The four truths of the principle of contradiction

The Maverick Philosopher responds to this scientific experiment, which someone advanced as an empirical refutation of the principle of contradiction:

A team of scientists has succeeded in putting an object large enough to be visible to the naked eye into a mixed quantum state of moving and not moving.

Andrew Cleland at the University of California, Santa Barbara, and his team cooled a tiny metal paddle until it reached its quantum mechanical “ground state”– the lowest-energy state permitted by quantum mechanics. They then used the weird rules of quantum mechanics to simultaneously set the paddle moving while leaving it standing still.

Most of what I’m going to say about this overlaps with what MP says. (I won’t expand on his thought that journalists writing about science should be read cum grano salis, though it is important to keep in mind whenever one reads claims about what QM teaches us about reality.  Guys need to get grants and feed their kinds, and you don’t sell books with modest claims. This sort of PR stuff goes way back- Galileo was an underappreciated master of it)

St. Thomas usually explains the principle of contradiction as the inability to simultaneously affirm and deny. Note that this is principally a truth that we verify within ourselves. It is principally a statement about how we think. We attain truth by a judgment that consists, minimally, in affirming or denying some form of a subject; and the repugnance of affirmation and denial of the same thing to one subject is the principle of contradiction. Thus, the POC is a consequence of our knowing with a subject. But what is it to know with a subject? A subject is clearly imperfectly known, since it requires that we add something to it in thought. The first things we know are not truths, still less are they “beliefs” (justified or otherwise) they are subjects that we must add to in thought- even when these additions express identities on the side of the thing. It is the fundamental imperfection of our thought that makes the POC necessary to us. We know by gathering together a multitude of diverse thoughts that each perfect an imperfectly known subject. In the measure that the first thing known is perfect the POC becomes less and less necessary. The divine Word in no way requires an addition in thought in order to perfect some initial subject-thought. The angels have something only analogous to the POC (they do not add to an imperfect thought discursively, but they do have a multitude of thoughts), but this analogous principle is less important the higher the angel gets, since, as his starting point becomes more perfect, he has less need for a multitude of concepts.

On the one hand, the experiment is a clear case of an affirmation, sc. “a quantum state can be induced in larger scale objects”. The whole point of the experiment is to cease being indifferent to affirming or denying this, and to come down definitively on one side or another. In the face of this experiment, it’s not only that we can’t affirm and deny simultaneously (whatever that would mean) but it is unreasonable to do so. When you see the terms “quantum state” and “inducible in large-scale objects”, you’re supposed to affirm the latter of the former, and never deny it. Another unremarkable use of the POC.

But there is also a clear difficulty in what we do when we encounter the terms “paddle” and “in motion”. Apparently, we are supposed to affirm and deny the latter of the former.  Here it’s important to notice the exact character of a denial that is contrary to an affirmation. It is true that something is either moving or not. “Not-moving”, however, can be taken in more than one way: a bolted-down anvil, God, the intellect, and last Tuesday are all not moving, but the “not” does not signify exactly the same thing in each case. The bolted down anvil doesn’t move in the sense that it is at rest; God does not move because he utterly transcends the difference between motion or rest; and last Tuesday fails to meet a minimum requirement for either being at rest or being in motion (so does “the present King of France”). Whenever we use the principle of contradiction, therefore, we have at least four possibilities! For any proposition SP, we can be absolutely certain that if SP is false, S~P is true: but it can be true in three ways: . ~P must be analyzed into:

1.)   ~P simply speaking,

2.) ~P because transcends P and ~P,

3.) ~P because it fails to meet a minimum condition for being P or ~P.

(2 and 3 are different ways in which something can fail to be P simply speaking or simpliciter–  and in this sense they fall after a prior logical division.  I divide them up here into two options because the distinction between the simpliciter and secundum quid is less well known to us contemporary persons.)

The principle of contradiction founds our means of knowing, and is therefore proportioned and therefore limited to certain objects. At the same time, our mind is open to being as such, and so it has no limitation in what it knows. The elegant solution to this paradox is the principle of contradiction. In order to use it correctly, however, we have to recognize that our openness to all being (which is still somehow limited) requires that a negation can be understood in three ways. The quantum paddle is therefore not moving, but because it fails to meet some minimum condition to be in motion or rest. It is not the first entity to do so: What Aristotle understood by the term “matter” was neither in motion simply speaking nor at rest simply speaking- since it failed to meet a minimum requirement for either. Motion itself was neither a being nor a non-being simpliciter- for it failed to meet a minimal requirement of what exists simply speaking.

Again, our language and thought is attuned to a particular bandwidth of reality, even while it is open to all being. As a result, we have things in our bandwidth that we can name with simple names and understand by direct concepts, but we can also use these things to speak of what exceeds the reality of our bandwidth, and that which falls short of it. Here is the crucial aid that QM can give to us: it shows us new ways in which our bandwidth is limited. It seems that it is not merely bodies that we are proportioned to understanding, but bodies in “normal” environments. The word “normal”, of course, is perfectly obscure and perhaps not that helpful, but we know at least that there will be some times when we will encounter bodies that, under certain conditions, will fail to fall within the bandwidth of things we understand well. We will have to understand them by negation. If some one asks “is the paddle moving? ” The correct answer is no. The yes claim is false. BUT to say that the paddle is “not moving” does not mean we are saying it is at rest.

Three Platonisms

Joseph Pieper summarized Plato marvelously saying “he [Plato] cared less about making a system than in not leaving anything out”. This is clearest when we look to what he says about the ontologically first principle. His dialogues present us with at least three different accounts of what is ontologically first, and until one sees understands all these accounts, it is impossible to fully appreciate the philosophy which developed from Plato. Which is all of it.

The most familiar Platonic answer to the question of the first being is the Platonic form. X is a participation in X itself, and this latter is “the form”. There are at least three reasons why this doctrine is the most well-known:

1.) It is advanced in Plato’s most well-known dialogues: The Republic, Phaedo, Meno, Timaeus, Symposium. These are the best “beginner” dialogues in the Platonic corpus, and so it’s easy to think that this is all that Plato thought about the first principle.

2.) The doctrine of the forms was the Platonic doctrine most heavily critiqued by Aristotle. For those who learned their Plato from Aristotle- which was everyone from the fall of the Academy to the Renaissance- this was their dominant view of Plato.

3.) Plato himself is clearest about the forms. We know why he posited them, he makes the character of Socrates argue for them (except in Timaeus), and his arguments are clear and direct. 

Nevertheless, it’s clear that Plato was aware of the difficulties in positing the forms, and in his later work he makes a very clear attempt to move away from them. The later Platonists (Proclus  Plotinus, Pseudo-Dionysius, etc.) place greater emphasis on another doctrine of Plato, which he speaks of most extensively in The Parmenides: the doctrine of The One. Proclus, in fact, claims that the fullest expression of Plato’s theology is in Parmenides. The Platonic forms- which are heavily critiqued at the beginning of Parmenides- are clearly many, and so could only be themselves participations in The One. The One is thus clearly prior to them. But once we make the forms participations in another, it becomes very difficult to give a reason for them to exist; and at any rate they cannot be ontologically first so long as we allow for the existence of The One.

The most interesting answer that Plato gave to the question of what is ontologically first came at the very end of his last dialogue: The Laws. Hidden away in the tenth book, the Athenian stranger argues that the state must be theist, and he proves this theism by arguing- rather extensively- that nature is moved by another that moves itself, and all that moves itself is soul. Here soul considered precisely as the self mobile is set up as that which is prior to all natural beings. Notice that this is the fist time when any Platonic first principle acts. On what appears to be Plato’s first account of action, forms can’t act- this would be contrary to their very nature, since the form is only introduced to explain motion. The One appears to be in a middle state: we suspect that it must be able to act, since it’s a God of one kind or another, but Plato is not clear as to what exactly its action would consist in, or how he would reconcile an acting first principle with the objections that he leveled against change when he articulated his doctrine of forms.

And so Plato progresses from forms, to The One, to soul. Aristotle, of course, got to see this progression first hand- he might have well been in the room when Plato was writing. One cannot fully understand Aristotle’s doctrine of act and potency without seeing that act is a single concept forged from these three Platonic answers. Form, the one opposed to the many, and soul are all energia and entelekia for Aristotle. Aristotle takes the analogously common element in Plato’s three answers and then says that it is at the ontological basis of everything. All being is a procession or participation in what is just act, or pure act (it took a great deal of theory to show how this could be the case, but it’s to Aristotle’s eternal credit that he was the only one to figure it out- most likely because he was the only one who got to see the difficulties in Plato’s system up close.). If one makes the first principle anything less general than act, then it will collapse into contradiction. One will be able to explain why things are many (by Forms or The One), or why they act (by soul), but not both.

If chance exists…

God alone can cause a concrete effect to occur by a chance cause (or “by chance”). We can do this in an abstract sense: we can choose that someone will win the lottery we set up or that we will have some child (who is to be conceived by a random seed among billions) but the divine power can will that this person win the lottery by chance or that this child arise from the random seed that is to generate him. The effect of chance fall outside of the agents that happen to act towards them, but it does not fall outside of being as such, since chance exists. The per se cause of being is thus the per se cause of chance, even so far as it lacks a necessary (or even probable) relation to the result that arises from it. This one reason why, as St. Thomas says, chance is a sort of divine thing, since if chance exists it is truly random and causeless (as a chance cause) even while God alone causes the relation from the chance cause to its effect (as existent).

On denying the antecedent in design arguments

The design argument is if design, then a designer. “Design” can mean more than one thing (and it is perhaps not the best word). Sometimes, it means the beauty one finds in nature; other times it means some complicated sense of biological “information”; but for St. Thomas it means intended action (where the end plays  a role in causing the process that leads to it) as opposed to chance (where it does not).  So St. Thomas’s consequence is if natural action is intended rather than chance, there is a mind ruling it. Such a mind certainly deserves to be called divine in some way or another.

But what about the times when we deny the antecedent? What if we consider natural action so far as it is by chance, or if we find some reason to argue that natural action is fundamentally by chance? This is a separate argument, since no conclusion follows from denying the antecedent. But if we consider the kind of designer that one is speaking about in a theist argument (even if we make no claim about whether there is such a being) it is by no means clear whether such a being is not prior to chance events in nature too. Since the designer we speak about in design arguments is prior to nature (the ID crowd doesn’t get this, and it’s a grave problem) he is prior to chance in nature as well. Even if we couldn’t  confirm the existence of something prior to nature by appealing to a design argument, the very possibility of something intelligence prior to nature allows for the possibility that there is some intelligence prior to chance in nature.

Necessary consequences of tristitia

In treating of the sins against charity, St. Thomas eventually treats of sloth, which is contrary to charity by being contrary to the first necessary effect of charity: joy. He says:

As Aristotle says in the Eighth book of the Ethics, no one can remain very long in sorrow (tristitia) without enjoyment. Two things must arise from sorrow: that man shun the sorrowful and that he go to something that gives him joy, just as those who cannot rejoice in spiritual enjoyments go to carnal ones

ut philosophus dicit, in VIII Ethic., nullus diu absque delectatione potest manere cum tristitia, necesse est quod ex tristitia aliquid dupliciter oriatur, uno modo, ut homo recedat a contristantibus; alio modo, ut ad alia transeat in quibus delectatur, sicut illi qui non possunt gaudere in spiritualibus delectationibus transferunt se ad corporales

Note how matter-of-factly St. Thomas speaks: two things must arise… just as those who cannot rejoice…

The Latin tristitia is broader than the English sorrow. St. Thomas speaks of rust being the tristitia of iron- it is the state of being run down and corrupted. In human beings it is depression and other like feelings.

No human mood is ever continuous, but some predominate. And if we don’t enjoy spiritual things we will just seek happiness in physical ones. St. Thomas speaks of enjoyment-seeking as pretty much automatic.

Kant’s ethics held up unpleasant action as the ideal of virtue. Those who forever “toughed it out” or followed sheer rational duty without enjoyment were most ideal. Isn’t there some plausibility to this? Virtue seems above all manifest in difficult and unpleasant circumstances, so why not think that continuous perfect virtue would be continuous unpleasant circumstances? St. Thomas appears to think such virtue is not only not ideal, but that it is simply impossible. The man who lived that way- taking no spiritual joy- would, in short order, be wallowing in purely physical pleasures.

Hypothesis and demonstration

All inquiry begins with questioning, but this is not the same thing as beginning with a hypothesis, though both speak to an initial indetermination of the intellect. The hypothesis is one tool to answer questions, the demonstration the other. The difference is whether the argument itself starts with a premise taken as determined to one side of a contradiction, as happens in demonstration. The premise deserves to be taken in this way under a pretty strict set of guidelines that are difficult  to meet, but not impossible.

The distinction between demonstration and hypothesis is in one sense relative: there is no impediment to using a hypothesis to establish a premise that eventually meets the criterion for a demonstrative premise, and then using it to demonstrate from. In another sense, there is an absolute distinction between the two, so far as, absolutely speaking, we either start with something known demonstratively, or not.

3 / 17 / 10

It might help to divide the academic problem of evil from the experiential problem of evil. They are as different as the problem of dividing up the meanings of depression for the DSM and the problem of actually being depressed. The first seeks to judge the matter by argument; the second seeks to judge by a certain experience. The first finds arguments exiting and appropriate; the second finds arguments inappropriate, pointless, hollow, and extremely irritating. Neither way of considering the problem is ever totally separate from the other- and so we will always speak about the problem even while we know- to a greater or lesser extent- that we aren’t totally looking for an answer in speech.

Two notes on Pascal, pt. I

Pascal had a mystical experience that changed his life, and the first words he wrote to describe it (or remind himself of it) were “the God of Abraham, Isaac, and Jacob, and not the God of the philosophers and the learned”. Lamentably, the distinction has become a slogan, and I’ve seen it quoted many times in a way that would have horrified Pascal. How did he understand the distinction? Two notes:

– The distinction has overtones of Gospel language: “I give you thanks Father, for what you have hidden from the learned and the clever you have revealed to merest children”

-Pascal never doubted that the philosophers came to the truth about God and human beings, but he did not believe that any one of two contrary philosophies had gotten even a general view of the whole. Whether one considered the skeptics vs. those more optimistic about knowledge (Pascal calls them “dogmatists”. English as no word for them.) or the atheists vs. theists, or those who say man is the marvel of the universe vs. those wo say he is insignificant; all sides had parts of the truth, but neither side could finally refute the other, and  the nature of this stalemate was not taken as evidence for the truth of skepticism, or agnosticism, or obscurantism about human dignity. Pascal’s answer is more radical – a human being is the sort of thing that must give rise to such conflicted and opposing accounts. Pascal would speak of a human being as “a deposed king”. There is no simple answer to whether such a being is dignified or wretched, capable of commanding or not, having any authority or not, etc. The philosophers have divided off into opposing camps since they could not see that the very subject they studied was the root of opposition.

Pascal claims that only Christianity has taught the truth about human beings. philosophy, too dedicated to consistency and setting up schools, shunned the truth about human beings and was unable to account for their fundamental inconsistency, paradoxical relationship to knowledge, etc. Pascal’s account of theistic proofs is illustrative: we learn them, are convinced, and then half an hour later wonder whether we made a mistake. The process repeats itself in various ways, with more or less time of spent in knowing or in crisis.  So do we know them or not? Is this evidence for skepticism or its opposite?

Verifications- UPDATED

What is confirmed or verified by sensation is natural, and so supernatural causes are not confirmed or verified by sensation. So long as we stare out the window of what sensation confirms and verifies, we will not and cannot see anything divine.

There is no doubt about verification by sense, and so if we do not explicitly divide two sorts of verification, and require verification for science (or even knowledge), then there is no science or knowledge other than physical science. Even “philosophy” will ultimately reduce to a kind of physical science.

The difficulties with limiting confirmation to sense are well-known (people have been trying to do this since Kant, and all attempts have passed away) but this is not to say that we have accepted that confirmation apart from sense is possible, still less how we can articulate such a thing. St. Thoma saw such confirmations as the proofs for the existence of. Natural science does not need a proof for the existence of in the strict sense-  though it proves that things exist (black holes, black swans) it only does so definitively by manifesting something to sensation, either of itself or through some proxy. In a PFTEO, a possibility is definitively and perfectly reduced to act through a proof, in natural science, such perfect and definitive reduction is only by sight. Recall Einstein reserving his judgment on Relativity until he saw the light of the star bend around an eclipsed sun.

Why is a PFTEO possible? Because it is appropriate to some subjects! It is, briefly, the best way for a being that knows through sense to know certain objects. The sensible is verified by sense; the metaphysical in another way. But the latter proofs make no sense if they are judged by the standards of physical science- they establish nothing more than (perhaps) possibilities. Like all verifications, they depend on simply seeing. If we had evolved no power to taste (not hard to imagine) then we could never verify that acids were bitter- and we could only wonder why other animals winced at them. There are enough impediments to seeing metaphysical objects to effectively render whole populations unable to verify them. Such populations read at St. Thomas and wonder what madness he is suffering from (must be some sort of religious quirk that is making him say these things…)

(Mathematics verifies existence in a third way, sc. by construction within imagination. But this does not conclude to a subsistent thing, and so it is not a “challenge” to natural science by positing a new kind of existing cause.)

St. Thomas on the historical or literal sense

St. Thomas sees the literal sense of scripture as synonymous with the historical sense, but he as a much different sense of what counts as literal and historical than we do. The literal sense of something in Genesis can be explained by the Book of Revelation; the literal sense of something in the book of Exodus (I am who am) can be explained by concepts first taught by Avicenna. St. Thomas knew full well that the Moses did not write in response to the Book of Revelation; and he knew that he could not have studied Arabic metaphysics, but his sense of what literal and historical meant in scriptural interpretation allowed St. Thomas to interpret as he did.

« Older entries Newer entries »