Can Someone Deny the Principle of Non-Contradiction?
Traditionally it has been understood that the principle of non-contradiction (i.e. that something cannot both be and not be under the same aspect; positively stated: that A is A, and not not-A) cannot be demonstrated directly but only defended indirectly by showing the consequences of its denial are impossible – that is, by deploying a reductio. The PNC, in other words, is a first principle of thought and that from which everything else flows.
However, metaphysicians contend the PNC is not just a principle of thought but a principle of being – it is, as it were, a rule of thinking and of existence — that follows upon notions of unity/identity and restrictedness/boundary. For example, once being has a set of boundaries (either intrinsic or extrinsic) to distinguish itself from some other being, such boundaries necessarily exclude or “block out” the possibility of having another set of boundaries in the same aspect. For example, to have the boundary of a square is just not to have the boundary of a circle. And notice it matters not where those boundaries inhere, whether in our mind, a block of wood, a piece of paper, etc.
In other words, to be is to be in some way. Thus, to assert a contradiction is to say that something is not what it is, and that is a denial of being. Thus, to the extent something exists it is logical.
All of which is to say the PNC is not just a logical principle but an ontological principle which means that just as no proposition can be both true and false in the same aspect neither can any being both be what it is (have this set of boundaries) and not be what it is (not have this set of boundaries) in the same aspect.
Naturally, for theists, who think God both is subsistent truth and subsistent being itself – and completely boundary-less (= God is causally compatible with all possible realities; see my argument in How to Think About God) given absolute divine simplicity – there is a nice fittingness between logic and God, given that 1) logic has a thought like structure inasmuch as the laws of logic are truths about truth (intentionality, as they say, is the mark of the mental; and if God is truth, then there you go) and 2) are necessary and eternal. Indeed, this is why many theistic philosophers argue logic is somehow housed in the nature of God if not analogically identical to God. (for accounts of this, see Greg Welty’s contribution here and Ed Feser’s Augustinian proof here). Logic is the structure of Gods thought and God as classical theists maintain is identical to thought – an unrestricted thought thinking itself.
Back, however, to our point about people who deny the PNC.
Again, the PNC is often defended by pointing out how any attempt to deny it must assume it and that denials of the PNC are self-refuting. Statements can be self-refuting when their very utterance undermines what is being asserted; for example, “there is no absolute truth.” The problem is well known: If that statement is true, there is at least one absolute truth which means the assertion is false. Otherwise, it is false.
Regarding the PNC all attempts at denial (to be denial) must assume language has a definite meaning (namely, we mean what we mean and not its opposite), which can only be the case if the PNC is true, otherwise we could not know that what we mean is not its opposite. Without the PNC, the possibility of language having definition is obliterated and everything becomes meaningless. Thus, any explicit denial of the PNC is an implicit affirmation. If somebody claims to deny the PNC they affirm it, otherwise their statement is meaningless in which case there is no denial. What is more, even to say, “I don’t know if the PNC is true,” assumes a definite meaning and once again affirms the PNC. The most somebody can do is remain silent but even then their silence is an implicit affirmation – an action in response to understanding a definite meaning.
So, there really is no coherent way to deny the PNC which is why vanishingly few professional philosophers – that is, people of strange variety who are prone to deny pretty much anything – try to deny it. Of course, that doesn’t mean people haven’t tried.
Because, as we know, various paradoxes are occasionally brought up to challenge the PNC.
Famously, “This statement is false.”
(Allegedly) if the statement is true, then it must be false, which then appears we have something that is both false and true at the same time, which means a counterexample to the PNC has been discovered, which proponents of PNC claim is impossible. Alternatively, if we say that “this statement is false” is false, then it must be true, and the problem reasserts itself.
The most popular solution to the Liar’s Paradox (as it is commonly known) is to suggest there is some linguistic sleight of hand happening: that we do not have a true contradiction but a trick of language.
For example, “this statement” is ambiguous as to whether it is referring to something else or itself. If referring to something else, then what is it? Otherwise, if it is referring to itself, there is nothing to evaluate; and no real truth claim is being made. Either way, because the statement does not tell us, there is nothing to evaluate as being true or false. Hence, the paradox is revealed to be a linguistic error, and the claim of there being a “true contradiction” is avoided.
There are, of course, other interpretations of the Liar’s Paradox but I would suggest they all run afoul of the same error at the end of the day. There are other proposed solutions to the paradox, as well. We need not get into those now. The point is this. That such paradoxes can be resolved should give confidence that further paradoxes can be resolved even if their resolution is different.
However, we should also remember this. Paradoxes are cases where we don’t see how something fits together or is resolved; contradictions are cases where we see something does not fit together. It should be obvious then that just raising paradoxes (or eyebrows) about the PNC casts no more doubt on the PNC than raising puzzles about the PSR (principle of sufficient reason) casts doubt about the PSR – what critics must do instead is show how anybody could coherently deny either; a project which cannot be done.
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