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# The Logical Law of Non-Contradiction?

Is it the case that proposition "x" must either be "p" or "-P"?

Do you believe this for only SOME propositions?  If so, how can this assertion be a basic law of logic?

Do you believe this for ALL propositions?  If so, wouldn't just one example of a proposition that is both true and false prove the case is only true for SOME propositions?  Thus, if the example is shown, how can the assertion be a basic law of logic?

I'm hoping for your opinion and some serious, light-hearted discussion on the matter.

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### Replies to This Discussion

Marc, you're throwing the baby out with the bathwater here. You are missing the possibility that the declarative statement in question is not sufficiently complete to allow a true or false determination at all. Surely any system of logic requires that we are completely clear on definitions. Otherwise we sink into a semantic morass.

The only way that "The cup on my desk is at rest" is both true and false at the same time is if the interpretation where the statement is true refers to a different scenario than the interpretation where the statement is false. You're just squeezing one end of a balloon so your problem bulges out on the other end. The more correct conclusion is to go back at your declarative statement to figure out what's ambiguous about it and resolve that before proceeding to a true/false determination.

More to the point, I fail to see what you hope to accomplish by weakening the distinction between true and false. Don't we already have enough trouble with that? My passing understanding of even Fuzzy Logic is that it attempts to assign a truth value somewhere between true and false, but still never true and false simultaneously. A fuzzy logic truth value of 0.5 would imply something like "partially true and partially false", rather than "simultaneously true and false". Partially true and partially false can certainly apply to very complex or multifaceted truth claims, as in a court case when trying to assign liability amongst several parties, but I strongly suspect that any such claims can be broken down into their component parts and analyzed using strict boolean logic (or perhaps Bayesian probability), time and effort permitting.

In any case, your particular example is clearly a case of imprecise definitions; properly defined, there is no contradiction inherent in the statement. Different frames of reference produce different truth values, but not simultaneously. Don't confuse the fact that both truth claims use the same English words in the same order with the idea that both meanings are the same. They are not. This is like saying "Chris is a man" is both true and false when there are two different people named Chris in the room. You don't have a simultaneously true and false declarative statement. You have (at least) two separate declarative statements masquerading as one. Suggesting that this calls for a radical new approach to logic (that would seem to throw out a key underpinning of logic itself) is missing the point at best, and a dangerous idea to an easily confused species at worst. The proper response is not to imprison George Boole in Schrodinger's catbox, but rather to ask, "What do you mean? An African or European swallow?"

This is a fabulous response to my inquiry !!!  It is well written and straight to the point.  I am not being fascetious when I say... Wow !!!

Yes.  I understand the caution which should be taken on this because it is, as you say, "a radical new approach to logic."  This is why I had already decided today to put a halt on posting out here on this topic and do my own personal writing on the subject.  Of course, when I got here I found your post.

This is because you are correct that "Surely any system of logic requires that we are completely clear on definitions."  In order for me to make the argument, I MUST be sure to clearly define each step in the process.  And it is clear to me, this is going to be a large project beyond the scope for what these Forums were designed.  (LOL  There's been too many posts I have seen that were so large and written so awkwardly that I simply said "Whew, I don't have time to read all of it and respond.")

So, I'm not conceding my position.  I have already identified several questions I will need to clear up.  Not least of all are several you and others have pointed out.  One that's been bothering me all day is:  "Marc, isn't (P and -P) simply just a subset of the excluded middle conclusion of (-P);  therefore it still falls within the (P or -P) strict classification?"  But I am currently writing up how this would not be the case.  Unfortunately, your second and third paragraphs are exactly what I claim is being done with the current excluded middle perspective because of the inherent tautology.  Furthermore, it is becoming clearer and clearer to me that my viewpoint is not "weakening the distinction between true and false."  It is not the traditional Fuzzy Logic which  "attempts to assign a truth value somewhere between true and false..."  I'm actually making allowances for additional classifications (conclusions) to be attributed to propositions rather than falling back into the excluded middle positions of other Informal Logic systems.  Clearly outlining this approach should both strengthen the distinctions between the true conclusions and the false ones, as well as, avoid having George Boole spend any time in the box with the cat.

But since this whole topic is clearly becoming a horde of words, I will actually concede that you have the favorite position.  I will keep working on it though.  Your responses (as well as everyone else's) have been PRICELESS !!!  Thank you

Marc, I'm glad you liked my post, and that you took it in the spirit intended. If you want to pursue this, I strongly suggest that your first step be to clearly understand what problem it is that you are trying to solve. What do you hope to accomplish by allowing logical contradictions to be logically valid? Seems to me that this will only serve to allow us to somehow feel good about ambiguity, rather than resolving ambiguity thru more rigorous investigation and analysis. Before you invest a lot of time in this, you should be quite sure that you're not simply enabling intellectual laziness. The traditional approach of disambiguation is quite powerful, if rather tedious. I am fairly sure it is actually indispensable, and that the shortcut you suggest (if I really understand what you are after) will only lead to more confusion, rather than more understanding.
And don't get me wrong. I like ambiguity. I think humor would be impossible without it. But clear understanding demands disambiguation.

LOL.  Yes, I think I would prefer a world full of comedians rather than a world full of zealots.

I'm breaking my promise not to post on this topic.  But you have such reasonable responses, I simply cannot resist.

I have a confession to make.  For me, this topic falls within the sociological and psychological realms more than the strict scientific.  You asked me to clearly understand the problem I am trying to solve and what I hope to accomplish by allowing logical contradictions to be logically valid.  To be sure, I admire your astuteness.

I think we would both agree, there is no shortage in supply of the intellectual lazers.  The history of humans seems to overwhelming show: it is far too easy for individuals to leave off pursuing the difficult tasks involved in a rigorous investigation, in exchange, for a quick (no matter how irrational or ultimately unprovable) ideation.  Ambiguities and perceived contradictions are observed.  A person in the community poses some Truth in answer, then the majority of the rest go with it because their daily life (especially in times of hardship) is more focused on trying to survive.

I have heard many hardliners insist, if everyone would simply use his or her mental capabilities, the perceived contradictions and ambiguities will come to light.  As you've stated, it is a rather tedious task.  And as much as I would love for that to happen, I wonder how effective it is in continuing to insist.

Am I enabling the intellectual lazers by promoting logical contradictions as logically valid?  My answer is: No more and no less than we already allow by only offering a (T or F) conclusion on the front end for those individuals who refuse to pursue the necessary rigorous investigations (not to mention the T or F conclusions made as mistakes along the way).  It's far too easy, with only (T or F), to grab onto some inspirational speech.  And, once one has made his or her stand, it's even more difficult to abdicate especially with only the complete opposite to adorn.

It would also be fair to ask if there is any added value in allowing for logical contradictions on the front end?  I would say yes.  It's a more practical educative methodology.  I would prefer leaving those who would only take Basic 101 with a lifelong fundamentality of a recognized, accepted category for logical contradictions rather than ONLY a foundation of either true or false.

Of course, you are correct.  The traditional approach of resolving ambiguities is quite tedious.  And it is quite powerful.  Intellectual lions, such as yourself, will continue to pursue it.  My proposal does not deny the classifications of truths and falsehoods.  Moreover, aside from being a bit annoying, my proposal does not weaken the proper method of scientific approach.  Ambiguities will be moved from the "and" classifications to the (T or F) by those willing to further investigate.

And again, you are correct. (How does this keep happening???) It does offer a comfortable, safe, acceptable place for lazers to put their perceived contradictons without the imposed pressure of having to classify absolutely.  If he or she is not going to pursue the rigorous investigative tasks anyway; yes, I'd rather they feel good about ambiguities rather than mis-categorize a falsehood as truth on the front end.

My question to you is:  Are we in the business of conversion?  Because, I'd be satisfied living in a world where people don't endanger my life with Holy Wars.

Hmm. Intellectual lion cub, perhaps.

Marc, is it black-and-white thinking that you are trying to ameliorate? I agree that black-and-white thinking is too limiting for most real-world topics, and teasing apart every black and white pixel in the gray-scale around us is generally not possible (at least not quickly enough to deal with the things we must in life), but you seem to be saying you want people to hold contradictions as simultaneously true and false, rather than see that many answers lie between. For those issues that truly lie on a continuum (or a very finely graded set of discrete steps), excluding the middle (insisting on a false dichotomy) is a mistake, and a classical logical fallacy. But when you have an actual dichotomy, I think you have to just say that true and false (along with unknown) are the only possible answers. Some things really are just boolean, and many things that don't appear to be boolean can be fairly quickly decomposed into just a few boolean choices.

As usual, you are right on target.

No, it is not black-and-white thinking I am suggesting should be more tolerated.  I am right there with you at the distaste involving someone's illogical conclusions being made 'concrete' based on irrational and non-logical precepts.  I do abhor the incredible waste-of-time others impose upon us (and we at times impose upon ourselves) with questions and improper investigations at the heart of which are fallacious.  I assure you.  I understand how much my position appears to be making the claim you suggest.

It is no easy task for me to stand behind my own proposal.  The pragmatic part of me screams "Why can't people just do a little study, use their own brains, and witness with what nonsense ideas like gods are?"  I get it.

But the utilitarian, the soli, and the fallibilist parts of me ask "What's the least I would actually accept (what's the most I could reasonably expect) as a change from those who've become hard-wired into unreasonable mindsets?"

It is at this point where it appears we diverge.  The absolute atheists (Christopher Hitchens comes to mind) practice a methodology which has the same effect as fighting fire with gasoline.  What kind of practical sense does it make to affect another's irrational, religious psychology by devastating their codified mental processes with ONLY the other option - false?  Of course they are going to hold on tightly to what has become comfortable.  The absolute atheists are asking them, in effect, to mentally up-end their whole life.  It's as if we all wouldn't be a lot better off with a world full of agnostics.

So, do I disagree with your correct classification concerning the logical proof of the existence of gods?  No.  That is perfectly fine with me.

However, do I disagree with your choice of educative methodology?  Yes.  This is why I stand by the reasonable conclusion that the cup is both in motion and at rest at the same time.  It really is ok for us to live with categories of (T and F) and (-T and -F) as legitimate logical classifications.  Furthermore, it is perfectly fine for we Ivory Soapers (99%'s, Non-Theists, agnostics, etc.) to live with these logical contradictions.  It helps us provide a more homeopathic treatment when dealing with, i'm confident we all agree is, the majority illogical mindset.

All I ask is to please remember:  At least on the particular topics of gods, the (-T and -F)'s do often rest on their laurels as an ally with (-T).  But even if they don't.  At least they're using their brain enough, attempting to do even the tiniest bit of the rigorous work required, not to be mentally hard-coded in the dangerous category of (T).

OK, so if I understand you Marc, your goal is not to introduce the possibility of (simultaneously true and false) into formal logic, but rather to use it as a rhetorical tactic in discussions with theists to avoid hitting them over the head with their incorrect conclusion about the existence of their god(s), yes?

It's all well and good to take a softer line with people, though in my experience, those who insist that their god(s) exist(s) aren't susceptible to a soft sell either. Now if you mean that we should find common ground with theists and work together with them toward the common good (reducing poverty, expanding opportunity, fighting crime, educating people, etc, etc) while agreeing to disagree (or at least to not talk much) about metaphysics, then sure. Plenty of theists are decent people who are interested in the same practical things I am.

But if you mean we should give a winking acceptance to the theist proposition during debate, sort of suggesting that their point of view is somehow valid, then no, I can't go along with that. That smacks of postmodernism/relativism, which is a self-negating philosophy (if all viewpoints are equally valid, then so is the one that says all viewpoints are not equally valid). Worse, it seems rather condescending. "Well sure, god is real for you, because you're special." I might say something like that while backing away slowly, but I wouldn't say that if I wanted to engage in serious debate with a theist.

And anyway, if we hope to deconvert people, I think we owe them our best reasoning, however blunt. Most deconverts (like me) lost their belief in god thru the death of a thousand cuts, usually over a decade or two. The first barrage is not likely to be effective, because the psychological defenses are up. But eventually the little bits of nonsense inherent in theism start to wear you down. "Well the Noah's Ark story is obviously a complete fairy tale, and evolution makes a lot of sense, and the earth is clearly way older than 6,000 years, and there's this whole Big Bang thing that would seem to obviate any need for a deist creator, and anyway there's this infinite regress problem with that, and there are a ton of mythical figures predating Jesus that have awfully similar stories, and Mary was a virgin who got pregnant from an angel instead of just making shit up because she got knocked up by some villager? Really?" At some point, if you're paying attention at all, the whole house of cards just collapses under its own weight. For those who lack the intellect to grasp the totality of the nonsense, no amount of persuasion is going to knock them back to reality, kind, blunt, or otherwise. We might as well be up front and honest, because then if we don't convince them, at least we were up front and honest, which is more than you can say about a lot of theist apologists.

Well put.
Jason, the reply button is missing on your last post... but it's just as well I put it here anyway.

You have described my position very well concerning the rhetorical tactic of using (true and false) with religious hardliners (maybe even hardliners on other topics as well). The soft sell (it seems we both agree) could be the more appropriate in some situations. I, like you, have come through the process of de-conversion which has taken decades. And, after discussing this issue with you, I would not be risking too much by stating you obviously portray the character quite capable of discerning which individual would respond best to what type of approach - recognizing your own ethical firmness, of soundness in logical proof, could actually prove dysfunctional toward the greater good. And yes, a more formal debate might require a stricter stance.

So, I must further confess... I am still having quite a bit of trouble wrapping my brain around the original question I offered on this thread. I know I am asking for this discussion to regress. For that, I do apologize. However, we have so quickly jumped forward to what could be more functional, educative motives; I am not fully capable of desisting from (T and F) as a practical category of logic.

I do hope I have proven thus far that I do not wish to follow the path philosophers can tend - constant objection over any responses and endless rhetoric. I would very much like to be on the same page with you as well as everyone else about contradictions.

So, before I can appropriately respond concerning your claim of my relativistic perspective, I hope you can cut right to the chase for me over the following:

Investigation #1

You and I are standing over a leaf.

You say, "The leaf is burning."
I say, "The leaf is freezing."

Upon further investigation we find that the leaf is in fact on fire.

The proposition "The leaf is burning." is true.
The proposition "The leaf is freezing." is false.

By the self-effacing identity of the leaf and the cumulative and associative nature of the propositions concerning the prepositions, it is logical to conclude that this event does not produce a contradiction. Observations will continue to produce conclusions that objects do not both burn and freeze at the same time. [Furthermore, there is no need to add anything to this investigation - like relative perspective. No matter who, or what perspective is taken, it will continue to be observed that objects will not both burn and freeze at the same time.]

Investigation #2

You are standing over a cup on a table in your backyard. I am on the moon with a telescope which allows me to see the cup.

You say, "The cup is at rest."
I say, The cup is in motion."

Upon further investigation we find something strange.

The proposition "The cup is at rest." is true.
The proposition "The cup is in motion." is also true.

By the self-effacing identity of the cup and the cumulative and associative nature of the propositions concerning the prepositions; it is logical to conclude that this event does in fact produce a contradiction. Observations will continue to produce conclusions that objects on the Earth will both remain at rest and be in motion at the same time. [Again, there is no need to add anything to this investigation - like relative perspective. No matter who, or what perspective is taken, it will continue to be observed that objects do both move and remain at rest at the same time.]

Marc, the cup is only apparently both at rest and in motion at the same time. Appearances can be deceiving. There is no actual contradiction upon further investigation, and it's simply laziness that precludes further investigation in this scenario. It isn't even a particularly complex scenario. Change it to a person sitting next to a cup on a moving train. Nobody would think that is a contradiction; they would simply agree that whether the cup is in motion or at rest depends on the perspective of the observer. Many, many things do, and that's no reason to throw up your hands and embrace apparent contradictions that aren't even slightly mysterious or complicated.

If you want to mollycoddle muddled thinkers by affirming that their falsehoods are actually some baffling kind of correctness, that just seems guaranteed to perpetuate confusion, and is in any case condescending. I think it's impolite to talk religion or politics in certain situations, but if I am actually debating religion or politics with somebody who wants to engage me on them, I don't see the point in beating around the bush. I definitely don't see the point in indulging somebody's logical deficits (or outright fantasies) just to make them feel better. Logical flaws need to be pointed out; it's much too easy to persist in bogus conclusions if nobody ever mentions the holes in your logic. It's not necessary to be cruel, but pretending that we can have it both ways when we can't is just evasion for the sake of getting along. That rarely works in the long run, and is discourteous to begin with.

Though I would love to, I couldn't possibly state anything any better than this. ^^^

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