Can We Escape the Law of Non-Contradiction?

A while back, I met with a local pastor to talk about apologetics—the defense of the Christian faith. During our friendly discussion, we got on to the subject of the nature of truth, at which time I made a case for the correspondence theory of truth.

This particular pastor subscribed to a postmodern view of truth—that there is no objective truth and that truth is a social construction based on linguistic practices.

While making my case, I referred to the laws of logic, and specifically, to the law of non-contradiction. The pastor immediately denied the law of non-contradiction. I was completely taken aback and could not believe what I was hearing. It was bad enough that I had to argue for truth, but now I found myself arguing for something as foundational as the laws of logic.

For those who don't know, the law of non-contradiction states that A and not-A (where A is a proposition) cannot both be true at the same time and in the same sense. For example, my car cannot be parked in my driveway and not parked in my driveway at the same time and in the same sense. This just seems so obviously true, and yet this notion was being rejected.

This pastor was convinced that the law of non-contradiction is just a Western convention. Furthermore, he indicated to me that he believes that Western “Either-Or” logic is too arrogant, dogmatic, and exclusive. He prefers to use the Eastern “Both-And” system of logic. Fortunately for me, this conversation that I found myself in was beginning to sound a lot like a story I heard Ravi Zacharias tell during one of his keynote addresses. You can listen to the story in the video below. (If you're in a rush, you can start listening at the 2:25 minute mark.)

During my conversation with this pastor, I asked the very same question that Dr. Ravi Zacharias asked the American philosophy professor in his story. I asked, “Are you saying that it’s either the Eastern ‘Both-And’ system or nothing else?” He didn't catch it the first time, and simply responded, “Yes!” The question was worth repeating, but this time I put emphasis on two significant words.

I asked, “Are you saying that it’s either the Eastern ‘Both-And’ system or nothing else?” That's when you could see the light bulb go on. A simple smile let me know that he got it!

The “Either-Or” logic is impossible to avoid. Ironically, this person needed the law of non-contradiction to try to prove the “Both-And” system. The very fact that he disagreed with me communicated that he really did believe in the law of non-contradiction. The law of non-contradiction isn’t just a Western convention. In fact, it’s not a convention at all. The laws of logic aren’t invented; they’re discovered. They are facts about reality—the way the world really is.

There’s no doubt in my mind that this challenge would have caught me off guard if it wasn't for this video by Dr. Zacharias. This short YouTube clip changed everything. Don't ever underestimate the power of a 10-minute YouTube video or a podcast. You just never know when God is going to use what you’ve learned for his glory!

Comments

[RonH]

The Convention of Non-Contradiction.

It (still) seems to me there's not much too this.

If I say "A", what do I mean?

By the convention in use here, "A" stands for any 'statement' at all.

And what is a statement?

By definition (convention), a statement is an utterance* that has either the 'true' property (whatever that may be) or the 'false' property, but not both.

So by convention alone A stands for any statement at all except not-A.

We all know we don't need the universe's cooperation to make our 'statements' either true or false but not both.

We're going to use statements means were going to assume the lnc for some of our utterances.

There's your lnc. There is no need to argue to the lnc from there.

The lnc just another way of talking about statements being true or false but not both.

We find 'statements' useful and we have more than one way of describing what they are.

This is a sufficient explanation of the lnc.

If you think, in addition, that there's a 'law' out there somehow preventing A and not-A from happening at the same time you are welcome to give some evidence.

*Utterance, not sentence, to express the idea that the sentence "It's raining" can be true where I am but not where you are while my present, local, utterance of the sentence is either true or false and not both.

[Tom Deeke]

This is of of my favorite Ravi stories. As I was reading your article, it immediately came to mind. Thank you for sharing.

[scbrownlhrm]

".......Can you imagine how ridiculed religious people would be if, in order to maintain our view, we had to renounce logic and probability theory? Finally, the tack taken by these thinkers is ultimately counter-productive for them and helpful to theists, for it just is to admit that theism is more logical and more probable than atheism...."

Read more: http://www.reasonablefaith.org/atheistic-physicists-repudiation-of-logic-and-probability-theory#ixzz3qCc2gbU6

In other news, quarks are volitional and self-aware.

[scbrownlhrm]

The problem of presuppositional confrontations, which is by Vincent Cheung, ties in here, in part indirectly and in part directly. It begins with “the preconditioning of meaning” and then moves into the suppression of truth on page 8 of an 83 page PDF, and, then, it subsequently moves on into the wider arena of presuppositional confrontations. A few pages in:

“Paul says that this is what humankind has done with their knowledge about God. He states that some knowledge about God is innate, so that every person is born with some knowledge about God, but because man is sinful, he refuses to acknowledge and worship this true God, and thus suppresses and distorts this innate knowledge..... People often complain that there is insufficient evidence about God and Christianity, but the Bible says that they already know about this true God, only that they are suppressing this knowledge because they refuse to acknowledge or worship him. Knowledge about God is "evident within them," because he "made it evident to them." The problem is not a lack of evidence, but an artificially manufactured set of presuppositions that suppresses their knowledge about God. Some think that this passage provides justification for empirical arguments that lead to a knowledge of God. However, we have established by our illustrations and by biblical examples that observation can provide no intelligible meaning or information. Therefore, the passage cannot mean that an observation of creation can provide knowledge about God; rather, certain ideas about God are already resident in the mind apart from any experience or observation.”

Of equal utility on these fronts is the Stanford Encyclopedia of Philosophy on the problem of induction and also on the problem of perception.

[scbrownlhrm]

In other news, the convention, the *As-If* of ought, the convention, the *As-If* of intention, the convention, the *As-If* of volitional love, the convention, the *As-If* of aboutness, the convention, the *As-If* of mind, the convention, the *As-If* of logic, the convention, the *As-If* of the non-eliminative, the paradigmatically irreducible.

None of it is actual.

-Tis but a reverberation......

-Tis but Neitzchei's Deicide Dance whereby the Non-Theist hopes to assert his vacuous "Argument Against God" from what he claims is the "Problem of the Hiddenness Of God" whereby he hopes to at once annhilate the all pervasiveness of the Divine's contours while yet retaining the Necessary.

Such is the madness of the dance.

[RonH]

Focus scbrownlhrm,

I said

If you think, in addition [to explanation for the LNC I give above], that there's a 'law' out there somehow preventing A and not-A from happening at the same time you are welcome to give some evidence.

[scbrownlhrm]

RonH,

No one is interested in your straw man of conjuring up fake laws and insolvent chains of IOU'S.

The interest is, rather, in reality.

[Sam Harper]

That pastor sounds like one of my philosophy teachers in college. I'm always floored when I run into somebody who says those kinds of things out loud and seems, by body language and everything, to actually believe it.

[NWC]

Dear RonH,
I'm commenting here on your first comment. Here are some things worth thinking about:

1) Tim Barnett was not talking about "sentences" but "propositions." A proposition is a non-linguistic entity that can be had by many sentences at the same time. The same* proposition expressed in the English sentence "Snow is white" can be expressed simultaneously in German, French, Latin, etc. it can also, arguably, be instantiated in non-linguistic thought. This is important for Barnett's argument: it's not sentences or utterances that bear truth or falsity, but propositions.

2) As Barnett clued us in, he was arguing for the correspondence theory of truth. On this theory "truth" (and "falsity")--on the most common construal--are not properties but relations. A relation like "beside of" or "on top of" or "the brother of" require two things to be instantiated, not one. For example, a desk cannot be "beside" nothing; rather, there must be another object in relation to which it bears the beside-of-relation. On this account, a proposition cannot itself have the property of being true by itself anymore than a desk can be beside nothing. Rather, propositions are true in so far as they bear a certain relationship to reality, the correspondence-relation. Here, a proposition is true if a proposition exists, and at some time tn that proposition stands in the correspondence-relation to reality or some subset thereof (i.e., a fact). Truth is a relation--a matching or isomorphism relation. And such entities cannot be had by solitary objects.

3) I agree with you that there is no "law" of non-contradiction. The locution "law of non-contradiction", while in common usage and used, I think, with colloquial intent by Barnett, seems to commit one to some sort of "laws of thought" view: they are tools of the mind used by it in thinking and only mysteriously map on to reality. Taking this a step further we get an almost Kantian view:they are only laws of thought and don't necessarily map on to reality. A more ancient and persuasive view is held by Aristotle (and the host of those who follow him well into the modern era) in Metaphysics G: non-contradiction is not a law of thought; it is a fact about existence or being itself. Reality is structured such that contradictions are impossible; thought merely maps on to that structure. Call it a "law" if you like,although this seems to misleadingly suggest that it is a product of will or Will. It is indeed inviolable though as a baseline fact about existence itself (even God's existence), and thus about all existence. If this is one's view and is what one discovers about reality by both conceiving of it and experiencing it, it would seem that one is well within their epistemic rights to assert it. The burden, it would seem, is on those who deny that reality just is such as one reasons and experiences it to be.

Best to you, RonH.
NWC

[RonH]

NWC,

Tim Barnett was not talking about "sentences" but "propositions."

And I am too. I used the words 'statement' and 'utterance', but I'm just fine with 'proposition' too. And all that I said still applies.

2) You can see that our notions of proposition and truth value are just the same thing as the LNC without any theory of truth. It is irrelevant what truth is here.

3)

I agree with you that there is no "law" of non-contradiction.

and then

Reality is structured such that contradictions are impossible

Hm. You seem to contradict yourself - as I understand you.

As for the second one regarding the structure of reality: Try, for your own edification if for no other reason, to generate some evidence for this.

[scbrownlhrm]

Try, for your own edification if for no other reason, to generate evidence that you both exist and do not exist.

The price of no-god may be..... at some ontological seam somewhere..... the price of gaining freedom from one's own mind.

[RonH]

Try, for your own edification if for no other reason, to generate evidence that you both exist and do not exist.

Why? Did I make such a claim?

[scbrownlhrm]

A) "Reality is structured such that contradictions are impossible."

B) Try to generate evidence for "A".

C) I exist. I don't exist.

D) "C" has the appearance of a contradiction, and hence seemed a valid candidate for "B".

"A" could be wrong. Or right. Hence B. B, hence C.

That's all. No one said you claimed anything. Is doing what you asked a claim of a claim?

Really?

[WisdomLover]

Tim Barnett was not talking about "sentences" but "propositions."

And I am too. I used the words 'statement' and 'utterance', but I'm just fine with 'proposition' too. And all that I said still applies.

Actualy Ron, no, you aren't fine with that.

The reason you aren't fine with that is that your argument is based on the idea that the Law of Contradiction is based on a linguistic convention.

If you take the non-linguistic turn suggested, you are not going to be able to talk about linguistic conventions anymore. You are going to need to talk about the reasons such conventions are adopted in the first place.

Why did we adopt the convention for "is true", "is false" and "and" such that "P is true and P is false" is always false? The reasons weren't arbitrary and they weren't, themselves, conventions.

[RonH]

Nice. Very nicely put down. Thanks.

"C" has the appearance of a contradiction

Of course C is a contradiction!

(It's also something I never said and therefore needn't defend.)

C is a contradiction because 'I exist' is a proposition which means (whatever else it may mean) that the other proposition, 'I don't exist', is false.

That's enough for me.

It works every time.

But you say there's something more.

So tell me about the the LNC and the 'structure of reality'.

[WisdomLover]

C is a contradiction because 'I exist' is a proposition which means (whatever else it may mean) that the other proposition, 'I don't exist', is false.

Why does "I exist" have this meaning? Because you chose that convention? We are not free to adopt just any convention we like. Why is that?

[RonH]

WL,

Of course I'm fine with 'proposition'.

I never mentioned 'linguistic' convention.

And I certainly never said anything that tied me to English as opposed to German as NWC thought.

We've defined 'statements'.

It's a language independent term.

A statement, or proposition, has exactly one of two possible 'truth values': true or false.

Every time someone utters the proposition 'A' we know, independent of the structure of realty and independent of any theory of truth that he means to say 'Not not-A'.

If you think, in addition, that there's a 'law' out there somehow preventing A and not-A from happening at the same time you are welcome to give some evidence.

[WisdomLover]

The only kind of convention operative here is a linguistic convention. You didn't need to say "linguistic convention" because there is no other kind.

When we say that X is true by (linguistic) convention, we mean that we have a firm determination to use words such that X is true.

What on earth do we have a firm determination to use to make the meaning. X, correspond to reality? Either that meaning does or it doesn't correspond to reality and our firm determination to use anything be damned.

And, BTW, I've already given incontrovertible evidence for the law...We are simply not free to adopt any convention we like.

[RonH]

Hey, if there's no other kind of convention, then I guess it's a linguistic convention.

:)

We are simply not free to adopt any convention we like.

Sure we are.

[scbrownlhrm]

"Sure we are".

So by convention, I don't exist can in fact mean I do exist, assuming we agree that No equates to Yes. And so on.

I can live with that, only, first you'll have to define the "evidence" that I in fact don't exist, and, then, you'll have to define the "evidence" that I in fact do exist, and, then, you'll have to explain how both sets of observational evidence fail to contradict.

Etc.....

I feel a yawn coming on.... standard shuffling of conflations, equivocations, and all thaaaawwwwnnnn.... Hmmm sorry.... epistemic items are commonlyyyyyywwwwwwnnnnn..... hmmmm. There it is again.... Sorry...

[WisdomLover]

We are simply not free to adopt any convention we like.

Sure we are.

So glad you agree with me.

[scbrownlhrm]

RonH,

I just noticed you asked for a law.

Again.

We've already told you that we're not interested in your straw man of conjuring up fake laws and insolvent chains of IOU's.

The interest, rather, is reality.

[RonH]

So glad you agree with me.

Go ahead.

Explain why you said that.

[Brad B]

Well, nothing new, the world according to RonH with no grounding, just appeal to popular use as a form of best practices for successful navigation through life so long as it doesn't include the thought of God. Oh, and by the way, that last part italicized makes the whole effort depart from reality.

The Christian worldview however, has no epistemic problems accounting for the universal laws of logic that exist and hold fast apart from what men think about them or how they attempt to explain them.

Gen 1 In the beginning, God created the heavens and the earth

Psalm 33:6 By the word of the LORD the heavens were made, and by the breath of His mouth, all their host.

John 1 1 In the beginning was the Word, and the Word was with God, and the Word was God. 2 He was in the beginning with God. 3 All things came into being through Him, and apart from Him nothing came into being that has come into being. 4 In Him was life, and the life was the Light of men. 5 The Light shines in the darkness, and the darkness did not comprehend it. 6 There came a man sent from God, whose name was John. 7 He came as a witness, to testify about the Light, so that all might believe through him. 8 He was not the Light, but he came to testify about the Light. 9 There was the true Light which, coming into the world, enlightens every man. 10 He was in the world, and the world was made through Him, and the world did not know Him.

1 Cor 8:6 yet for us there is but one God, the Father, from whom are all things and we exist for Him; and one Lord, Jesus Christ, by whom are all things, and we exist through Him.

Col. 1:16 For by Him all things were created, both in the heavens and on earth, visible and invisible, whether thrones or dominions or rulers or authorities--all things have been created through Him and for Him.

Heb 1:2 in these last days has spoken to us in His Son, whom He appointed heir of all things, through Whom also He made the world.

[WisdomLover]

So glad you agree with me.

Go ahead. Explain why you said that.

Because, adopting whatever linguistic conventions strike my fancy, it was so clear to me that you agree with everything I said.

[scbrownlhrm]

Do we, in fact, know things? EA or Epistemic Anxiety is part one, seeming to hint at a part two:

A genealogy in philosophy is a dangerous undertaking. The historical roads are long, winding and overlapping, often doubling back and forth. However, I think a genealogy of epistemology, fraught with danger though it is, can be reasonably established along the following lines.

Epistemic anxiety (EA) tends to be thought of as a fairly modern phenomena, generally emerging with Descartes. This anxiety, possibly more than anything else, defines modern philosophy. How do we know? What do we know? Do we, in fact, know things? This is not, however, a strictly modern attitude. As much as we like to think of epistemic anxiety as a post-cartesian condition, it is quite clearly something that afflicts the ancients.

I think we can establish something that looks like this: EA afflicted the ancients, did not afflict the medievals until the later medieval era, and reemerged with a vengeance by the dawn of the modern era. Consider Plato as a case study in the ancient era.

Plato is interesting in that he combines what we would call metaphysics and epistemology – if we were to divide his theory of knowledge in half, one half would be a modern-esque question of justification – what justifies a person in making a knowledge claim – and the other would be a near-kantian question – what must the world be like given the fact that we do know things? His epistemology is inseparable from his metaphysics, and though a large part of Plato’s writing is spent teasing out the question of justification (Socrates being the star of this particular show), just as much if not more time is spent on the metaphysical aspect of the question of knowledge, where this cashes out to his ‘theory of forms’. Here we have a metaphysical (we might today call it a ‘transcendental’) explanation of knowledge and the possibility of knowledge (taken to task by Aristotle, but that’s another story for another day).

Now, as we move to the medieval era, let us take Aquinas and William of Ockham as case studies in both non-skepticism and the beginning of skepticism.

What appears to happen is that by the medieval era, epistemology is separated from (but grounded in) metaphysics, and becomes wedded to psychology, Aquinas being the key example of this. As Fr. Copleston notes, it is futile to look for, in Aquinas, a proof of the certainty of knowledge or a rebuttal against subjective knowledge on favour of objective knowledge. The problem for Aquinas is how to justify and safeguard metaphysics, as opposed to justification of belief in the external world. Knowledge at this point in philosophical history seems to be simply given. Indeed, there are skeptics of knowledge of God – Scotus and Aquinas both argue that we can, in fact, have knowledge of God – but not skeptics of knowledge by itself. However, towards the end of the Middle Ages, loosely situated around William of Ockham, epistemic skepticism slowly begins taking shape – Gilson traces the twofold nature of this skepticism (epistemic and metaphysical, having to do with Ockham’s empiricism in both epistemology and causality, both of which were, if not entailed then strongly implied, by his nominalism) in ‘The Unity of Philosophical Experience’. Simply put, Gilson locates the error of Ockham in his proto-humean psychologism – that is, the mistaking of the’ description of our ways of knowing with the correct description of reality itself’, (p 71). Gilson argues that a consequence of psychologism is that, ‘Left without objective justification, human knowledge becomes a mere system of useful conventions, whose practical success remains a complete mystery to the minds of the very scientists who made it.’ (p. 72)

The space is thus cleared for the setting of the stage of modern epistemic anxiety – though some hundreds of years in the future, as Gilson astutely notes, once Ockham’s thought took root in the universities of Europe, medieval philosophy was on, ‘the straight road to skepticism’. (p. 72)

[scbrownlhrm]

It may be of some help to look at the nature of truth predicates as well as anti-realism’s relation to truth for a bit of context.

[RonH]

Because, adopting whatever linguistic conventions strike my fancy, it was so clear to me that you agree with everything I said.

[RonH]

That's WL I'm quoting there. It bears repeating.

Because, adopting whatever linguistic conventions strike my fancy, it was so clear to me that you agree with everything I said.

[RonH]

Do you think I agree with everything I said, WL?

[RonH]

Sorry, my last was a typo.

I meant to ask: Do you really think I agree with everything YOU said?

[WisdomLover]

What do you think Ron?

I don't think we really can adopt just any convention we like.

But if we could, then, of course, of course, I would believe that you agree with everything I said. (I also wouldn't believe that.)

[scbrownlhrm]

Quote:

I think your use of logic is in error. The problem is one of referent equivocation, which can be shown by explicitly clarifying which claim(s) you are referring to in your analysis by restating your analysis as follows:

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

“Either I am wrong, right now in making this very claim [that the laws of logic are *not* truth preserving], or you are wrong in your general position [that the laws of logic are truth preserving].”

Let's apply the laws of logic to that previous statement; namely the statement that [“Either I am wrong, right now in making this very claim [that the laws of logic are *not* truth preserving], or you are wrong in your general position [that the laws of logic are truth preserving]”].

By the law of excluded middle, *it*; namely the claim that [“Either I am wrong, right now in making this very claim [that the laws of logic are *not* truth preserving], or you are wrong in your general position [that the laws of logic are truth preserving]”] is *either* true or false.

If it; namely the claim that [“Either I am wrong, right now in making this very claim [that the laws of logic are *not* truth preserving], or you are wrong in your general position [that the laws of logic are truth preserving]]” is true, then there are two possibilities:

1) I was wrong to make the claim [that the laws of logic are *not* truth preserving]. That means it [the claim that the laws of logic are *not* truth preserving] wasn't true, which by hypothesis is false.

Or

2) You are wrong in your general position [that the laws of logic are truth preserving]. This is the only remaining possibility on the "true" hypothesis.

If it; namely the claim that [the laws of logic are *not* truth preserving] is false, the laws of logic imply that my [*DIFFERENT!!*] claim; namely, that [“I am wrong, right now in making this very claim” [that the laws of logic are *not* truth preserving]] was not wrong, which means that it; namely the claim that [“I am wrong, right now in making this very claim” [that the laws of logic are *not* truth preserving]] was true. This is a contradiction, so it is not false.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

*There is no contradiction*. The falsity of your claim [that the laws of logic are *not* truth preserving] is perfectly compatible with the truth of the very different claim that you were [“wrong, right now in making this very claim” [that the laws of logic are *not* truth preserving]]. You have equivocated on your referent with respect to the word “claim” in your analysis. The claim that [“I am wrong, right now in making this very claim” [that the laws of logic are *not* truth preserving]] is indeed true, precisely because the very different claim that [the laws of logic are *not* truth preserving] is false. The former claim is a claim about you and the propriety of making a certain claim, whereas the latter claim is a claim concerning the properties of the laws of logic. Without establishing this contradiction, the rest of your argument collapses.

End quote.

[scbrownlhrm]

There's a difference in the “property of thought” verses the "property of claim-making" verses the "property of logic" verses the “property of the world”. Thought – Word – World – impinge upon the proverbial mapping of reality. Which, of course (if claims of mapping onto and off-of reality is what is in play) is just the particular kind or ontic-category of interfaces we expect. Reality mapping neither annihilates thought, nor word, nor logic nor grants the absurd claim that we can just invent *any* convention such that, say, we can by convention in our reality mapping claim that A both exits and does not exist, or whatever, because we are, well, mapping reality amid the different metaphysical categories of thought, word, and world. Granted, for the Philosophical Naturalist, all three are “nothing but” chemical reactions, that continuous and singular stream of particles which is but one, singular metaphysics, (or whatever) and, hence, there can be *no* factual distinctions in kind/category amid thought, word, and world. "Reality" is (per PN) nothing but that one, singular stream and the fallacy of "emergentism" is nothing more than an appeal to magic – or to self-aware quarks – or to intentional quarks – or to some other sort of magic. Hence Hume's rabbit-randomness and induction's (metaphysically) insolvent chain of (metaphysical) IOU's leave all but the Theist scrambling for lucidity – aborting at some ontological seam somewhere the eyes of logic.

[scbrownlhrm]

Clarification on Quote: Have tried a few times to link the article and com-box from which the earlier QUOTE was taken but neither web addresses nor html links are "taking" here for the moment......

[scbrownlhrm]

An important necessity to grasp here is the key concept of Transposition

Rishmawy adeptly points out that, in fact, it is true – there is that which exists which is the Text, or Voice, or Word that can and does break through the fog. A qualitative difference perhaps (perhaps not), sums to no true difference at all *if* it is the case that whatever it is that we are actually “seeing” (assuming God, and not the fog, is the end of sight) is *not* that which we are seeing through. Perhaps in all our seeing we are in some sense seeing through frail and mutable contingencies and (finally) seeing to the reality itself – there in this or that contour of the Divine. A brief excerpt from the linked essay on transposition:

“…….This error of conflating the two sides of a transposition is rife within reductionist philosophical theorizing. Think, for example, of Hume’s claim that concepts are “nothing but” impressions or mental images, or Berkeley’s claim that physical objects are “nothing but” collections of the perceptions we have of them, or subjectivist theories of value that claim that judgments about what is good or bad are “nothing but” expressions of various sentiments……….. As [C.S.] Lewis notes, however, it isn’t just materialists and other reductionists who are guilty of confusion where transpositions are concerned. Religious believers are prone to it as well to the extent that they collapse the supernatural into the natural…….”

[scbrownlhrm]

Well, still unable to link to the QUOTE from earlier. It's from the com-box of "Red herrings don’t go to heaven either" over at Feser's blog etc.