The set of all facts

Jayman raises an interesting point regarding Leibniz’ cosmological argument (as summarized by Pruss).

Pruss’ second point is: “there is a contingent fact that includes all other contingent facts.” Let us assume, for the sake of argument, that the material universe is not contingent. Nonetheless you seem to admit that there are contingent facts. This entails that there is a contingent fact that includes all other contingent facts (the union of all contingent facts).

I’m not sure what point Jayman thought he was proving by that, but it does suggest an interesting line of philosophical inquiry.

Suppose we define Reality as the union of all facts (i.e. the set which contains all facts). Notice I did not say “contingent facts” but simply “facts.” This is quite deliberate, since Leibniz wants to reason from the existence of contingent facts to the existence of a “necessary being” (which he wishes to identify with the Christian God). Obviously, this necessary being must also be part of Reality, since the set of all contingent facts cannot be explained by a “necessary being” that does not actually exist in Reality. Thus, if we consider Reality to be the set of all facts, including the fact of “necessary being,” then Reality must necessarily contain the explanation of its own existence. Since the existence of Reality is necessary in order to explain the existence of any god or gods which may happen to exist, it follows once again that Reality is not contingent (since it contains the explanation of its own existence) but any and all gods are contingent (since their existence requires the existence of Reality as at least part of the explanation for their own existence). The only possible God, therefore, is the pantheistic Alethea, QED.

Next, I was going to look at the set of all sets which do not contain themselves, but it’s Sunday, and I’m lazy…



  1. anatman says

    throwing around concepts like ‘union of all facts’, you have to watch out for russell’s paradox. it is easy to end up in a contradiction if you don’t.

  2. Aspect Sign says

    Not far off the Buddhist position that for gods to exist they must be part of reality and as such are no better off than humans when it comes to existential issues and that in fact their greater knowledge and powers would act as a distracting hindrance in gaining understanding of existence, positioning human beings in the better position as to existential understanding. Hence all the mythology abounding with gods sucking up to the buddha. Though in buddhist philosophy a core position is that all that exists is contingent, arising from no-thing and mutually codependent.

  3. David Evans says

    I don’t think your concept of Reality does the work you want it to do.

    Suppose there is one necessary being, God, and a universe of contingent beings. Reality is defined as the union of these two things, R = {God, universe}

    What sense does it make to say that God is contingent on R? R has the particular form it has only because God exists. That particular form of R is contingent on God, not the reverse.

    • Deacon Duncan says

      Hello, David. The problems you’re citing stem from the arbitrary assumption that God is the necessary being, with the implicit assumption that His being is not contingent upon anything else. I suggest, however, that you cannot reason from that assumption to any reliable conclusion about the real world, because if you define God in this way, then His existence is not contingent upon the existence of Reality. That puts God’s existence somewhere outside of Reality, which means He’s not real and therefore does not really exist.

      Reality is not just the union of all things that are real, it is also the context within which it is meaningful to speak of things as having real existence. In the absence of such a context, it is meaningless to speak of God having any real existence, therefore if He did exist, His existence would necessarily be contingent upon the existence of Reality.

      • David Evans says

        I’m really uneasy about this. You appear to have a purely verbal proof that God does not exist. How is that any better than the ontological argument, a purely verbal argument that he does exist? Facts about the world must, in the end, be established by looking at the world.

        I also think your argument about the absence of a context is flawed. Let’s consider 2 possible states of affairs:

        #1 God alone exists
        #2 God and the universe of contingent things exist.

        In both cases, Reality exists:

        In #1, Reality = {God}
        In #2, Reality = {God, universe}

        Are you really saying that #1 is somehow impossible? Sure, if there were no universe, we would be unable to speak meaningfully of God’s existence (because we wouldn’t even exist!) But God would presumably be able to speak meaningfully of his own existence, and in that situation his opinion would be the only one that counted.

      • Deacon Duncan says

        You appear to have a purely verbal proof that God does not exist. How is that any better than the ontological argument, a purely verbal argument that he does exist?

        Perhaps it merely illustrates the fundamental flaw in all such proofs? At the very least it is amusing to show how easily philosophical arguments for God can be turned into arguments for a specifically Alethian God. Rather frustrating for the Christian apologist, but not one that can readily be attacked without undermining the Christian apologetic as well.

        Let’s consider 2 possible states of affairs:

        #1 God alone exists
        #2 God and the universe of contingent things exist.

        In both cases, Reality exists:

        In #1, Reality = {God}
        In #2, Reality = {God, universe}

        Are you really saying that #1 is somehow impossible?

        No, I’m saying that in case 1, the existence of God necessarily implies the existence of Reality, and therefore you cannot have the case that God exists when Reality does not. It is therefore more correct to make God’s existence contingent on the existence of Reality (since Reality could also exist without God), than the other way around.

      • SAWells says

        Inclusion of the third case, “Reality=(universe)”, should make the point clearer that we can conceive a reality without any gods.

      • David Evans says

        “(since Reality could also exist without God)”

        That’s formally true, because of the way you have defined Reality, but I don’t think it’s a substantive truth.

        By analogy, if I define “I” as the contents of the space bounded by my skin, it’s true that my brain’s existence is contingent on that of “I”. It’s also true that the existence of “I”, so defined, is not contingent on that of my brain. That does not lead me to contemplate the removal of my brain with equanimity. Without it, “I” would not be the same person.

        Similarly, a Reality without God is not the same as a Reality with God, and it’s misleading to use the same term for both.

  4. The Lorax says

    I am not a philosopher, I am not well-read, I know a bit of logic and I had to actually look up the definition of “contingent”… but I enjoy learning and I’m going to take a stab at this. If what I’m about to say is incredibly incoherent, well, I’m an idiot.

    So basically, if Reality is defined as the set of all facts, it would therefore include the explanation of its existence. This explanation cannot exist without Reality, because we have defined Reality to be all facts, therefore a fact cannot exist without Reality to encompass it. However… could it be the case that Reality could not exist without an explanation for its existence? We say for Reality that it must have an explanation for its existence, that’s sort of implied. It couldn’t exist without an explanation. It should be said, then, that all facts within Reality should have an explanation for their existence as well, and thus, every fact, including Reality itself, must have an explanation for its existence.

    Therefore Reality and its explanation for existence must be simultaneously existent or non-existent.

    … is that a verbal proof for the Big Bang?

    I think I’m following it though… I guess what it boils down to is that no god could have created Reality, due to the problem of Reality being the set of all facts, including the god that created it. It is logically impossible to create a set of all facts, unless the creation itself is not a fact… which means that nothing has been created.

    Does it sound like I have any idea what I’m talking about? I feel as though I’m just re-wording the same thing over and over…

  5. Dan L. says

    Similarly, a Reality without God is not the same as a Reality with God, and it’s misleading to use the same term for both.

    That seems strange to me. It has always seemed to me that God does not exist but other people assure me He does. So I am forced to conclude that a world without God actually looks a whole lot like a world with God — apparently, I can’t even tell the two apart!

    So I’m not so sure about your conclusion.

    Besides that, “your terminology is misleading” is not usually acceptable as a philosophical argument if the person has gone through the trouble of defining terms in the first place.

  6. John Scanlon, FCD says

    Set Theory (1969)
    I must have spent a lot of time looking at the poster on the north wall of my kindy classroom, the room at the south-west corner of the ground floor of Cammeray Public. I don’t remember precise details of colour or arrangement of the figures, but the poster showed, in a few simple Venn diagrams and symbols, the basic concepts of set theory.
    I had learned reading and the idea, at least, of writing at home; I remember playing with a typewriter, trying out all the keys and symbols and pestering my brother for spelling help with what turned out to be an extremely short story in a Western idiom. But on the first day of school, probably before I saw any pencils or books, I saw this poster, and it was magic.
    Sets, it showed me (‘show, don’t tell!’) were things you could draw a circle round; some things were inside, the rest outside.
    For any two sets, there is another set called their union with everything in it that is in either of the others, and one called the intersection, a set with anything that is in both.
    Nothing is also something, and there is a special empty set with nothing, and nothing else in it. Nothing is in every other set, too; you can’t keep it out. It’s the intersection of all sets.
    Everything together is something, and it is a very special set – the union of all sets. They called it the Universe.
    Now, there was that time every week when the classes were split up along lines I didn’t understand or question, and someone came in to talk about religion. For our class, coincidentally, the someone was often my mother. I don’t remember much specific about what was said, except for clearing up the wording of the Hail Mary – up till that time, I’d been some sort of heretic by thinking that ‘fruit of thy womb’ was some kind of poetic reference to a worm in an apple, possibly the same one as in Adam and Eve’s story. I later decided there was a kind of truth to that – but I digress.
    One of the things religious people tend to say, and certainly told me about that time, was that ‘God made the world’. As this was 1969, horizons were expanding, and somebody, probably my mother, used the word ‘Universe’ instead of ‘world’. That made me think.
    The Universe, I already knew, is the set that contains everything. I knew what that meant, and I haven’t changed my views because it was simply a matter of definition. There is nothing that isn’t in it (but nothing is also in it; you can’t keep it out). Every thing, and every set; everything you can see, hear, touch or whatever; everything that you can imagine. But also everything that you can’t see and can’t imagine. Everything true; and everything false.
    God is in the universe, that was obvious (he lived in a box with a red light on it, near the altar in our church, and was somehow everywhere else as well). Nothing – no, not even nothing – is outside the universe. So he can’t have made it. No way.

Leave a Reply

Your email address will not be published. Required fields are marked *