Consistency and perfection

As long as we’re dabbling in a bit of amateur philosophy, I thought I might bring up another notion some of you might find interesting. I spend a lot of time thinking about the principle that truth is consistent with itself, both in the non-contradictory sense and in the cohesive/unified sense, and it has led me to some unexpected conclusions. One of the under-appreciated implications of this self-consistency is that it means we have a faulty conception of what perfection is, for the most part, and I think this is where a lot of Greek philosophy and its derivatives went astray.

This is just armchair philosophizing, of course, so feel free to chip in your own two cents worth, but it seems to me that once you accept the idea of truth being cohesive, you must inevitably accept the conclusion that there is ultimately only one truth, of which all lesser truths are merely aspects. And yet, we are finite beings, whereas truth is potentially infinite, and is definitely greater than any mortal mind can comprehend. It follows, then, that our knowledge of the truth is necessarily incomplete, and therefore imperfect.

We respond to this problem by approaching knowledge as a set of abstractions: we take individual aspects of the truth and isolate them from the rest of the truth, and then, paradoxically, label them as “ideal” or “perfect.” For example, real-world circles are fairly complex things and not a few of them (e.g. planetary orbits) aren’t strictly circles at all. But our brains are finite, and we have limited resources for dealing with all the variations and perturbations that affect real-world circles, so we simply ignore the “imperfections” (as we call them) and define a theoretical “perfect circle” in terms of a mere center and radius.

Notice, we derive what we call a “perfect” circle by taking away information. In the process of simplifying a circle for more convenient (finite) thinking, we’ve removed the actual nature of the real-world circle, and taken just a few bits and pieces of out-of-context information, and declared them to be the “essence” or “ideal” of what a perfect circle really is. It’s like when you find that you can’t fit the whole elephant into the shoebox, you go out and find a smaller box.

This isn’t necessarily a bad thing, and certainly we can learn a lot about the real world by zeroing in on individual aspects of real-world truth and honing our understanding of their inherent properties. But it can give us a misleading notion of “perfection,” and might tempt us to think that reality is some kind of complex composite constructed out of various combination of ideal perfections. Hence the problems with Greek astronomy, and the countless wasted hours spent by early astronomers, trying to get celestial bodies to follow some combination of perfect, unvarying circles.

What we need to learn from this is that when we analyze and philosophize and theorize, we are always necessarily working with imperfect approximations of what reality actually is. That’s why we can’t afford to be dogmatic—we must continually keep going back to the real world, and comparing our projections with the actual, complex, complete nature of reality itself, to correct the errors that creep in and accumulate over time. Any dogmatic description of the truth, even when initially correct, is incomplete, and needs to be expanded and corrected as our experience grows.

Religion does not work that way, and therefore it accumulates error. It tries to reduce a complex reality to a dogmatic combination of abstract “perfections” that allegedly take precedence over what we can see in the real world. And that just won’t work. Presuppositional apologetics (the inspiration for this post) isn’t really a means of discovering the truth, it’s a technique for avoiding discovery of the truth, by overruling the error-correction that you’d otherwise be able to obtain by observation of reality. And without this ongoing, reality-based error correction, your religious beliefs are only going to get more and more out of sync with real-world truth over time.

There is no perfect faith, there is only a perfect reality. And even then it’s perfect in the sense of being complete, not in the sense of being abstracted or simplified or purged of all the unpleasant bits. If we want to get as close as possible to perfection, we need to abandon dogmatic faith, and embrace a continually self-correcting scientific worldview.


  1. dcortesi says

    It’s all Plato’s fault, the whole thing. He’s the one who in effect deified abstractions as capital-F Forms. Based on that, the neo-Platonists decided there had to be a big daddy Form behind the multiple Forms and dubbed it The One — just in time for the Christians to come along and cop that idea, combine it with the Hebrew Yahweh, and get a single perfect God.

    But I can imagine people could argue and hand-wave forever whether the Form of the Circle is less than a real circle, i.e. information has been discarded, or it is more than any real circle in that it has infinite resolution and isn’t made up of infinitesimal straight segments. And on and on.

    • mikespeir says

      It’s incredible to me when I see apologists denying the influence of Greek thought on the Christian religion. How can anyone read Colossians or, especially, Hebrews and not think, “Platonism”?

      Col 1:15 Who [Jesus] is the image of the invisible God, the firstborn of every creature:

      Is it possible this is what lay behind the idea of Christ’s deity, that Jesus was the earthly abstraction of a divine form? Then, later, the notion of hypostasis developed once apologists began to realize Platonic Forms Theory left them with a Christ who wasn’t concrete enough. Or something.

  2. daenyx says

    …but it seems to me that once you accept the idea of truth being cohesive, you must inevitably accept the conclusion that there is ultimately only one truth, of which all lesser truths are merely aspects.

    This snagged for me, and I toyed with it a bit and hopefully will now be able to articulate why.

    What I’m reading as your definition of truth, in the physical sense, is the idea that there is only one state for the universe at any given point in time. (If this is an incorrect read, then, well, the rest of this isn’t going to be terribly relevant, but I’ll say it anyway!) At a quantum level, it’s easy to argue that the states are describable, but unless we could collapse everything into a definite state at once, the universe effectively exists in many states.

    I guess my major issue is that I’m not convinced that coherency of variables implies unity of truth. If you take a Bayesian network that describes some set of mutually-affecting conditions, there are multiple sets of values for the nodes that are coherent with one another, i.e., are mathematically possible per the guidelines of the edges. If some of the edges are drastically different (and in the kinds of systems I work with – biological ones – they often are), then you can have varying degrees of “play” in any given variable regarding how much or how little changing that variable affects its neighbors.

    If truth is a comprehensive description of the state of the universe, then, it is either not a unique solution, or it is a probability distribution encompassing a multiplicity of variable state-sets. (Or you could define it at the level of the each variable, but that didn’t seem like what you were talking about.) I think the latter is the more useful way of looking at it, but I’m also doing my PhD research in systems biology, so I’m a bit biased because that’s how I’m trained to look at things.

    I reject the possibility that there IS a single state of the universe that we simply will never be able to access on the practical grounds of that not being a very useful line of thinking. It may or may not be true, but if it’s true, then answering it with certainty should be impossible. It’s an interesting question, but not a helpful one. (And certainly not something to base a religion on… oh wait.)

    I enjoyed your discussion and rejection of “perfection” as a minimal state of existence, particularly because it ties into the discussion of the trade-offs we make so much in engineering. In mathematics and non-stochastic modeling, we take away information until we get a reliable, known solution. In engineering (or at least, my flavor of it), we take a step back and try to find a way to deal with all that messy information that makes results seem capricious in a meaningful way that can predict bulk behavior over time. Both are useful, but glorifying one with value-loaded terms like “perfect” and “ideal” both illustrates and reinforces our tendency to try to avoid messy reality in favor of made-up variables we can actually hold in our brains all at once.

    • says

      daenyx, I just have a pedantic comment on the quantum mechanics thing. As far as I understand things from my physics training, it’s not really correct to say that the universe is in multiple states at the same time. In fact, the universe is in a single state, but in terms of measurements we can actually make, that state is a superposition of many different possible measurement outcomes. It’s like when you solve a constant-coefficient second order linear differential equation with a specified set of boundary conditions and the answer is sin(x) + cos(x). This doesn’t mean that the system represented by the equation is simultaneously in the state of being a sine and the state of being a cosine, it means it’s in the single state sin(x) + cos(x), which just so happens to be interpretable as a superposition of sine and cosine solutions.

      The analogue to quantum mechanical “collapse” in this case would be us asking this system whether it’s a sine or a cosine. It’s not really either, but when we make a quantum mechanical measurement of the property of sine-ness vs. cosine-ness, we’re insisting that the system be one of those two things only, so it picks one at random (according to the relative weighting of the two components), and then that’s the result of our “measurement”. After that, the system will be just the thing it’s told us it is and will lose any other components in the superposition (e.g., if the measurement result is “sine”, the new state of the system will be sin(x), and the cos(x) term will be gone), and that’s the so-called “collapse” of the wavefunction.

      So we could still talk about there being one true state of the universe, but every time we make a measurement, we destroy part of that state and the information contained in that part, because we collapse the superposition. But at this point we start getting into the question of what quantum mechanics really means, and that’s a hard-fought question with no clear good answer at this point, and this derail of mine is already pointless and confusing enough without getting into all that… 😀

      • daenyx says

        Not pointless, probably useful to someone. 😉 I understand quantum superposition about as well as a non-physicist typically can, though I couldn’t have explained it that well. At any rate, my point about there being multiple states didn’t assume those states could be simultaneously observed. I suppose it’s thoroughly up for argument whether the the observational collapsing behavior should constitute a single or multiple simultaneous states, since superimposed states that you collapse by observing is about as useful as a description of multiplicity in this context as the question of whether or not we (humans) are fundamentally capable of accessing absolute state information – not very.

      • says

        daenyx, my point is that the system *isn’t* in multiple states. It is in *one* state, but there are different ways that one can decompose that one state in terms of observations, and the particular unknown state that happens to exist right now might not (probably doesn’t) line up nicely with a single observation that we know how to make.

        If we go back to my sin(x) + cos(x) example, if I measure whether the system is a sine or a cosine, I’ll force the system to choose to be one or the other (with 50/50 probability) and lose all information on whichever one it doesn’t choose. However, if I happen to decide instead that I’d like to measure whether it’s (sin(x) + cos(x)) or (sin(x) – cos(x)), then, since the system exactly matches the first thing, I won’t mess up the state by making this measurement. Instead I’ll just find out that it’s in state sin(x) + cos(x) and the system will be unaffected by the measurement. Or I could choose an even crazier way to measure it — I could ask whether it’s 1 or x or x^2 or x^3 or …, in which case the relative probability of each of those outcomes would be based on the coefficients of the Taylor series for sine and cosine (because the Taylor series for a function is just that function represented as a polynomial). Once the measurement is made, if the outcome is that the system is x^10, the new state of the system will be x^10.

        Because of this, ultimately the true total quantum mechanical state of any existing single system is unmeasureable, as the state is automatically projected onto our measurement axes when we do the measurement, and there’s no way to ensure in advance that our measurement axes will happen to line up with the “true” state and so leave it unperturbed. The only way we can gain evidence that the concept of “true states” has any meaning at all is to prepare a bunch of quantum mechanical systems in an identical way, make identical measurements on them, and look at the distribution of results. This will retroactively tell us what true state results from that particular preparation process. And the only way we can know the exact quantum mechanical state of any particular system is to prepare the system in some desired state in advance. If we don’t know the process that was used to prepare the particular system we have in our hands, we can’t know what it’s state is, all we can do is project its state onto some desired set of measurement axes, after which we’ll know that we’ve pushed it into the state that corresponds to our measurement outcome.

        So quantum mechanics really does mess with our notions of “truth” pretty hard.

  3. smrnda says

    I really think that the whole notion of ‘idealized forms’ or whatever not only does a lot of damage, but also tends to make people think in terms of serving ends that are abstractions rather than things ends that are attainable and real. The more concrete you stay, the less room you have to go wrong since you stay more grounded in reality.

    I’ll give an example – our understanding of mental illness is far from perfect, but a lot of psychiatrists and ordinary lay people clung to defective and unfalsifiable psychoanalytic theories simply because they sounded like great explanations even when they rarely did any good in practice. In fact, you run into people who seem nostalgic for when mental illness ‘meant’ something, as if they lament that they can just take a med to avoid symptoms without the symptoms fitting into some grander narrative.

    Plus, the abstractions, as you pointed out, are simplified so they often fail to explain reality, or offer explanations that are too simplistic to be useful. It’s like when preachers say that the problem is “sin” and the solution is “God” – as if human motivations weren’t a whole lot more complicated than that.

  4. Larry Clapp says

    > truth is consistent with itself … there is ultimately only one truth

    This seems to equivocate on “truth”. As near as I can tell, In the first case you use it in the sense of “a set of observations about reality”, and thus two different sets of measurements should be consistent. In the second case, you seem to be using it as some reified thing about which you can meaningfully speak on its own, and I just don’t see that.

    Maybe all you’re saying is that reality is consistent with itself, and ultimately there’s only one reality. But in that case I have no idea what you’d mean by “of which all lesser truths are merely aspects”

    • Deacon Duncan says

      That’s a good point. I think it would be better for me to say that there is only one truth, of which all the lesser things we perceive as individual truths are merely aspects (though that’s evolving into a pretty awkward sentence). I like to treat “truth” and “reality” as interchangeable terms, because any “truth” that fails to conform to objective reality isn’t really true (an untrue truth?), and thus by definition they ought to be interchangeable. And yet there is a sense in which the term “truth” has a strong subjective component that reflects our imperfect and potentially incorrect perception of self-consistent reality, so perhaps there’s a useful distinction to make there. Objective reality is the standard against which our subjective truth must be measured, in order to assess the quality and value of our subjective perception.

  5. EdW says

    It’s a fascinating thought, and I’ve been thinking along the same lines with regards to all of mathematics and physics – Even something as simple as 1 + 1 = 2 is only a rough abstraction. 1 apple + 1 apple = 2 apples, but by what standard do you measure one apple? Surely one has greater mass, a different color, different chemical content, etc. Applied to observational science and physics, this means all the constants and equations we use are ultimately estimations at real-world phenomena. Very useful estimates, and extremely accurate for our purposes, but they aren’t and can’t be perfect themselves.

  6. Charles Sullivan says

    @EdW: No empirical estimates or measurements are geometrically perfect. But we know this by comparing them against the idea of geometrical perfection, e,g. perfect circle, sphere, triangle, etc. Otherwise, how would we know they’re imperfect?

    • Deacon Duncan says

      What is it that constitutes imperfection, though? It might be simpler to define a sphere in terms of a set of 3-dimensional points at a fixed distance from a common center, but any real object is going to have a more complex shape than can be represented in such trivial terms. In that sense, our measurements are imperfect precisely because they approach the simplicity of the “ideal” and “perfect” mathematical models, because simplicity is obtained by deviating from the actual truth about the thing we’re trying to measure. The term “perfect” implies some sort of theoretical maximum in quality, but in fact the closer our measurements get to this alleged “ideal,” the farther we’re getting from a truly accurate measurement.

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