world (outside of a chess set) a collection of items that relate to each other in the same fashion as a the pieces of a chess set and board.
    […]
    If you show me just these two examples, out of the possible millions I could also give, then I’ll consider you right– until then I’ll continue with in my non-empirical view.

    0.o  You switched from varieties of math to board games and whether a game can be said to exist.
     
    In elementary school, I sometimes plucked blades of grass, arranged them into a grid, and moved objects around to play chess during recess.
     
    Was *that* a chess set? Was that an empirically accessible instance of chess itself? If I define a house rule, was that still chess? What if I hadn’t had occasion yet to apply the rule, and appeared to play as normal? If there were no chess sets, could chess be said to exist in a platonic realm? What if I blindly generated a variant rulebook and never read it? Duuuude.

  43. CompulsoryAccount7746, Sky Captain says

    @peter golinski #47:

    Why does he think that the logic(s)/deductive system(s) he uses is/are appropriate for debating about the supernatural?

    You keep using the word “supernatural”. What distinctive characteristics do you use to populate that category and refer to its members under a shared label?
     
     

    Or if you like, How does he justify that they’re “functional” ([Monacle’s] word) when debating about the supernatural?

    To my knowledge Matt is not promoting formal proofs of non-existence. He is pointing out that others’ existence proofs are flawed. This necessarily involves adopting standards of validity/soundness of the logic used in their proofs, for the sake of argument.
     
    His empiricism comes in due to finite patience. Theist arguers propose proofs of a shy/feeble god whose interactions with the empirical world are indistinguishable from nothing in everyday experience. They then equivocate to cite that proof is support of a host of unrelated baggage from their sect, with practical ramifications to everyday experience. Dissecting the proof is a derail of limited entertainment value.
     
    His response to deists (who might put such proofs to less dishonest use) is roughly: “What convinced you of this!?” and “What’s the point of adopting a belief that irrelevant?”

  44. peter golinski says

    @CompulsoryAccount7746, Sky Captain says #50

    Your chess set made out of pieces of grass is almost the exact opposite of empiricism. Empiricism goes from real-life observations towards the abstraction, you’ve gone form the abstraction towards the observation.

    By-the-way: I’m rather confident in predicting that if you surveyed mathematicians they would agree that games like Chess, Go, Checkers/Draughts, tic-tac-toe/naughts-and-crosses even though broad games are maths systems. While games like Hungry-Hippo, Snakes and Ladders, and Monopoly aren’t (although, you may still use maths to analyse them- eg: in Monopoly, you may produce statements like “if I roll a total of six then I will land of Mayfair, therefore, if I roll 2 one one die and 4 one the other, I will be have the opportunity to buy Mayfair”

  45. peter golinski says

    @corwyn#42

    I agree that that was a bad example, it would have been better if I said instead, “It has explicit logic statements such as ‘and’ and ‘or’.”
    I hope were able to see over this single mistake and understand the basic thrust of what I was saying.

  46. CompulsoryAccount7746, Sky Captain says

    @peter golinski:

    you’ve gone form the abstraction towards the observation.

    You requested “a collection of items that relate to each other in the same fashion as a the pieces of a chess set and board” yet was not a “chess set”. That depends on deciding what IS a chess set?
     
    Your criteria somehow involved the abstract notion of the rules of Chess and real-world objects. I provided an example of objects I used to implement those rules to test if that met your criteria of a “chess set”.
     
    If the criteria to be a “chess set” is simply the relations, regardless of materials, EVERY collection of such objects would be a “chess set” by definition, and your challenge was really show you a real-world member of the empty set.

  47. corwyn says

    @52:
    Nope. Your personal history was of no help in figuring out what you were trying to say about logic. Nor is it clear what your thesis even is. Do you have an actual an example of how teaching formal logic is ‘indoctrination’. Or how using a different logic would come to a different answer? Most people are taught addition using integers, but addition of complex numbers is left to higher math classes. Is that indoctrination?

  48. EnlightenmentLiberal says

    Ugg, I might regret joining the conversation, but I’m still at a loss what anyone means by “different logic”.

    Responding to peter golinski:

    There’s only one kind of logic, and that is the logic of propositional logic, which can be extended to create first-order logic and second-order logic. I occasionally hear about modal logic, and I have no idea what that is. Other than that, what other kinds of logic are there? The notion that there are other kinds of logic seems incredibly wrong-headed, and it’s probably because the speaker is using a Straw Vulcan notion of logic.

    Chess is not a system of logic. Chess is a game that one can analyze with the one and only conventional logic, the same logic (propositional logic, first-order logic, and second-order logic), that is used everywhere else.

    It was only after doing advanced maths recreationally that I learned of the many different schools of thought/philosophical views regarding maths and how some of these require/use different logic. (By “advanced maths” I mean the deeper, low level philosophical maths such a meta-maths and foundational maths; not the advanced higher level maths like calculus, linear algebra, tensors, etc. that engineers are taught.)

    I was of course taught that there are many different theories, some which have contradicting theorems, eg: Euclidean v’s Non-Euclidean Geometry, but this is deeper than that. This is not at the level of which theory you are working in, but at the level of proof/logic. In fact, the vast majority of the population aren’t aware that the in many respects maths is quite arbitrary, but not only maths- so is rational thinking in general, because the rules of logic/deductive system are a personal choice in that you can choose what formal system you use to “reason rationally”.

    It seems that you are confused.

    The particular axiomatic foundations of math are arbitrary in the sense that they’re axiomatic. That is correct. And depending on what axioms you use, you can obtain Euclidean geometry, or various non-Euclidean geometries. That is also correct. The theorems of Euclidean geometry do not “contradict” the theorems of the various non-Euclidean geometries. They are different formal frameworks with different axiomatic foundations. In particular, they do not contradict in the sense that they are logically inconsistent in the formal sense of propositional logic, or first-order logic, or second-order logic.

    I have a good background in a lot of what you are discussing, with but a mere undergrad major and degree in mathematics, and I have no idea what you’re talking about. Perhaps it does exist, and I’m simply ignorant, but I think not. All of the systems of mathematics that I’m familiar with still use the logical rules of derivation like modus ponens, distribution of conjunction over disjunctions, etc.

    In particular, before circa 1900 IIRC, many practicing academic mathematicians did have different axiomatic frameworks for their work, and there were philosophical arguments about which axiomatic approach was best. These arguments were largely concluded, and now basically everyone works in the axiomatic framework of Zermelo-Fraenkel set theory. (Oftentimes they work in ZFC, with a preference towards ZF where possible.) However, these arguments were not about actual formal logic itself. Everyone already agreed to the basic rules of propositional logic, and first-order and second-order logic (although some preferred avoiding second-order logic where possible). All of the other axiomatic foundations of mathematics still used the same logic in the sense of the logical rules of derivation, what it means to be logically consistent and inconsistent, etc. They used the same methods of logic; they just started with different axioms.

    And finally, if someone wants to use different rules of logical derivation, or some other rules (or non-rules) for obtaining new beliefs from old beliefs, then their position is incoherent, the intelligent part of the conversation is over, and it’s probably time for ridicule.

    Ridicule is the only weapon which can be used against unintelligible propositions. Ideas must be distinct before reason can act upon them;
    – Thomas Jefferson

    Why do I adopt my particular beliefs and values that my system of logic, truth derivations, etc., is better than other systems? Because I say so. Because it tends to work out well, when using my logic to evaluate how well it works (a circular argument). If you’re looking for an independent epistemological justification, I have no intention of giving one, and I have none.

  49. peter golinski says

    @ CompulsoryAccount7746, Sky Captain #53:

    Empiricism is where you make observations of the real-world, notice patterns and then abstract those patterns into rules. eg: One day a child may release a rock, the rock falls, she notes this behaviour. The next day she does the same thing. Then again she may do it, but with something different such as a toy. Then she might do it at another place. Then she might get someone or something else to do it. And so on and so on. After making many such observations, she then abstracts the general rule “Unsupported things will fall towards the ground”.

    Now, you said “…. objects I used to IMPLEMENT those rules … “, this is where you’re failing to understand the difference between Empiricism and what you’ve suggested. Empiricism doesn’t start with rules, but rather ends with the rules. But, in the case of your grass chess set, you’re starting with the rules of chess, and then (by your very own words) implementing them and reporting (observing) the result of this implementation. This is obviously NOT an empirical investigation. I’m sorry if you can’t get this, but I can’t make it any clearer: perhaps you should ask other people to explain it to you.

    It may be that you don’t understand why I mentioned that you had to find an example outside of a chess-set. This is becuase, I’m allowing for possibilities such that you’ve never seen chess before and have happened to stumble across people playing it. In this case you can use an empirical investigation to derive the rules of chess simply by watching them play (of course you’ll never be sure that these rules are all that there is). However, this is why I previously specifically said: “..there are many types of maths that have been developed that have absolutely no evidence that they describe real world interactions that were observed/known about at the TIME THAT THEY WERE INVENTED” (sorry about the caps- I don’t know how to underline or bold with this editor). The very first instance of the rules of chess weren’t empirically discovered (well this is actually my assumption, but I feel most people would agree)- it doesn’t matter if they have been empirically discovered many times since.

  50. CompulsoryAccount7746, Sky Captain says

    I wasn’t trying to demonstrate empiricism. I was parsing your walls of text to clarify what you were saying through Q&A.
     
    @peter golinski #47:

    there are many types of maths that have been developed that have absolutely no evidence that they describe real world interactions that were observed/known about at the time that they were invented. An example is Chess
    […]
    For these branches of mathematics, it is almost the exact opposite of empiricism: ie, the observation comes after the abstraction. If you show me just these two examples […] I’ll consider you right

     
    @peter golinski #51:

    Your chess set made out of pieces of grass is almost the exact opposite of empiricism.

    I could invent variants of chess with one or more added rules. If I happened across folks moving pieces on a board consistent with one of my variants, will I have discovered my variant in the real world? What does that correlation say about the predictive value of the other variants?
     
    What if I invent a game from scratch, then crank out variants and look for them until I “find one”?

  51. peter golinski says

    @CompulsoryAccount7746, Sky #56

    You said: “What if I invented a game from scratch, then crank out variants and look for them until I “find one”?”.

    Well, thank you for explicitly stating that at least some maths (ie: in this case games) can be arbitrarily INVENTED FROM SCRATCH are thus on the whole maths is not empirical. This was my very original claim- now maybe you can convince monocle smile of this, cause he is claiming #40 that maths is empirical.

    PS: Note that, I’ve never said that the whole of maths is not empirical- indeed I’ve already stated that I agree some of it is, eg. arithmetic, however, vast tracts of it are not empirical especially a lot of the modern esoteric stuff.

  52. CompulsoryAccount7746, Sky Captain says

    @peter golinski #57:

    on the whole maths is not empirical. This was my very original claim- maybe you can convince monocle smile of this, cause he is claiming #40 that maths is empirical.

    Have I resolved your vexation with Matt?
    Do you have other lingering objectives (claims/questions) buried within earlier posts? Maybe form a bullet list to reiterate them concisely and discretely?

  53. peter golinski says

    @corwyn #59

    Well, let my clarify things a bit: What I’m really saying is that I’m absent of the belief that ALL of maths is empirical. In fact, as I’ve explained, I’m willing to believe it is empirical based on the slenderest of evidence, eg. all you have to do is show to me that the extremely simple example of Chess is empirical (Indeed, I specifically stated that I acknowledge that it is an non-grounded assumption I make when I say that Chess isn’t empirical). If you return to my original post I say: “The problem that I have with the full empirical view point is that there are many types of maths that have been developed that have absolutely no evidence that they describe real world interactions that were observed/known about at the time that they were invented.” I’m not claiming here that it is not empirical, but rather that it hasn’t been sufficiently demonstrated to me that it is empirical. Note that I’m not making a positive claim here.

    However, a person claiming that maths is empirical is making a very, very bold positive claim, thus the burden of proof is on them.

    So all up I don’t have to prove anything for you. (If you don’t understand what I’m going on about, google “burden of proof”)

    [PS: I admit that once I did previously explicitly say that maths is not empirical, in the very last sentence, of the post-script of my last post (the text you copied/highlighted). This was a bit of an accident, caused more by me getting carried away by discussion then anything.]

  54. Monocle Smile says

    @Peter Golinski
    I think you are extremely confused. At no point did I say that math was empirical, and it takes an extremely dishonest or extremely laughable reading of my post to come to that conclusion.

    Math ORIGINATED from empirical observation. Once a formal system was established, it became possible to delve deeper into further abstraction without the necessity for more empirical observation…though of course, said abstractions were only of any use when checked against empirical data. Otherwise you get stuff like the Rayleigh-Jeans law of blackbody radiation, which is only accurate for part of the EM spectrum as opposed to Planck.

    This has fuck all to do with your wibbling about “supernatural.” You started by chiding Matt for not justifying his use of some kind of logic, and I’m in agreement with EL that there’s only one kind. I’m really not sure if you even have a point.

  55. Monocle Smile says

    @Peter
    Here’s the short version:
    We determine whether or not something exists in the reality we experience through empirical inquiry.
    We use reason to draw conclusions from our observations.
    A theist claiming that a god exists (as in, it affects the reality we experience; the classical definition of existence) is thus making an empirical claim.
    The bit about math is a non sequitur, as far as I am concerned.
    What’s your complaint?

  56. peter golinski says

    @ EnlightenmentLiberal #55

    You are the prefect example of what I mean by being “indoctrinated”.

    So, after 16 or so years of education, with a degree in math no less and never once were you told that there are many, many different types of logics/deductions systems. The only logic you know is predicate calculus. In fact you are so immersed in it that you explicitly state that it is the only kind that there is, but not only that, the notion that there exists other kinds is “incredibly wrong-headed”.

    I’m just curious: You do know that there are people, called Logicians, who study logic as a profession, don’t you? You do know that logic has been studied for thousand of years?
    So what do you think they’ve been doing all this time: petty much nothing? Does it seems reasonable that after all this time the only thing they’ve come up with is predicate logic– a system which takes just a few of months to master?

    No! Of course they’ve being doing stuff and as a consequence there is a multitude of logics out there. Each one has different properties and are typically used for different settings.

    For maths, there are particularly two that are used (but others are as well): one is predicate calculus (usually first order) the other is intuitionistic logic. These logics are associated with different philosophies. One of the major differences between math proofs performed according to these logics is that predicate calculus allows proofs by contradiction whereas intuitionistic logic doesn’t. This results from the fact that intuitionistic logic doesn’t have the law of excluded middle nor the elimination of double negation as axioms.
    Now, during your maths degree I’m predicting that you’ve seen 100’s of proofs that use proof by contradiction- well guess what, NONE of these proofs are valid to a mathematician who uses intuitionist logic (these mathematicians are normally aligned with the philosophy of intuitionism/constructivism.).
    Eg: for a constructivist, the ancient Greek proof by contradiction that sqrt(2) is irrational is simply rubbish/meaningless. In other words, these two groups of mathematicians, even when working within the same theory (ie: starting with the same axioms), will produce a different set of theorems which they considered proved/true.

    All up, the choice of logic/deduction system that you use is actually purely personal choice. However, this choice has drastic consequences on what you consider “true”/”proved”. Unfortunately, for most people, there are never made aware that they have this choice.

    Now, I’m speculating here, but I guess that you’ll continual to use predicate calculus for reasons like- “it’s worked for me so far”, “it’s what my professors taught me”, “it’s what I know / It’s all that I know”, “it’s too hard now to change because I’ve just spent 4 years learning proofs/theorems which I’d have to reject”, “everyone else does”, “don’t really care much about the philosophy of maths and what is “truth” I just do maths”, etc.. Congratulations- you’ve been indoctrinated.

    [Oh, by the way: not everybody works with ZFC: ZFC didn’t bring about the uniformity that you claim. Indeed, new frameworks were created as a reaction specifically to ZFC. In myself don’t like some parts of ZFC, for me the axiom of infinity stinks- if you Google Professor Norman Wildberger you’ll find that he has a lot to say about our current understanding of infinity, a lot of what he says speaks volumes to me.

    PS: According to legend (though of doubtful veracity), Hippasus, the first two prove by contradiction that the sqrt(2) is irrational was murdered by Phythagoras because of this discovery- so for him constructivism would have been a way better logic to use 🙂 ]

  57. peter golinski says

    @Monocle Smile #63
    You said:…..
    Here’s the short version:
    We determine whether or not something exists in the reality we experience through empirical inquiry.
    We use reason to draw conclusions from our observations.
    A theist claiming that a god exists (as in, it affects the reality we experience; the classical definition of existence) is thus making an empirical claim.
    The bit about math is a non sequitur, as far as I am concerned.
    What’s your complaint?
    …..

    My complaint is with this line “We use reason to draw conclusions from our observations.”. The problem is, is that there are many different ways to reason- because formal deduction is inextricably linked to the logic used. And the logic you use is a personal choice, but different logics give different results! Thus people can obtain different conclusions even though they have correctly argued according to their choice of logic.
    The reason I went into maths, is because this is a completely formal system- it doesn’t require any knowledge of the workings of the real world/observations of the real world, you just can blindly generate theorems and yet even within this system, different mathematicians may derive different results from the same axioms. This demonstrates how the choice of logic system is critical to conclusions reached.

  58. Monocle Smile says

    @Peter
    So your complaint has to do with you stripping a single sentence out of the context of what’s being discussed and venturing off on a non sequitur.
    I can’t find half a shit to give. What does this have to do with the reality we experience?

  59. EnlightenmentLiberal says

    I really wish I could make this shorter, and I kept rewriting it, but there’s too much stuff I wanted to cover.

    Prescript: Non-classical logic is a fringe position in academia, contrary to some of your assertions. (Assuming, of course, that you can give agreement that we live in a shared reality, and that there are right and wrong ways of learning about this shared reality.)

    You know how ridiculous the positions of Wildberger are, and the positions of other constructivists and ultra-finitists, but others do not, so let me share.

    Consider the classical statement:
    (∀n∈ℕ)(odd(n) ∨ even(n))
    Which, translated into English, roughly means “Every natural number is even or odd”. In various versions of their “math” and “logic”, I cannot prove that statement from first principles. In other versions, I cannot even write down the statement because it doesn’t have the tools for me to do so!

    As another example, IIRC, with these incredibly weak math and logic, one cannot prove that sqrt(2) is not a Rational Number!

    Real Numbers are right out. Almost all of calculus is right out.

    Finally, I have strong philosophical objections to Wildberger et al.

    These people often object to formalism, which pisses me off. For example, the inventor / creator of intuitionist logic, Brouwer, wrote much of his work in natural language English prose! ~shudder~ Wildberger displays similar foolish tendencies. For example, in many videos, Wildberger complains that ZF is not rigorous, but in another video, he gives his own definition of Natural Numbers as “marks on a chalkboard”! I don’t know how someone so obviously educated and intelligent can say something so ridiculously foolish.

    As far as I can tell, their particular ultra-finitism and constructivism is actually merely facets of the deeper problem: a Platoncist view of the world, and of math and logic. Wildberger put it perfectly in one of his videos. He complains that modern mathematicians are simply playing games with symbols on paper, and argues like a Platonicist that math is not just playing games with symbols on paper. I cannot disagree more vehemently. I am a kind of positivist, or post-positivist. Platonic reasoning in this fashion is not right. It’s not even wrong. Math and logic are just playing games with symbols on paper, and Wildberger et al’s views to the contrary are actually nonsensical (in the formal sense of positivism). One cannot be rigorous unless one carefully spells out the rules of deduction and the starting positions, something which ultra-finitists and constructivists are often loathe to do, while magically claiming that their approach is more rigorous – whatever the fuck they mean.

  60. EnlightenmentLiberal says

    To Peter
    Quoting someone else (I think):

    We determine whether or not something exists in the reality we experience through empirical inquiry.
    We use reason to draw conclusions from our observations.
    A theist claiming that a god exists (as in, it affects the reality we experience; the classical definition of existence) is thus making an empirical claim.
    The bit about math is a non sequitur, as far as I am concerned.

    I believe that you brought up different logic systems in the context of defending the hypothetical theist who reaches the conclusion that there is a god. It’s a non-sequitir because none of the logic systems that are even remotely interesting or researched can allow an honest and informed person to reach the conclusion that a god exists.

    Serious question(s): Suppose we’re together in a room, and I pick up a hammer from a table, and I release the hammer at a height, and it falls, and I repeat this several times. Are there any alternative systems of reason, logic, math, etc., which would allow someone to reach the conclusion that next time I release the hammer, the hammer will fly up to the ceiling and stay there? In other words, do all respectable and noteworthy systems of reason, logic, math, etc., arrive at the conclusion that the hammer will (probably) fall next time it is released?

    If you do not give agreement to the conclusion that the hammer will (probably) fall next time it is released, then this is about the spot in the conversation where I say that you are a sophist, and I stop engaging seriously with you, and I ridicule what you say as my whimsy leads me.

    Otherwise, I expect that you will retract your earlier rantings that this discussion has any relevant bearing on the practical questions of whether a Christian, Muslim, etc,. is justified in their religious beliefs.

  61. EnlightenmentLiberal says

    And last multi-post for a while (sorry).

    To answer some of your questions peter: I am not a Platonicist. To me, logic and math are just playing games with symbols on paper (and any equivalent). They are invented tools. These particular tools were made, and it was found that they were incredibly useful in empiricism aka science. I don’t view classical logic as obviously “more right” than intuitionist logic in any normative way. I just view your particular fascination with intutitionist logic to be wrong-headed because you are the one making normative claims about which math is “more right” or whatever you Platonicists are talking about.

    Regarding the earlier example:
    (∀n∈ℕ)(odd(n) ∨ even(n))
    I believe that this is not a statement about empirical reality, aka natural + supernatural reality, aka material + “non-material” reality, aka the reality that is bound by cause and effect, etc. There is no such thing in reality as “one”, “two”, “even”, “odd”, etc. Instead, these are simply inventions of humans with no direct relation to reality. What we do is we create scientific models aka empirical models using the formalism of math. While there is no such thing as “one” in empirical reality, the term “one apple” does name something in empirical reality.

    The principle of excluded middle has shown to be amazingly useful for creating predictive models about observable reality. On this empirical basis, I am simply wondering “why the f would anyone seriously advocate the use of intuitionist logic in place of classical logic?”. It makes no sense. I’m not making a normative judgment that classical logic is “right” (which is a claim which I think is incoherent, in the formal sense of positivism). I’m making an empirical judgment that classical logic is useful. In the view of positivism, useful is the foundation of truth. Some claim about reality is true only to the extent that it’s part of a demonstrated predictive model of observable reality. In that sense, “useful” and “true” are different facets of the same concept.

  62. peter golinski says

    @EnlightenmentLiberal
    You said “I’m making an empirical judgment that classical logic is useful”. This may well be the case for many things but have you ever heard of Schrodinger’s cat? Non-classical logic can also be very useful.

    Overall, I think you’ve misunderstood my position: I use predicate calculus. However, the important point is that I realise that there are other alternatives which some people choose to use them instead for their own personal reasons.

    By-the-way, constructivists do have real numbers (https://en.wikipedia.org/wiki/Constructivism_(mathematics)). In general, from what I understand, they have enough “maths” for anyone who needs it for real-life applications, such as business owners, engineers, builders, statisticians, surveyors, etc.

    Regarding Christians and Muslims, I get the impression that I mustn’t have done a very good job of explaining what I was trying to say when I mentioned them. I brought them up as an example of the main reason why I use predicate calculus and not others; because I was raised in that tradition. That is, I’m aware that I’ve been indoctrinated into it. This is similar to why most Christians are Christians and not Muslims, because people raised since birth in a religious family tend adopt the religion of the parents. I’m not trying to defend their beliefs. I think there beliefs are rather crazy.

  63. corwyn says

    @61:

    “The problem that I have with the full empirical view point is that there are many types of maths that have been developed that have absolutely no evidence that they describe real world interactions that were observed/known about at the time that they were invented.”

    To which I reply, who cares? Any math which is at all non-obvious must be invented BEFORE it can be used to describe real world interactions. Forming the math to fit some observation is an easy way to get the math wrong. And even *that* you don’t feel you need to prove. So, really, who cares? You aren’t saying anything even remotely interesting.

    different logics give different results!

    So your constructivists think that the sqrt(2) is rational? (This was your example after all). What are the integers A and B such that A/B = sqrt(2)?

    On the other hand if your constructivists think sqrt(2) IS irrational, but can’t prove it, that isn’t a different result, just a lack of result (on their part).

    If you are going renounce your example please give another one.

  64. EnlightenmentLiberal says

    You said “I’m making an empirical judgment that classical logic is useful”. This may well be the case for many things but have you ever heard of Schrodinger’s cat? Non-classical logic can also be very useful.

    Yes, I have. What’s your point? I think you’re trying to make one, but I don’t fully understand what it might be. Please make a point, rather than merely insinuate one and leave me guessing.

    Normal classical logic works just fine for doing quantum theory. I don’t understand why you think it wouldn’t.

    Having said that, the measurement problem of quantum theory is IMHO a real concern. From a purely philosophical standpoint, I really like the spontaneous collapse family of hypotheses. It solves the measurement problem very nicely, and preserves a sort-of classical approach of a real world. It’s also testable, which makes it way more interesting than manyworlds and Bohmian mechanics. However, my worldview would not crumble if the manyworlds interpretation was somehow demonstrated to be correct. Bohmian mechanics is also interesting, and it might solve the measurement problem – I don’t know enough to comment on Bohmian mechanics.

    Overall, I think you’ve misunderstood my position: I use predicate calculus. However, the important point is that I realise that there are other alternatives which some people choose to use them instead for their own personal reasons.

    And none of them get you to the justified belief that there is a god. At least, none that are worth respecting and considering.

    In general, from what I understand, they have enough “maths” for anyone who needs it for real-life applications, such as business owners, engineers, builders, statisticians, surveyors, etc.

    I doubt it. The proponents like to think that it’s true, but AFAIK, it introduces an amazing amount of contortions that they have to go through to do even the most basic things. For example, consider the engineering project of GPS. It requires computations in full general relativity. I strongly guess that trying to write the computer programs of GPS without a proper classical approach to Reals, calculus, tensor theory, etc., is going to be much, much harder than what it needs to be.

    Concerning this:
    https://en.wikipedia.org/wiki/Constructivism_%28mathematics%29
    As I said, I find it utterly incomprehensible that Wildberger can complain that classical approaches are not rigorous, when actually it’s constructivist approaches that are far less rigorous.

    For example, look at how wikipedia describes the constructionist approach of reals:
    > All pairs of functions (f, g), so that f is a function from positive integers to rationals, g is a function from positive integers to positive integers, and
    > (∀n)(∀i,j≥g(n))(f(i)-f(j)|≤(1/n))

    The above is rather loose. Strike one for lack of rigor. I assume they mean the following:
    > All pairs of functions (f, g), so that f is a function from positive integers to rationals, g is a function from positive integers to positive integers, and
    > (∀n)(∀i)(∀j)(j≥g(n)→|f(i)-f(j)|≤(1/n))

    The above is still rather loose. It doesn’t specify the domain of quantification. I assume it’s quantifying over the Naturals. Strike another point for lack of rigor.
    > All pairs of functions (f, g), so that f is a function from positive integers to rationals, g is a function from positive integers to positive integers, and
    > (∀n∈ℕ)(∀i∈ℕ)(∀j∈ℕ)(j≥g(n)→|f(i)-f(j)|≤(1/n))

    And again, we see English prose, when we should have formal symbolic logic. Strike another point for lack of rigor.
    > R = { (f:ℕ→Q,g:ℕ→ℕ) : (∀n∈ℕ)(∀i∈ℕ)(∀j∈ℕ)( j≥g(n)→|f(i)-f( j)|≤(1/n)) }

    Finally, the above is something that is actually pretty rigorous and formally specified in an unambiguous way.

    Unfortunately for constructionists and intuitionists like Wildberger and Brouwer, they eschew this approach in favor of the less rigorous and more ambiguous English language prose. Unfortunately for them, this requires quantification over an infinite set, another faux-pas for constructionists, intuitionists, and finitists.

    Like, for example, how would one do a simple proof with the peano axiom of induction in constructivist logic and math? I spent a while looking for it, but I couldn’t find an example by Wildberger or anyone else. And particularly, can I formalize it in symbol notation without quantification over an infinite set?

    I honestly don’t know, because I haven’t really bothered to look into any of this nonsense with sufficient detail. I decided I would not spend any real time on it as soon as I learned that with these systems, one cannot prove that sqrt(2) is not rational.

  65. EnlightenmentLiberal says

    > I decided I would not spend any real time on it as soon as I learned that with these systems, one cannot prove that sqrt(2) is not rational.

    Alternative phrasing: I decided that I didn’t care as soon as I learned that one cannot prove: ¬(∃n∈ℚ)(n*n=2)
    Or however one would write an equivalent statement in this other sort of silly logic and math.

    Further, as I said, I’m still confused about quantification in these other math systems. What symbolic logic notation do they have to express this simple idea:
    > ¬(∃n∈ℚ)(n*n=2)
    ?

    Forget about proving it. Can the claim / statement even be represented!? Can it be done in formal symbolic form? What does it look like? What is it?

    Or do they have to resort to natural language English prose? If yes, that is an automatic failure according to my standards, and this entire system of math and logic IMHO warrants no further investigation, and I say that it belongs to cranks like Wildberger et al. By “crank”, I admit that Wildberger is very educated on these topics, and knows what he’s talking about, but his particular philosophical positions of finitism, constructivism, and disdain of formal, rigorous, symbolic, axiomatic approaches – that is worthy of the epitaph “crank”.

  66. Monocle Smile says

    @Peter

    I use predicate calculus. However, the important point is that I realise that there are other alternatives which some people choose to use them instead for their own personal reasons.

    Do these people exist? And if so, how are they still alive? I realize you’re desperate to get away from any kind of discussion relating to empiricism, but that just makes your posts annoying and eventually dishonest. Again, this has fuck all to do with “supernatural”

  67. Christopher Lowe says

    As a born and raised atheist, I challenge any theist to convince me, using verifiable evidence, that your, or any other god, exists. I know that your religion exists, but tell me what in your foundational texts or your acknowledged authorities gives you, as a person of faith, any knowledge denied me?

  68. peter golinski says

    @corwyn #72

    You said: “So your constructivists think that the sqrt(2) is rational? (This was your example after all). What are the integers A and B such that A/B = sqrt(2)?”

    This was certainly NOT my example. I have NEVER said anything like this- if you think I wrote this then find it and quote it!! This is definitely NOT what constructivists think. No constructivists on Earth thinks that sqrt(2) is rational!!!

    You also said: “On the other hand if your constructivists think sqrt(2) IS irrational, but can’t prove it, that isn’t a different result, just a lack of result (on their part).”

    Some constructivists may wish that sqrt(2) is irrational or they may think it would be nice that it is so, I’ve no idea what any given individual constructivists thinks about it: you would have to ask them. However, what I do know, is that none on the planet, who remain true to constructivism, have used a proof by contradiction to prove that it is irrational (they’d still be proud/satisified of not using proof by contradiction even if they think it would be nice that sqrt(2) is irrational).

    I’ll try to give a simple explanation of Construstivism later, I don’t have time now.

  69. EnlightenmentLiberal says

    I’ll try to give a simple explanation of Construstivism later, I don’t have time now.

    Please. I would be most interested, especially in an example proof using Peano axiom induction.

    For example, how would you prove something as simple as the following?
    (∀n∈ℕ)((n≠0)→[(∃p∈ℕ)(S(p)=n)])
    Where “S(p)” is the successor of “p”, aka “S(p) = (p+1)”. In English, one can read this as: “All non-zero natural numbers are the successor of some natural number.”

    Off the cuff, I would go about proving that from Peano axioms as follows. My apologies for the extreme verbosity, but I’m trying to make a point about rigor. Even still, I’m skipping a few steps. (Yes, my Math professors hated me – because I was often needlessly verbose in my proofs for high level college math courses. “Hate” is an exaggeration. I am pedantic anal to a fault.)
    .
    Let’s use this formalization of the induction axiom:
    (∀K⊆ℕ) [(0∈K∧(∀n∈ℕ)(n∈K→S(n)∈K)) → (K=ℕ)]
    Equivalently:
    (∀K∈P(ℕ) [(0∈K∧(∀n∈ℕ)(n∈K→S(n)∈K)) → (K=ℕ)]
    Where “P(ℕ)” is the power set of ℕ.
    .
    Let K = { n∈ℕ | (n=0) ∨ (∃p∈ℕ)(S(p)=n) } … allowed by the ZF axiom of restricted comprehension
    .
    ⇒ (0∈K) ↔ (0∈ℕ ∧ ((0=0) ∨ (∃p∈ℕ)(S(p)=n))) … by definition of the set K
    ⇒ (0∈K) ↔ (T ∧ ((0=0) ∨ (∃p∈ℕ)(S(p)=n))) … true by Peano axiom
    ⇒ (0∈K) ↔ (T ∧ ((T) ∨ (∃p∈ℕ)(S(p)=n))) … true by basic classical logic
    ⇒ (0∈K) ↔ (T ∧ (T)) … follows by basic rules of classical logic
    ⇒ (0∈K) ↔ T … follows by basic rules of classical logic
    ⇒ 0∈K
    .
    Let x be some member of K … Note: Allowed because we know the set is non-empty, because we just showed that 0∈K
    ⇒ (x∈ℕ) ∧ ((x=0) ∨ (∃p∈ℕ)(S(p)=x)) … by the definition of set S
    ⇒ x∈ℕ … by basic rule of classical logic (dropping conjunction clause)
    ⇒ S(x) = S(x) … by basic rule of classical logic
    ⇒ (x∈ℕ) ∧ (S(x) = S(x)) … by introducing a conjunction of previous steps
    ⇒ (∃p∈ℕ)(S(p)=S(x)) … by existential generalization on the previous step
    ⇒ (S(x)=0) ∨ (∃p∈ℕ)(S(p)=S(x)) … by basic rule of classical logic (adding an arbitrary disjunction)
    ⇒ S(x)∈ℕ … because S:ℕ→ℕ
    ⇒ (S(x)∈ℕ) ∧ (S(x)=0) ∨ (∃p∈ℕ)(S(p)=S(x))) … by introducing a conjunction of previous steps
    ⇒ S(x)∈K … by definition of the set K
    ⇒ x∈K→S(x)∈K
    ⇒ (∀x∈ℕ)(x∈K→S(x)∈K) … by universal generalization
    .
    ⇒ (0∈K) ∧ ((∀x∈ℕ)(x∈K→S(x)∈K)) … by introducing a conjunction on previous steps
    .
    ⇒ K=ℕ … by invoking the Peano axiom of induction, and universal instantiation, and modus ponens,
    .
    ⇒ (∀x∈K)( (n=0) ∨ (∃p∈ℕ)(S(p)=n) ) … by definition of the set K
    ⇒ (∀x∈N)( (n=0) ∨ (∃p∈ℕ)(S(p)=n) ) … by substitution
    ⇒ (∀x∈N)( ¬(n=0) → (∃p∈ℕ)(S(p)=n) ) … by basic rules of classical logic
    ∴ (∀x∈N)( (n≠0) → (∃p∈ℕ)(S(p)=n) ) … notational

    Thus, by using only the Peano axioms, and the basic axioms / rules of classical logic, I have proved that every non-zero Natural Number has a predecessor that is a Natural Number.

    Apologies for any typos and gross errors.

  70. corwyn says

    @77:

    So I am still waiting for an example of when different logics produce different results, as you claim (with exclamation point).

  71. peter golinski says

    @corwyn #79:

    I feel that you’re taking the Mickey here. How can you not see that different logics give different results when I’ve repeated an explicit example, ie sqrt(2) being irrational or not, a few times now? Also I’ve mentioned in a way earlier post that intuitionist reject the standard proof by contradiction that the primes are infinite. And lastly, EnlightenmentLiberal, who obviously is knows mathematics very well, more than confirms that intuitionist logic gives different results (It appears, to me at least, that he is of the vehement opinion that not only are they different, ie: the fact that intuitionism produces fewer* proofs for a given theory, but that this difference is repugnant to him.)

    Well, anyway -fool that I am- I’ll give it one last go:

    Seeing how you can just can’t seem to understand the difference between intuitionist logic and classical; I’ll use a different class of logics, ie: paraconsistent logics. Now I have to admit I only know this logic in a light, passing fashion but nevertheless, here we go-

    Let’s move away from maths and take an example from physics, since you don’t seem to handle maths concepts well.
    Hopefully, you’ve heard of the Schrodinger’s cat though experiment (if not then google it, cause I can’t be bothered explaining it). Now, in the following I’m going to assume that some person does believe in the Copenhagen Interpretation, so for this person then the Schrodinger’s cat result is real/true (or more correctly would be if the experiment was actually performed).
    For this person let’s examine what we can establish by reason using too different logics:
    ————-
    A) Classical logic: The cat is Alive AND it is dead (ie: NOT alive). From this we derive FALSE. From FALSE we conclude that I’m God and everyone should worship me.
    This is a perfectly valid argument! (If you wondering about the last step: it is a rule in classical logic that from FALSE anything/everything follows- this is called the “Principle of Explosion” or if you want to use supercilious fancy latin “ex falso (sequitur) quodlibet (EFQ)” or “ex contradictione (sequitur) quodlibet (ECQ)”. Thus this person must acknowledge that it is TRUE that I’m God!. Ie: For all those here who use traditional logic (which seems to be most responding to me) either you don’t consider the Copenhagen Interpretation TRUE or it is TRUE that I’m God.
    —————
    B) Paraconsistent logic. The above proof is NOT valid! Because in paraconsistent logics a statement can be TRUE and FALSE at the same time and so the first step fails.
    ————-

    So, can see that there is a difference now?
    Hopefully, now I’ve demonstrated that the logics that you choose drastically effect the conclusions that you may draw.
    .
    *[Before anyone here pedantically corrects me: I’m using the word “fewer” here in the sense that classical logic produces every theory that intuitionism does plus more. Yes, I do know that both will actually produce an infinity of theorems for a given theory.]

  72. CompulsoryAccount7746, Sky Captain says

    @peter golinski #80:

    The cat is Alive AND it is dead (ie: NOT alive).

    You relied on a pop-sci narrative of superposition.
     
    Even when a system is in superposition, the math of quantum mechanics does not describe it IN a either state – it’s not IN both simultaneously. It’s a matrix in a composite state (its values influenced by both), without a meaning on its own, but transforming it with an operation will result in a prediction of what you’ll see if you measure the system.
     
    The principle of explosion wouldn’t apply because there is no contradiction.
     
     
    Article: Wikipedia – Copenhagen interpretation, Metaphysics of the wave function

    A wave function represents the state of the system. It encapsulates everything that can be known about that system before an observation
    […]
    The results provided by measuring devices are essentially classical, and should be described in ordinary language.
    […]
    The Copenhagen Interpretation denies that the wave function provides a directly apprehensible image of an ordinary material body or a discernible component of some such, or anything more than a theoretical concept.

  73. EnlightenmentLiberal says

    in the following I’m going to assume that some person does believe in the Copenhagen Interpretation […] A) Classical logic: The cat is Alive AND it is dead (ie: NOT alive). […] This is a perfectly valid argument!

    Yes, but the argument is totally not sound. The premises are not true. A cat in a macroscopic superposition of alive+dead does not fit the classical-physics definition of “alive”, nor the classical-physics definition of “dead”. It is neither alive nor dead. Those classical-physics definitions only apply to scenarios that are governed by the rules of classical physics. A macroscopic superposition is well outside the domain of classical physics, and it’s inappropriate to use notions of classical physics when describing the cat.

    In particular, your argument is borderline nonsensical. Asking questions “is it alive?” concerning a macroscopic superposition makes as much sense as asking “what is the square root of a pork chop?”. The square root function is not defined to operate on pork chops, and the predicates “is-alive” and “is-dead” are not defined to operate on quantum systems of macroscopic superpositions.

    In other words, a cat is alive if and only if the cat exists in a classical-physics state that matches the usual biological definitions of “alive”. That’s the obvious and straightforward definition. As soon as the cat enters a superposition of alive+dead, it is incorrect to say that the cat is alive, and it is incorrect to say that the cat is dead. It is neither alive nor dead. Rather, it is in a quantum mechanical state that is the combination of the classical states “alive” and “dead”. Again, it is not in the classical-physics state “alive”, and it is not in the classical-physics state “dead”. It is not in a classical-physics state!

    In other words, the quantum mechanical description of this macroscopic superposition is perfectly describable using classical logic without contradiction. There is no requirement in classical logic that we adopt models of the world which include the terms “alive” and “dead”. In order to properly describe the situation, you must abandon such simplistic classical-physics notions like “alive”, “dead”, “absolute position”, “absolute velocity”, etc. Seemingly, that’s not the way that the world actually works.

    There’s more problems with your line of argument, but I think I can stop here for now.

    either you don’t consider the Copenhagen Interpretation TRUE or it is TRUE that I’m God.

    As I hopefully just demonstrated, not at all.

    You’re in way out of your league here in math, epistemology, and philosophy. Albeit you have a passing knowledge of some esoteric “logic systems”, which is admittingly more than I have at present.

    PS: I am still curious if you know enough intuitionist logic to answer my earlier technical questions, such as the request to prove that all natural numbers except zero have a natural number predecessor, in some formal, rigorous, symbolic form.

  74. peter golinksi says

    @ CompulsoryAccount7746, Sky Captain and EnlightenmentLiberal

    I suspected when I gave this example it would cause dissenting comments about the actual physics. What I think your failing to realise is that you’re comments in no way detract from what I’m trying to point out to Corwyn. This is because it is not the soundness of the argument here that highlights the difference between the two logics but the validity.
    In case A the argument is VALID, in case B the argument is not compatible with paraconsistent logic. Whether it is sound or not is irrelevant to what this scenario is demonstrating. Corwyn wanted me to demonstrate how different logics can theoretically produce different results from the same starting assumed truths. This scenario demonstrates this when you assume the cat is alive and not alive.

    [PS: EnlightenmentLiberal, I’ve had a very, very quick look at your proof and am a little confused. I think I must have missed something very obvious so I’m asking for clarification: Why do you think that your proof is not compatible with intuitionist logic? Did you rely on the law of excluded middle or double negation elimination somewhere and thus made it incompatible with intuitionist logic?]

    [PPS: I have to go to bed now so can’t respond anymore after this sorry]

  75. CompulsoryAccount7746, Sky Captain says

    @peter golinski #80:

    Let’s move away from maths and take an example from physics

    #84:

    I suspected when I gave this example it would cause dissenting comments about the actual physics.

    You don’t seem to handle physics concepts well. We were informing you of that.
     
    When namedropping physics jargon is irrelevant to your point, your composition would benefit from omitting the extraneous words.

  76. Monocle Smile says

    @Peter
    I’m still bored to tears. This continues to be a non sequitur.
    What does this have to do with gods or “supernatural?”

  77. CompulsoryAccount7746, Sky Captain says

     
    Article: Wikipedia – Dialetheism

    Dialetheism is the view that some statements can be both true and false simultaneously. More precisely, it is the belief that there can be a true statement whose negation is also true.
    […]
    In some logics, we can show that taking a contradiction as a premise (that is, taking as a premise the truth of both “p” and “not p”), we can prove any statement […]. (This is often called the principle of explosion, since the truth of a contradiction makes the number of theorems in a system “explode”.)
     
    Because dialetheists accept true contradictions, they reject that logic alone can prove anything at all because anything at all is possible. According to dialetheists, evidence is always needed, and we cannot conclude anything for certain outside of our own immediate experiences, which cannot be described perfectly with words.

  78. corwyn says

    @80:

    How can you not see that different logics give different results when I’ve repeated an explicit example, ie sqrt(2) being irrational or not, a few times now?

    Because you wrote this:

    This was certainly NOT my example. I have NEVER said anything like this- if you think I wrote this then find it and quote it!! This is definitely NOT what constructivists think. No constructivists on Earth thinks that sqrt(2) is rational!!!

    You are contradicting yourself. You are not worth responding to. PLONK.

  79. EnlightenmentLiberal says

    PS: EnlightenmentLiberal, I’ve had a very, very quick look at your proof and am a little confused. I think I must have missed something very obvious so I’m asking for clarification: Why do you think that your proof is not compatible with intuitionist logic? Did you rely on the law of excluded middle or double negation elimination somewhere and thus made it incompatible with intuitionist logic?

    I presented the proof how I would normally do it. I expressly asked for if one can prove the same conclusion in another “logic”, and how it can be done.

  80. EnlightenmentLiberal says

    Further, I asked that question as part of my overall argument that if your other so-called “logic systems” cannot even deduce a basic fact like that, then your logic systems are obviously silly. A sort of reductio ad absurdum, which of course you do not admit in intuitionist logic and other logics, but I don’t care.

  81. peter golinski says

    @ Monocle Smile #86

    What is has to do with God and the supernatural is that it is trivial to produce a 100% valid proof that God exists in some logics. However, for the proof that I have in mind right now, I suspect that if I phoned in the show and presented the proof the hosts would not accept it*. They won’t accept it not because the reasoning is flawed (they can’t because it’s a valid proof), they would reject it because they wouldn’t approve of the logic/ deductive system used. If they reject some logics but not others than they have some sort of criteria in mind by which they assess logics by (unless of course it’s just random or some inner personal choice that they can’t really explain). For example, one criterion may be that any logic which permits a valid proof of god is unacceptable.

    Also, Matt has one than once encouraged people the read about and use “logic”, but he’s only given general hints about which logic he means. I’m assuming that he has a/some particular one(s) in mind. At the end of the day, the logic you use is a personal choice, so I’m curious which one(s) he’s chosen and why.

    *[I also, while acknowledging that the proof is valid, am not really convinced by it either.]

  82. peter golinski says

    @EnlightenmentLiberal #89.

    I’m sorry but I’m still very confused.
    I’ve read your proof again (actually I did it twice). This time with more attention and I still cannot see how it is not a valid intuitionist proof. Maybe a keep missing the same thing, but every step to me seems to be a valid intuitionistic deduction. I admit that it is quite easy for me to miss a non-intuitionist step, cause I normally (more like only ever) use predicate calculus so maybe I slipping back into that even though I’m meant to be looking for a non-intuitionist steps.

    It’s because it seems you’ve actually given me a nice, valid intuitionist proof (along with valid classic proof of course, since intuitionist proofs are a strict subset of classic proofs), that I’m confused. Specifically, why would you give me a classical proof which is at the same time a valid intuitionist proof and then challenge me to prove the same conclusion using intuitionist logic? All, I have to do is just give you back the exact same proof you gave to me. I can’t see how you think that you’re demonstrating that in this case intuitionistic logic is found wanting. If what you really mean is that you want me to give you back some different proof then no worries I pick some place at random in the proof insert a benign introduction followed by an elimination to reverse the introduction so that now the proof I give back will now be different from yours.

    I’ll read the proof again to see if I’m mistaken about it being intuitionistic, but it would be a lot easier if you showed me the exact line(s) where you claim you’ve made a classic but non-intuitionist step (eg: have you used double negation elimination somewhere?).

  83. EnlightenmentLiberal says

    What is has to do with God and the supernatural is that it is trivial to produce a 100% valid proof that God exists in some logics.

    That’s nice. I’m pretty sure I stopped caring for a while now.

    You are right that one logic is just as “correct” as any other logic, in the formal sense that all correct epistemologies are a combination of foundationalism and coherentism, aka a combination of presuppositions and circular reasoning to form the starting beliefs. My “choice” to use classical logic, as opposed to these asinine alternatives, is in part “because I say so”, and in part because using it has worked really well in the past as part of behavior to get what I want, and therefore I expect that I will continue to work in the future as part of behavior to get what I want.

    For an epistemology 101, I suggest the following link.
    http://richardcarrier.blogspot.com/2006/11/epistemological-end-game.html
    > Epistemological End Game
    > blog post by Richard Carrier

    I’ve read your proof again (actually I did it twice). This time with more attention and I still cannot see how it is not a valid intuitionist proof.

    English ****!? Do you know it!?

    Quoting me from above:
    I presented the proof how I would normally do it [in classical logic]. I expressly asked for if one can prove the same conclusion in another “logic” [such as intuitionist logic], and how it can be done [in intuitionist logic].

  84. Monocle Smile says

    @Peter Golinski

    They won’t accept it not because the reasoning is flawed (they can’t because it’s a valid proof), they would reject it because they wouldn’t approve of the logic/ deductive system used

    If we agree that we give a fuck about stating accurate conclusions about the reality we experience, then your boring-ass castles in the air are utterly irrelevant. If god exists in a fictional world, I don’t give a fuck.
    This is what happens when you care only about validity and not soundness. You lose touch with reality. I care about reality. The math thing is STILL a non sequitur. It has nothing to do with anything.

    For example, one criterion may be that any logic which permits a valid proof of god is unacceptable.

    Sweet, so you’re just going to assume the hosts are being dishonest. Is this really your position? Shit, you’re every bit as annoying as a presuppositional apologist.

    At the end of the day, the logic you use is a personal choice, so I’m curious which one(s) he’s chosen and why

    You are not dead, so I think you’re being totally disingenuous here.

  85. peter golinski says

    @EnlightenmentLiberal says #93

    Yes, one can show that it can be done in another logic. Your proof is actually an example of just how it can be done in intuitionist logic! In otherwords- I just hand your proof straight back to you and say “Here is an intuitionistic proof of what you asked me to prove”. Remember, the set of all intuitionist proofs are a strict subset of classical proofs. You picked a proof which happens to be an intuitionist proofs and thus AT THE SAME TIME a classical proof.

  86. peter golinski says

    @Monocle Smile #94

    When you say “This is what happens when you care only about validity and not soundness.” you’re revealing that you’re not really understanding the problem here. I’ll try to explain it but I fear I might make it worse for you, sorry but I’m probably not the best to explain this.

    The proof I can give them would be perfectly valid and sound. Soundness only means that your starting axioms actually do correspond to the real world. This is not about that. This is acting at the lower level of the which logic/deductive system to use. The question of validity and soundness can only be asked once you’ve decided upon a logic to use. The question of which logic has to be settled BEFORE you can start worrying about soundess and validy. The empirical nature of soundness doesn’t relate to the question of which logic to use.

    By-the-way: I don’t think the hosts are dishonest. They are very forthright in what they say. I was only giving an example of a possible criterion. As far as I know, they’ve not in anyway said that this is a rule they use.

  87. Monocle Smile says

    @peter
    I don’t believe you when you say you can provide a valid and sound proof of god. You can only do this with Insane Troll Logic, as far as I know.
    http://tvtropes.org/pmwiki/pmwiki.php/Main/InsaneTrollLogic
    How about you post this proof? Then we can discuss. Because if a logical system does not reliably produce accurate conclusions about the real world given sound premises, then it is a useless-ass system.

  88. EnlightenmentLiberal says

    To peter golinski
    Cool. Thanks. I am still quantifying over an infinite set. Is there a way to do the proof without quantifying over an infinite set?

  89. peter golinski says

    @EnlightenmentLiberal # 98:

    Your confusing a logic with a philosophy of maths associated with the logic. The logic is intuitionist logic the philsophilosphy/school of thought is Intuitionism/Constructivism.

    A proof is written within a theory using a logic/deductive system. The theory of your proof is I’ve assume is ZFC. While the logic of your proof was predicate calculus.
    The theory of my proof is also ZFC while the logic is intuitionist logic. I can use ZFC because as far as I know every axiom is compatible with intuitionist logic- its been a while since I’ve seen the axioms, over 15years, but as I remember no axiom has an invalid intutionistic logic formula from a purely syntactical point of view. Since it is compatible then I’m allowed to work with the theory, however I’m only allowed to derive new theorems using intutionistic deductive steps.

    So my proof in answer to your question can use any set that is generated by the ZFC axioms by using intuitionist logic. This includes an infinite set that you can use to represent the natural numbers. Ie, you can quantify over this set.

    Therefore the plain answer your question: YES

    —-

    However, there is philosophy of maths called Intuitionism/Constructivism (note that actually it’s not a unified single philosphy, there variations of it). It deals with questions such as which theories (which obviously need to be compatible with intuitionist logic) align/compatible with this philosophy. And some adherents say that the axioms of ZFC are compatible (remembering of course that you may only derive new theorems from them using intuitionist logic). While other say that they are not: especially regarding the axiom of inifinity (some also have issues with the axiom of choice while others reject the whole notion of sets). Those that are prepared to work within ZFC have inifinite sets, however, they don’t have the “bigger” infinities such as aleph1 because to prove these exist you use a proof by contradiciton- which as you know are not allowed for them.

    Note that your question was: “It is possible to produce a proof of this with intuitionistic logic?”, which I do by handing it straight back to you. It wasn’t a question of whether I can produce a proof that aligns with some variant of a philosophy.

  90. EnlightenmentLiberal says

    No, I think have those things clear. Thanks for being clear and cooperative.

    Still, I must side with Monocle Smile et al.

    In particular, all of the logical systems that you have thus far put forward cannot show that a god exists.

    Further, as part of my foundation of my epistemology, I am going to use classical logic (or something very much like it), and I not interested in radically different logic systems. There may be other logic systems which can derive the existence of a god, but if you cannot also do it in classical logic, then I almost certainly do not care.

    Finally, if you think this makes me indoctrinated or something, or if you think that this makes me unreasonable, or if you think that this makes me just as faith-based as Christian presuppositionalists, then I really do not care. PS: You would be right that my epistemology is based on presuppositions (and circular justifications), but this is true of every epistemology. I don’t know if I linked this previously – I probably did – but here it is again:

    > Blog post
    > Title: Epistemological End Game
    > by Richard Carrier
    http://richardcarrier.blogspot.com/2006/11/epistemological-end-game.html

    I do want to emphasize that the only things that I presuppose are things like:
    * I should use classical logic,
    * I should conform my beliefs to the evidence
    * I should further the goals of humanism for everything, with a slight preference for myself

    Whereas, so-called Christian presuppositionalists will presuppose that the Christian god exists. Note that in my epistemology, I do not presuppose that the Christian god does not exist. Rather, my belief that “the Christian god does not exist” is a proper tentative conclusion of the scientific method. The conclusion is not presupposed, but the method by which I arrive there – the scientific method – is presupposed. Further, it must be emphasized that had the evidence been different, that same method, the scientific method, would arrive at the conclusion that the Christian god does exist. But that’s not the world that we actually live in.