Maverick Philosopher

Footnotes to Plato from the foothills of the Superstition Mountains

More on the Law of Non-Contradiction and its Putative Empirical Refutability

A reader's e-mail with my comments in blue:

Nice post on the LNC. That topic is a real quagmire, isn't it?

I’ve lost the link to the Science Daily report of the Cleland experiment, so the details of how he confirmed the superposition are lost to me, but I’m really struck by the fact that you are defending LNC as a transcendental, not transcendent, principle. Kant doesn’t take this route in the First Critique, does he? LNC is not some form of sensibility, is it?

 

That's right, I am defending LNC as a transcendental, not a transcendent principle, and for two reasons.  First, I believe that LNC is well-nigh unassailable if presented as a transcendental a priori condition of  the possibility of (i) meaningful discourse and (ii) experience of the objects of Sellar's manifest image or of Kant's phenomenal world, with (i) being more unassailable than (ii).   Second, the transcendental defense  is all I need to turn aside what I take to be your conclusion from the Cleland experiment, namely, that there are macro-objects of direct perceptual acquaintance that serve as counterexamples to LNC.  To show that LNC applies beyond our thought and beyond our experience to whatever lies beyond our thought and experience, if anything,  is not so easy.  One cannot just dogmatically assume that a law of thought is automatically a law of reality, especially since this has been denied by any number of philosophers.  Aristotle in Metaphysics Gamma, 3, 4, attempts a proof by retortion of LNC, but as far as I can see, all he establishes is that LNC is a necessary condition of meaningful thinking and speaking, not that its validity extends beyond thought and speech and their objects to things in themselves.

 

I would also urge in passing against certain dogmatic Thomists that the Critical Problem — the problem of showing how a priori conditions of thinking apply to things external to us — is already present in nuce in Aristotle.  But that's another long series of posts.

LNC is surely not a form of sensibility for Kant, but it is a form of understanding.  Since there is for Kant no experience (Erfahrung) without a 'marriage' of sensibility (Sinnlichkeit) and understanding (Verstand), it seems reasonable to impute to Kant the view that no macro-object of experience can violate LNC.

One thing I think Cleland would say is that observing the paddle in the normal sense, i.e, bombarding it with lots of photons, disturbs the superposition and collapses the ambivalent quantum state into a moving or a not moving state. So he would seem to agree with you as far “seeing” in the ordinary sense goes. We don’t see something moving & not moving—and one could add: our eyes and brains are just not designed to experience such objects even if we could do so without disturbing them. But, seeing is  not the same as sensing, and presumably the paddle in its quantum state has effects (on us) that are unambiguously different from its effects in states where the superposition has collapsed. So, as you say, no naked eye observations of superposition, but perhaps that’s too narrow a focus and we should admit that we might experience a superposition is some other unique way.

 

You seem to be assuming the Copenhagen interpretation of QM.  But as you know, it is not the only game in town.  Bill Hill, a U.K. immunologist, e-mailed me the following, which is very helpful:

 

There are two main interpretations of quantum mechanics which are popular in the physics community (there are a few others, but they are mostly propounded by eccentrics).  The first is the "Copenhagen" interpretation, in which quantum events really do exist in multiple incompatible states at the same time, but only when there is no outside observer looking at them.  I am not making this up, though I should add that by "observer", they do not just mean conscious beings but any information-carrying system (such as a sensor) which can report data about the quantum event.  Though it is implausible at first glance, this interpretation does in fact solve the boundary problem that so vexes many scientists.  Because sub-atomic particles are too small for us to see, they are free to exhibit this behaviour.  But people, planets and so on are so large that they are always under observation in some sense, they cannot behave in this way.  Hence, when the little bit of metal in the article is observed, it will either appear moving or not moving to the person looking at it, but when nobody is looking it is in fact doing both.  This raises enormous questions about perception and causality, and many people are very unhappy with it as a result.  The important point is that your suggestion that there cannot be an empirical counterexample to the Law of Non-Contradiction remains intact under the Copenhagen interpretation.
 
The most popular alternative to Copenhagen is the "Many-Worlds" interpretation, in which the universe splits into two duplicates every time a quantum event occurs.  So when the little bit of metal in the article is put into its quantum state, in one universe it is moving, and in the other it is not.  Of course, it is impossible for us to tell which one we are in.  Many people (rightly, in my opinion) think that this is just silly, and embrace Copenhagen on grounds of parsimony.  However, it is consistent with the data, and also with the Law of Non-Contradiction, since two incompatible states cannot exist in the same universe under Many-Worlds.
 
So as far as I can tell from my limited experience, you are correct and neither the Copenhagen nor the Many-Worlds interpretations of quantum mechanics offer an empirical counterexample to the Law of Non-Contradiction, whatever other fascinating philosophical questions they may raise in their own right.

 

 

The salient point is that, on the 'many worlds' interpretation of QM there is no violation of LNC not even  on the micro-level let alone on the macro-level.  Given that there is no one settled interpretation of QM accepted by all physicists, the case against LNC at either level is bound to be weak.

 

This is very tricky stuff, but I think it is the paddle, a macro object that we can directly observe under other conditions, that is now in the superposition state of moving and not moving. We in fact have put it into this state. The paddle is not some ding an sich, but an ordinary object that can transition from existing “normally” in one state or its opposite to existing at once in both contradictory states. In principle any macro-object could be reduced to such a quantum ground state but we just can’t physically do so.

 

I am afraid that you are not making sense.  You have already granted that the paddle that we see with the naked eye cannot be seen by the naked eye to be both moving and not moving,  But now you are saying that that very visible paddle — and not some invisible micro-constituents of it – has been put by the experimental apparatus into a state in which it is  both moving and not moving.  This implies that one and the same visible paddle is both (moving & not moving) and not (moving & not moving).  Which is is higher -order contradiction.

 

Are you saying that there are two paddles?  Then they can't both be visible.

 

Furthermore, if you say, as you do above, following the Copenhagen interpretation, that observation of the paddle forces it into  one state or the other, then cannot also say that that very same visible paddle is in both states.

 

I am afraid  that the science  journalist's report on the Cleland experiment has delivered us into a realm of rank gibberish.

 

Your second point that LNC is also a “form of intelligibilty” is surely right, and it just invites incomprehension to say that the paddle is both moving and not moving. I guess we need to learn the jargon of the physicists here. I’m not sure exactly what they say but something like the paddle in its quantum ground state is in a superposition of motion and no motion.  That I get, and it says something remarkable about the really weird universe we apparently live in. I’m saving up my money and moving to a good old Newtonian universe at the first opportunity!

 

But now you are sounding like certain Trinitarian theologians who say that we should just repeat the creedal formulae without worrying whether or how they make any bloody sense.  It is curious that defenders of the coherence of the Trinity often bring up QM.  You of course grant no authority to the Bible or the Church.  Why then do you genuflect before the authority of scientists when they spout gibberish?  I am being intentionally provocative.  ComBox is open if you care to counterrespond.

Posted

in

,

by

Bill Vallicella

Tags:

Comments

11 responses to “More on the Law of Non-Contradiction and its Putative Empirical Refutability”

  1. William Avatar
    William

    A question: given that LNC has something to do with the meaning of the word ‘not’, what actually is the meaning of this word? For example, if it means ‘certainly’ then
    Snow is white and it is *not* the case that snow is white
    is ‘certainly’ true! But it certainly does not mean ‘certainly’. What does it mean then? I’m asking because we sometimes explain the meaning of words by giving examples of true and sentences which contain the word. Perhaps we could explain the meaning of ‘not’ by saying that
    p and not-p
    is never true? Just a thought.

    Reply
  2. William Avatar
    William

    That should read “by giving examples of true and *false* sentences which contain the word.

    Reply
  3. Joseph A. Avatar
    Joseph A.

    I just wanted to chime in and mention how nice it was to read the following:
    “Why then do you genuflect before the authority of scientists when they spout gibberish?”
    That is a sentiment not uttered or written often enough.
    One thing I’m curious of, if Bill (Valicella, not Hill) is willing to reply: You said that you recognize reality may in fact not conform to our logic, but at the same time rational discourse requires (if you wouldn’t put it this way, let me know) that certain ground rules, like the LNC, are true. Does that mean you’re saying that, if the LNC doesn’t hold, we can’t know this or will never know this (barring perhaps something like divine revelation)?

    Reply
  4. Bill Vallicella Avatar
    Bill Vallicella

    William,
    You ask what the meaning of ‘not’ is. And you seem to be suggesting that ‘not’ can be explained in terms of ‘never.’ But ‘never’ means ‘not at any time’ or ‘not ever’ so we move in a circle if we try to define ‘not’ in terms of ‘never.’
    Some notions are so basic that they cannot be defined in other, more basic, terms. But although we cannot provide a synonym or an analysis, we can show how to use ‘not.’ If proposition p is true, then not-p is false, and if p is false, then not-p is true. So if there are just two truth values, we can explain ‘not’ in this way.
    You are right that LNC and ‘not’ are closely connected: a proposition p and its negation (not p) cannot both be true.

    Reply
  5. Bill Vallicella Avatar
    Bill Vallicella

    Note that ‘not’ cannot be define din tewrms of ‘ralse’ since in a 2-valued logic, ‘false’ just means ‘not true’ — and so we move in a circle.
    ‘Not,’ if it denotes anything, denotes an operator on propositions, a negation operator. But ‘not’ can also function as a universal quantifier. Reflect on the ambiguity of ‘All men are not rich.’ That could mean: ‘not(all men are rich)’ or ‘No men are rich.’

    Reply
  6. William Avatar
    William

    >>But ‘never’ means ‘not at any time’ or ‘not ever’ so we move in a circle if we try to define ‘not’ in terms of ‘never.’
    Good point. Perhaps we could start with excluded middle. Whatever we put in the placeholder ‘p’, (it is the case that) p or not-p . Not asserting any fundamental truth, rather just explaining a rule of use. A further rule of use is that not-not-p = p. Apply the negation operator twice, and you are back to the original proposition. From this we get LNC, as follows.
    1. p or not- p (excluded middle)
    2. not (not-p and not-not-p) (1, De Morgan)
    3. p = not-not-p (meaning of double negation)
    4. not(not-p and p) (2, 3, substitution)
    Perhaps there is still a problem with ‘always’, or of ‘following a rule. Does this involve some prior concept of negation? If something is always the case, you have to grasp there are *no* exceptions.

    Reply
  7. William Avatar
    William

    On your second point ‘if p, then not-p is false’. I think this is fundamentally the same thing. Assuming ‘p is false’ means the same as ‘not p’, this gives ‘if p, then not-not-p’. This in turn means the same as ‘not (p and not-not-not-p)’, using an appropriate definition of ‘if… then’. Assuming double negation (p = not-not-p), this gives ‘not(p and not-p)’ which is LNC again.
    This takes us some way from quantum mechanics, though if it is correct that these fundamental principles are merely semantic laws, it follows that these explanations of quantum mechanics are flawed in some way: they would indicate a fundamental misunderstanding of *syncategoremata*.
    Conversely, and using the valid principle of modus tollens (negatio antecedentis sequitur ad negationem consequentis) if the quantum mechanics are not flawed, it would follow that these fundamental principles are not merely semantic laws.

    Reply
  8. Bill Vallicella Avatar
    Bill Vallicella

    William,
    I just realized who you are, our old friend ‘ocham.’ You really love to cover your tracks lest the U.K. thought police come after you for heterodox opinions in logic.
    Your derivation (1)-(4) is correct, but I am not sure what you are after. What was traditionally called the Three Laws of Thought are interdefinable. For example:
    1. p = p (Law of Identity. Read ‘=’ as triple bar.)
    2. (p –> p)& (p –> p) From 1 by defn of material equivalence.
    3. p –> p From 2 by Simplification
    4. ~p v p From 3 by defn of mat’l implication
    5. p v ~p (LEM) From 4 by Commutation

    Reply
  9. William Avatar
    William

    Yes it is I, Ocham. How did you guess? I was merely using my first name (which is the same as yours).
    Are you sure they are interdefinable. E.g. intuitionist logic holds that p implies not-not-p, but not conversely, and so accepts the LNC, but not LEM. That was why I mentioned double-negation.
    In my adherence to classical logic I am certainly not heterodox!
    I have some news for you Bil, is your email still good?

    Reply
  10. Bill Vallicella Avatar
    Bill Vallicella

    I identified you from your e-mail address which is included in an e-mail I receive from Typepad whenever a comment is left at this site. I am also informed of the IP # of the computer the commenter is using. This allows me to block undesirables. Yes, my e-mail is still good.
    I was joking about your ‘heterodox opinions.’ You are right about intuitionism.
    Does ‘p is false’ means the same as ‘not p’? That’s not clear to me for the same reason that it is not clear to me that ‘p is true’ means the same as ‘p.’ I do grant, though, that the truth predicate adds nothing to the sense of ‘p.’ But it does seem to put that sense into relation to something external to it. You will recall Frege’s claim that declarative sentences have both Sinn and Bedeutung, the latter being either the True or the False — whatever the hell they are! But I know what he is getting at: the truth predicate is redundant in one way, but not in another.
    There are a host of tricky questions here. I am still not sure what your concern is, or your thesis, if you have one.

    Reply
  11. William Avatar
    William

    I must go now. I was merely wondering how we could derive the laws from basic semantic principles.
    On ‘p is false’, as you know I subscribe to a form of the redundancy theory of truth, which we have argued about before.
    I will email you. I am thinking about giving up lens-grinding for a time, and take a sabbatical for philosophical purposes. On the other hand, I am not sure I could stand it.

    Reply

Leave a Reply

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