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Posted by on Aug 7, 2008 in sinner ministries' "proof of the existence of god" | 37 comments

The “missing” foundations of logic

One thought that may be bothering Sye (though who can tell?) is: what makes the laws of logic hold? What explains and accounts for their necessity? What prevents it from ever being the case that a proposition P is both true and false? What makes the law of non-contradiction true?

Ages ago I suggested one possible answer to this type of question: these questions may themselves be confused.

Suppose someone asks “What makes all stallions male? What is this strange force – a super force – that forces the world to be such that nothing is both a stallion and not male?

Clearly, this person is confused. Nothing is required to make it the case that all the stallions are male. rather, “stallion” just means male horse. Understand what “stallion” means and you are immediately in a position to know they will all be male. Indeed, there is nothing to make the case because “non-male stallion” does not describe some state of affairs that the world some conspires to prevent from obtaining. Rather, that combination of words makes no sense, given how “stallion” and “male” are used. So there is nothing to “prevent”.

Now consider this. “and” and “not” are defined in logic by truth tables (which is why I asked if Sye knew about truth tables).

“P and Q” is true if, and only if both P is true and Q is true, and false otherwise. “Not P” is false if P is true, and vice verse.

Given these definitions of “and” and “not”: “Not [P and not-P]” is guaranteed to be true. The law of non-contradiction obtains because of what “and” and “not” mean. To ask, “But what makes it the case that both P and not-P can’t both be true is to misunderstand how “and” and “not” are used in logic.

In short, the question: “What makes it the case that P can’t be both true and false?” is confused, and makes no sense. There’s nothing to “make the case”, because there is nothing to prevent. “P and not-P” does not describe some state of affairs that the world somehow conspires to prevent from occurring. It does not describe anything at all. That combination of words is just ruled out by the rules governing “and” and “not”.

So here, Sye, is another, different, atheist-friendly treatment of your request to “explain” or account for” the laws of logic. There’s actually nothing to account for or explain.

By the way, I am not endorsing this atheist-friendly answer either. Just putting it up for Sye to shoot down. Can he?

37 Comments

  1. Actually, Stephen, I think that’s a very good and cogent reply. Of course, we have to note that the question is ontic, not epistemic – but your answer replies to the ontic question admirably. Here’s two posts on IIDB that deal admirably with and espouse this objection.Here at 9/23/03Here at 9/24/03

  2. I realised today that if the laws of logic were a creation of God then that would strengthen the argument for the God of Eth.Surely a benevolent God woould fix logic so that we could have our cake and eat it?

  3. Actually, on a more serious note, it blows Sye’s whole argument out of the water. The usual “defence” against the problem of evil is that some evil is necessary for us to be fully good, or fully appreciate the good etc. etc.But if it’s God who makes it necessary then God is doing evil. And it’s His logical laws that make us conclude that: we know that God is evil because, assuming He is good, we cannot help conclude that He isn’t.

  4. Very good point, Tony. I hadn’t thought of that consequence of God being the basis of logic.Of course, since God ISN’T the basis of logic its only a problem for presuppositionalists like Sye.But since Sye doesn’t recognize basic facts about logic (like that logical impossibilities are IMPOSSIBLE under any circumstance) he will doubtless be oblivious to the problem no matter how carefully its pointed out.

  5. Stephen,Though I warned everybody about Sye’s strategies and trollism, I do appreciate the time you are investing. Though those who get engaged into the discussions, well, it is not you. You put a proposition, many engage Sye into this endless argumentation stuff. But I do see the educational value. To me it has been great to observe. I have learn much more about Sye’s “flowchart” (I think flowchart is a better description than script, but I do not mind either term), about logic, and many more things.So, out of curiosity. I would like to know if there are books about how these rules have evolved and so on (you know, history, problems, solutions, open questions …). Do you know of any? Have you authored any?G.E.

  6. “One thought that may be bothering Sye (though who can tell?) is: what makes the laws of logic hold?”This really IS a straw man! You know as well as I do that Sye isn’t bothered in the least about this – his “what” is God. Because the contrary is impossible.It really is pointless to go on and on trotting round his mulberry bush. He must be hugely chuffed that he is considered worth so much high-level attention.It’s getting like the Hunting of the Snark. ‘Ware Boojums!

  7. Stephen,I think there’s a slight technical mistake in what you wrote,“P and not-P” does not describe some state of affairs that the world somehow conspires to prevent from occurring. It does not describe anything at allYou seem to be saying that ‘p & ~p’ does not have any content: no situation is described by ‘p & ~p’. But, contradictions do not have null content; according to classical logic, they have maximal content.If you couple the two-valued semantics you mention in your post with a standard definition for logical consequence, then you get explosion. (Namely, S |= p if and only if every valuation which assigns every element of the set S True also assigns p True) That is, from a contradiction, every other proposition follows. This seems to mean that, classically, contradictions do have content: they describe the trivial (yet logically impossible) state of affairs where everything is true.

  8. get_education,I would like to know if there are books about how these rules have evolved and so on (you know, history, problems, solutions, open questions …). Do you know of any?Are you asking whether there are any logic textbooks out there? If so, the answer is definitely! Here’s a couple of suggestions:Mendelson — Introduction to Mathematical LogicBoolos — Computability and LogicHughs & Cresswell — A New Introduction to Modal LogicPriest — An Introduction to Non-Classical LogicBeal & van Fraassen — Possibilities and ParadoxSmullyan — First-Order LogicI’m no expert, but these are the best ones I’ve seen.

  9. Stephen said: ”So here, Sye, is another, different, atheist-friendly treatment of your request to “explain” or account for” the laws of logic. There’s actually nothing to account for or explain.”So, your answer to why are there universal, invariant laws, instead of ‘sound and fury signifying nothing,’ and how do you know it won’t be like that tomorrow is what? ‘There’s nothing to account for or explain???” Alright fine. God exists, there’s nothing to account for or explain. Again, not much of an argument. All you are doing is avoiding the tough questions, by pretending they aren’t there.”By the way, I am not endorsing this atheist-friendly answer either.”Of course not. Why won’t you committ Stephen?Cheers,Sye

  10. Sye,I’m not sure that you follow the trend of Stephen’s argumentation. You’ve made at least two claims:(1) The fact that there are universally valid laws of logic stands in need of explanation.(2) Theism is only way to explain that the fact that there are universally valid laws of logic.If I’ve understood him correctly, all Stephen has done is asked you to justify (1) and (2). Why think that the laws of logic need explanation? Why think that theism is the only possible explanation when there are other equally, if not more, plausible options available? If you can’t answer these questions satisfactorily, then why should anyone buy your proposed proof?

  11. Sye says: “So, your answer to why are there universal, invariant laws, instead of ‘sound and fury signifying nothing,’ and how do you know it won’t be like that tomorrow is what? ‘There’s nothing to account for or explain???” Why do you always answer with a question Sye? Do you have ANYTHING to contribute here except the unfounded assertion that god exists? We’re so tired of hearing your nauseating over commitment to the ignoratio elenchi fallacy and argument of repetition (also a fallacy just in case you didn’t know). Answer a question with an ARGUMENT, not another question! Sye also said “Of course not. Why won’t you committ Stephen?”It’s because Stephen doesn’t want to be like you: so certain in what he thinks he knows, he becomes blinded and “imprisoned in the prejudices derived from common sense…and from convictions which have grown up in his mind without the cooperation or consent of his deliberate reason (Russell).” Professional philosophers find certain arguments more persuasive than others, they aren’t so arrogant to presume they know the truth behind everything as you do. Focus on the counter examples being given to you, and quit attacking the presenter to escape committing YOURSELF to a position. That’s called an ad hominem! -I know it’s difficult to understand, try Google it helps.

  12. Phaedrus said: “We’re so tired of hearing your nauseating over commitment to the ignoratio elenchi fallacy and argument of repetition (also a fallacy just in case you didn’t know).”See, this is the thing, you people scream “fallacy,” but say that you don’t have to account for the laws of logic by which you call anything fallacious! Doesn’t that seem odd to you? I repeat the questions, cause in 2 weeks now, I have yet to get any anwsers.Cheers,Sye

  13. Sye says: “cause in 2 weeks now, I have yet to get any anwsers.”Oh really? Ditto! How do you like your argument now? (wink wink)

  14. Hey I thought you guys might enjoy this article about a summer camp that teaches kids how to develop more critical minds:http://www.npr.org/templates/story/story.php?storyId=93174374 “But at Camp Inquiry, which has a secular humanist focus, God takes a back seat to reason. Of course, the camp schedules familiar camp activities like hiking, swimming, and arts and crafts for kids ages 7 to 16; but the thrust of the camp is to teach children to think skeptically about everything, including religion and the supernatural.”

  15. Sye: Alright fine. God exists, there’s nothing to account for or explain. Again, not much of an argument. All you are doing is avoiding the tough questions, by pretending they aren’t there.You didn’t read Stephen’s explanation, did you?._.This recent trend of using dissimilar cases to try to turn back our arguments against us isn’t working Sye…Just so you can’t ignore Stephen’s post and where he clearly and helpfully explained the point:Nothing is required to make it the case that all the stallions are male. rather, “stallion” just means male horse. Understand what “stallion” means and you are immediately in a position to know they will all be male. Indeed, there is nothing to make the case because “non-male stallion” does not describe some state of affairs that the world some conspires to prevent from obtaining. Rather, that combination of words makes no sense, given how “stallion” and “male” are used. So there is nothing to “prevent”.Now consider this. “and” and “not” are defined in logic by truth tables (which is why I asked if Sye knew about truth tables).”P and Q” is true if, and only if both P is true and Q is true, and false otherwise. “Not P” is false if P is true, and vice verse.Given these definitions of “and” and “not”: “Not [P and not-P]” is guaranteed to be true. The law of non-contradiction obtains because of what “and” and “not” mean. To ask, “But what makes it the case that both P and not-P can’t both be true is to misunderstand how “and” and “not” are used in logic.In short, the question: “What makes it the case that P can’t be both true and false?” is confused, and makes no sense. There’s nothing to “make the case”, because there is nothing to prevent. “P and not-P” does not describe some state of affairs that the world somehow conspires to prevent from occurring. It does not describe anything at all. That combination of words is just ruled out by the rules governing “and” and “not”.Two helpful links on the same issue are here and here.

  16. Sye: See, this is the thing, you people scream “fallacy,” but say that you don’t have to account for the laws of logic by which you call anything fallacious! Doesn’t that seem odd to you? I repeat the questions, cause in 2 weeks now, I have yet to get any anwsers.You haven’t read Stephen’s posts, have you? Or mine? Or David’s?By the way, that *is* a fallacy. Care to respond to phaedrus?

  17. Rayndeon said: ”You didn’t read Stephen’s explanation, did you?”Sure I did. All Stephen is saying is that the laws of logic are true by definition, but that is an extremely simplistic view of logic. Sure, if there was universal agreement on logic, the question might be irrelevant, but that is certainly not the case. There isn’t even agreement on the laws of logic in this very forum. Why, for instance, isn’t the Buddhist approach to logic correct? Who gets to define what logic is? Whose definition is correct if there is a discrepancy? His answer does not tell us what the laws of logic are, why they are what they are, how he knows what they are, or how he knows they won’t change. Simply, “They are what they are by definition” is a cop-out.Cheers,Sye

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  19. Sye, definitions are conventional. They are not correct or not – they are agreed upon or not. For instance, it is a contingent fact that we have labeled square with the particular series of letters “square” and further associated that particular series of letters with the sound “square.” These are all arbitrary and agreed upon.However, given the definitions, is it arbitrary that a square has four sides? No. Likewise, there is a particular arbitrary definition that we use such that A “implies” B such that if A is true, then B is true. But, given that particular definition, is it arbitrary that if A is true, and A implies B, then B is true? No. So, the laws of logic are really nothing more than formal definitions, and there is literally nothing to be explained here, anymore than I should explain why bachelors are unmarried or why stallions are males.I also have no idea what you mean by Buddhist logic. Are you referring to Zen koans?

  20. Well Sye, one thing is for certain. Simply yelling “God exists by impossibility of the contrary!!” over and over again is NOT an argument by anyone’s standard. It’s faith. And I think you are confusing faith with knowledge. Faith is absurd, and that is why it is a “leap” from the bounds of reason. If faith was knowledge, it would be called “knowledge”. Impossibility of the contrary must be argued for by showing *WHY* the contrary is impossible.

  21. Sye is all “sound and fury signifying nothing”. His “God” is a no-thing. He can produce no evidence to the contrary except endless assertion. He is like the White Queen, making a virtue of believing six impossible things before breakfast.

  22. I too am curious as to “buddhist logic”. I had a period of strong interest in buddhism and buddhist philosophy but I don’t recall them using a different logic.

  23. Another, more succinct version of my argument for logic in an atheistic universe. One agreeing with the claim that the idea of a “foundation” of logic is based on a misunderstanding of what logic is:1. There are necessarily true propositions (logical truths). That is, propositions which cannot, under any circumstances, be false.2. If a proposition would not be true if God didn’t exist then it is, by definition, not necessarily true.3. Therefore, necessarily true propositions do not require that God exist to be true (by the impossibility of the contrary).Since Sye is so enamoured of the idea of “impossibility of the contrary” I thought someone should show him what it looks like to use it in an actual argument.

  24. Sye,Time for the counterattack. I’m gonna make it simple, because you I’m not that smart and you don’t understand the big words here either.(1) You read the bible.(2) Your senses and reasoning says the bible is true.(3) You call your reasoning based on sound logic.(4) You conclude there is a God.(5) You conclude God made your senses and logic soundly.(6) You conclude your reasoning is based on sound logic.However, as you can clearly see, steps 3 and 6 are circular.Note that also 5 is never said in the bible.So you need, just like us, a brute fact, an axiom, to bootstrap your logic with.While ‘attacking’ what we readily admit, you forget you’re not without sin. What was it you don’t see in your own eye?

  25. sye:If an argument is simple it does not necessarily mean it’s simplistic. Any argument which aims to explain things ought to be as simple as possible while still containing the essentials. It makes it more likely to be correct (no stuff hidden in small print) and less confusing.It looks to me as if in your quest for elegant simplicity you have omitted a couple of essential details.Firstly why does everything need something to sustain it? Surely God could (and would because it is a more perfect solution) create things whichrequire no sustaining? Unlike the works of Man which are subject to the ravages of time. if God requires that these things should change or cease then He can alter or destroy them at will.It seems to me that God’s underpinning of the laws of logic could be one of the following types:A) I, God, can see everything that ever has been and ever will be, and I can tell you that these laws hold everywhere now and forever.B) I, God created the laws of logic to be universal and unchanging. So they are.C) I, God created the laws of logic to be universal and I promise not to change them or create anyone else who can.D) I, God, know everything and I can tell you that Dr. Law, atheist that he is has got it right with one of his reasons. He got lucky and you wouldn’t be justified in taking what he says at face value on anything else but you can trust Me on this.No need to have logic be “sustained” at all and reduce God to being a sort of metaphysical plate spinner.

  26. tony lloyd”But if it’s God who makes it necessary …”yes and it makes Him the ultimate hard nosed utilitarian which seems to make Syes assertion of moral absolutes rather a problem.

  27. Again Sye, I am not producing an argument, I am producing a position, a position you say you can rule out. So rule it out.If you can’t, well….Whether it’s my position or not is irrelvant, of course. Point is, it could be….

  28. Sye,you said:”…. Alright fine. God exists, there’s nothing to account for or explain. Again, not much of an argument.”That is your argument, and you’re right, it’s not much one. All you’ve added to that argument is that the contrary is impossible. Oooo, you actually think that adds weight to it?You said that the laws of logic are absolute, but you’ve been able to prove that too.

  29. All Stephen is saying is that the laws of logic are true by definition, but that is an extremely simplistic view of logic.As opposed to repeating that the laws of logic are universal, abstract and invariant. That’s clearly a more sophisticated position worthy of a true scholar.Sure, if there was universal agreement on logic, the question might be irrelevant, but that is certainly not the case.So the laws of logic are universal, but there isn’t universal agreement on logic?Up creek stop send paddle stop.

  30. @ Paul C.I said: ”Sure, if there was universal agreement on logic, the question might be irrelevant, but that is certainly not the case.”You said: ”So the laws of logic are universal, but there isn’t universal agreement on logic?Up creek stop send paddle stop.”That people have differing views on logic, has exactly nothing to do with its universality. Just as moral laws being universal, does not stop you from being what you are.Cheers,Sye

  31. Stephen said: ”Again Sye, I am not producing an argument, I am producing a position, a position you say you can rule out. So rule it out.”I did, here: “All Stephen is saying is that the laws of logic are true by definition, but that is an extremely simplistic view of logic. Sure, if there was universal agreement on logic, the question might be irrelevant, but that is certainly not the case. There isn’t even agreement on the laws of logic in this very forum. Why, for instance, isn’t the Buddhist approach to logic correct? Who gets to define what logic is? Whose definition is correct if there is a discrepancy? His answer does not tell us what the laws of logic are, why they are what they are, how he knows what they are, or how he knows they won’t change. Simply, “They are what they are by definition” is a cop-out.”Cheers,Sye

  32. That people have differing views on logic, has exactly nothing to do with its universality. Just as moral laws being universal, does not stop you from being what you are.There are no “universal moral values”.

  33. “His answer does not tell us what the laws of logic are, why they are what they are, how he knows what they are, or how he knows they won’t change.”yes it does.it explains why the principle of non-contradiction holds, rather than, say, its negation.It explains how we can know it’s true -(we just have to understand what “not” “and” etc mean.)And it explains why they won’t change (definitions can change, but not a truth-by-definition. Changing the defintion of “stallion” won’t change the truth that all stallions are male, it’ll just change which truth “all stallions are male” wil express.You mention diagreement. Who disagrees about the principle of non-contradiction? And, even if there were disagreement, why would that show this view is wrong?It may be wrong. But you have not shown it to be wrong. Do so…

  34. That people have differing views on logic, has exactly nothing to do with its universality. Just as moral laws being universal, does not stop you from being what you are.What an inept comparison. Are you suggesting that people can break the laws of logic in the way that they break your alleged moral laws?Of course you have yet to demonstrate that the laws of logic are universal. I maintain that the most we can say is that they are local, and you have yet to produce an argument against that either.I used to think there was no smoke without fire, until I encountered people like you.

  35. Stephen,Who disagrees about the principle of non-contradiction?Dropping the law of non-contradiction is one possible approach to the semantic and set-theoretic paradoxes. It’s dialetheism, which is advanced by people like Graham Priest, Richard Sylvan, Jay Garfield, and Stephen Darwall. The locus classicus here is Graham Priest’s book In Contradiction.

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