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Can something be true if it is not logical? Can something be true if it does not follow logic? if I can't deduce it logically? or if it contradicts logic?

In other words: if someone says statement X is true, can it be that X contains some ilogical constructs, and still remains true?

Or again in other words if I find a logical flaw in a sentence which someone says, can it be still true?

  • Like the sky is blue? – Conifold Feb 23 '16 at 18:52
  • @Conifold That is true because we agree on what blue color means –  Feb 23 '16 at 18:53
  • @Conifold And if we agree what blue means, then it is logical to say sky is blue –  Feb 23 '16 at 18:53
  • Semantics of words in a language usually is not considered part of logic, which deals with forms of reasoning, not its content. Aside from that, "sky is blue" expresses a truth about similarity of the sky to that of other blue things, which presumably has nothing to do with even semantic conventions. – Conifold Feb 23 '16 at 20:57
  • @Conifold I meant if we agree what blue is, then it logically follows that sky is blue –  Feb 23 '16 at 21:09
  • That would be circular, "we agree what blue is" simply collects agreement on examples such as "sky is blue". What you need is empirical fact that people do agree on such examples, not logic. In fact, without some logic external truths at the base (empirical or otherwise) logic can give you nothing at all. All it does is combine and recombine them in various fashions. – Conifold Feb 23 '16 at 22:22
  • @Conifold You aren't following me. Can you give example of sentence which is true but is not supported by logic? Not only empirical randomly true facts –  Feb 24 '16 at 06:33
  • In what context are you using these terms? As terms used in contemporary logic, nothing can be true unless it is a wff which also captures a states of affairs in the world. In some other context, sure why not. So you need to make clearer the context of your question and also explain in the case where you don't mean philosophical logic, how this is a philosophical question. – virmaior Feb 25 '16 at 08:40
  • @virmaior Why it needs context? I am asking assume we accept some empirical facts, sky is blue, grass is green, and then derive some sentences from it logically - can such sentence be true, if in between deriving this sentence we made illogical connection? –  Feb 25 '16 at 17:11
  • The word logic has many different meanings. without context, I (and others) have no idea which context/meaning you intend. Within formal logic, nothing can be true that does not follow logic, because truth attaches to propositions. In some other context, the foot is one what you mean by true. – virmaior Feb 26 '16 at 08:47
  • @virmaior I mean normal logic used everyday. I say if we agree on some facts, can we derive true sentences from it, without following logic? IMO no –  Feb 28 '16 at 16:02

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Firstly, in a strictly formal setting, we note that Gödel's first incompleteness theorem tells us that truth is not reducible to proof, so there are many truths which are not derivable.

In a formal setting, we chose our axioms because we believe them to be self-evident truths - i.e., true for no (logical) reason. But why do we assume that only self-evident truths are not derivable.

More generally, beyond the formality of mathematics, if one accepts that nature includes random processes, then such processes may provide examples of brute facts which are true simply because they are true and for no other (logical) reason. For example, if one accepts that the human evolutionary process is driven by random mutations of our genetic material, then we are who and what we are for no logical reason. It is true that humans exist on planet Earth, but it is not a logical necessity and it could have been otherwise.

Regarding true statements that contradict logic, one might argue that quantum superpositioning may provide examples. Superpositioning is a phenomenon that is supported by experimental evidence, but it certainly appears to be illogical to assert that a particle can be simultaneously in two different states or two different locations. Having said that, it may follow logically from the formalism of quantum theory that superpositioning is a logical necessity. I'm not a physicist, so I'm not entirely sure.

nwr
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    Godel's theorems are about a specific class of formal systems and what theorems exist in them, and do not say anything about the nature of *truth* or *proof* as general concepts. – Era Feb 23 '16 at 23:09
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    @Era That's true. The reason I mention Godel is because the question is posed with regard to logical derivation. Also, Godel's result does say something about the general nature of mathematical truth if not truth in general, namely that our mathematical intuition transcends formal systems. I tried to deal with the more general case in the second have of my answer, thought I admit it is not very effective or convincing. – nwr Feb 23 '16 at 23:17
  • Yes Nick that is my point, assuming we agree on some facts, how largely do you agree that to construct a true sentence from these facts, you need to follow logic more or less? –  Feb 28 '16 at 16:04
  • Indeed there maybe some events in nature that are true simply just because, e.g., sky is blue - maybe there is no logical explanation to it, maybe there is –  Feb 28 '16 at 16:05
  • @user200312 Perhaps you could have a look at "Gettier problem" on wikipedia. Gettier highlighted cases where we obtain true knowledge by luck rather than purely logical means. His paper undermined the classical theory of knowledge as "justified, true belief" which had held sway since first proposed by Plato. Although there may be a logical basis for Gettier truths, the problem does undermine the role of logic. – nwr Feb 28 '16 at 17:18
  • @NickR Gettier problem is differentI think - I will have a look. I know when someone can guess that someone is guilty in court- that doesn't mean knowledge. is that what you mean? because he didn't use reasoning. Otherwise bring me example of simple true sentence which violates logic if this is so easy? –  Feb 28 '16 at 19:44
  • @user200312 Not exactly. The classic example of a Gettier problem is a stopped clock. A commuter arrives at a train station at exactly the same time each day for a number of years. However, one day, although he arrives at the exact same time and the station clock reads the correct time, in fact the clock stopped working exactly 12 hours prior to his arrival. It is true knowledge but it is not justified because it is based on the false assumption that the clock is functioning correctly. The logic is based on a false premise. – nwr Feb 28 '16 at 19:59
  • @NickR I have a feeling we have a miscommunication, I asked you to bring example (desirably several) of sentences which are true, and violate logical reasoning - (you can base the sentences on any empirical - correct ones though - facts you want) –  Feb 28 '16 at 20:29
  • @user200312 Ya, it's a difficult one. I'll have to give this some more thought. – nwr Feb 28 '16 at 23:23
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Perhaps you mean: "Can there be undemonstratively true truths?"

Aristotle, when resolving the infinite regress problem, shows, against those who believed no or all truths are demonstrable, that there are some truths which cannot be demonstrated to be true. Thus, Aristotle could be considered a precursor to Gödel.

See

(quoted here)

Geremia
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    Godel's theorems don't show that there exist truths which cannot be demonstrated or shown to be true. It has to do with proofs within a particular formal system. The Godel sentences of PA can be proved by ZFC, which in turn has its own Godel sentences that can be proved by a stronger system, and so on. The point is that no such system is *self-contained* as there will always be Godel sentences, but no *particular* Godel sentence is "unprovable full stop" as you seem to be indicating. – Era May 27 '16 at 15:47
  • @Era When you prove with a "stronger system" what was not provable in the "weaker system," you have introduced new axioms. Aristotle realized this weakness axiomatic systems when he said there are almost as many premises as conclusions ([_Posterior Analytics_ bk. 1 ch. 43 (88b4)](http://dhspriory.org/thomas/PostAnalytica.htm#43)). So, are you claiming every "_particular_ Gödel sentence" is provable, given a "strong" enough axiomatic system (i.e., one with enough axioms)? – Geremia May 27 '16 at 23:07
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Truth is a property of propositions. A proposition is true if it refers to a fact. Hence truth is a relation between a proposition, a sentence from language, and a fact, a component of the real world.

This kind of truth bears no relation to logic. Whether a single proposition is true or not, cannot be decided by logic. As an example take the proposition "On 1.1.2016 it rained in Manhattan."

On the other hand - and now without looking at the physical world -, one can investigate logical relations between different propositions. E.g., if a proposition is true for all objects of a certain kind, then the proposition remains true when restricted to one particular object. Textbook example: "All humans are mortal." "Socrates is a human." Hence "Socrates is mortal."

According to classical logic it is not possible that two propositions are true if they contradict each other (law of non-contradiction).

Jo Wehler
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  • Thanks Jo but I think you didn't understand me. I don't mean "rained in manhattan". Or sentence like "Shut the door". I mean if someone says statement X is true, can it be that X contains some ilogical constructs, and still remains true? –  Feb 23 '16 at 18:55
  • Must the sentence be logically justifiable to be true? –  Feb 23 '16 at 18:59
  • @users200312 According to classical logic any proposition of type "A and B" is false if B itself is false. I assume that the term "false" is what you denote by "illogical". - There are propositions which are true but not justifiable by logic. See my example about raining in Manhattan. – Jo Wehler Feb 23 '16 at 19:00
  • "On 1.1.2016 it rained in Manhattan." according to my definition this can also be justified by logic: We check if it did really rain in manhattan on that day, and then it is true(logical) to say it did. Do you follow me? My point is that something can't be true in the end if somewhere in between it contains some illogical facts? e.g. be it from real world, or reasoning fallacies? –  Feb 23 '16 at 19:14
  • @user200312 I agree with you that a check is necessary whether it rained in Manhattan. But the check is *empirical* not *logical*. – Jo Wehler Feb 23 '16 at 19:22
  • So can we say that for something to be true it must be both empirically *and* logically correct? –  Feb 23 '16 at 19:34
  • @user200312 In my opinion and due to my example the answer is "no". – Jo Wehler Feb 23 '16 at 19:46
  • Which example? Can you bring example of proposition(s) which is/are empirically and logically true but their combination not true? –  Feb 23 '16 at 19:54
  • Or do you mean something can contain no empirical information, and still due to logic be true? With this I could agree. –  Feb 23 '16 at 19:56
  • @200312 I agree with your last proposal: "(A and B) implies A" is true, independent from any content of A and B. – Jo Wehler Feb 23 '16 at 20:00
  • So do you agree for something to be true, depending on typeof sentence, e.g. if it contains real world data or not, it must be either logically correct, or logically and empirically correct? Or only empirically correct? (but this is separate thing because that empirical should be possible to be broken down in logical and correct steps IMO). –  Feb 23 '16 at 20:05
  • btw here in your answer: http://philosophy.stackexchange.com/questions/29904/can-something-count-as-true-without-support-by-logic-and-empirical-data, you seem to agree that if something is logically and empirically true, then it is true –  Feb 23 '16 at 20:08
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Can something be true ... if I can't deduce it logically

Logic in one sense, is truth-preserving; hence it isn't the art or techne by which finds out new truths, or how truths we now hold were first discovered.

This, for example, in Badious philosophy is the role of Love, Art, Science and Politics.

Can something be true ... if it's illogical ... or contradictory

This is the position of dialethism, which holds that there are such things as true contradictions; a position which is more common in Eastern philosophy than Western - for example, see Nagarjunas use of the cakaskoti however Graham Priest is a modern exponent of this, which should be carefully distinguished from his advocacy of non-classical logics, including notions of paraconsistency.

Mozibur Ullah
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  • Do you agree with the fact that for something to be true it must be both empirically and logically correct? –  Feb 23 '16 at 19:35
  • @yser200312: that's polling for opinion - which isn't what SE is about; but yes, but not wholly, and nor are the two as closely or as simply connected as you make them; since I happen to think that there are true contradictions, which doesn't mean every contradiction is true. – Mozibur Ullah Feb 23 '16 at 19:41
  • So there is no consesus on this? Do you have example of sentence which contains empirically true facts, is logical, and in the end not true? –  Feb 23 '16 at 19:55
  • Well, there's a spectrum of opinion, a range of positions; you should ask a new question, rather than ask them in comments; comments are for small corrections or clarifications. – Mozibur Ullah Feb 23 '16 at 20:02
  • Yeah but I just got the feel that I didn't get an answer to my current question –  Feb 23 '16 at 20:06
  • Well, the question isn't exactly well-posed; which means the community has to work out quite what you're asking! Questions that are focused are usually a good fit for SE. – Mozibur Ullah Feb 23 '16 at 20:10
  • I mean if I find a logical flaw in a sentence which you say, can it still be true? –  Feb 23 '16 at 20:10
  • Let us [continue this discussion in chat](http://chat.stackexchange.com/rooms/36136/discussion-between-mozibur-ullah-and-user200312). – Mozibur Ullah Feb 23 '16 at 20:13
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It can be true even if it does not follow logic. Because logic does not cover all aspect of life. The best explanation for logic is, discovering links between two things.

Let us say there exist some thing which you never experienced in real life.

How will you treat the event? Do you really do all logical mind kung fu or treat it as broadening of your awareness?

Logic won't cover every thing unless you know everything which is kind of paradox in itself.

It is the main reason why Indian philosophies look different from western point of view.

syamal
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  • that is not what i mean, although those explanations might still follow logic, e.g. why grass is green? there maybe logical explanation with that. I mean once you accept some empirical facts, and when you want to logically derive something –  Feb 25 '16 at 17:09
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It is perfectly possible to come to truthful conclusions while the logical arguments upon which those conclusions are flawed.

Herebelow are three examples of basic propositional logic where the conclusion is correct but something is wrong in the logical argumentation for it.

Example 1

  1. Sven is a man.

  2. All men have mustaches.

The logical conclusion of propositions (1) and (2) would be that Sven has a mustache.

Now, Sven indeed does happen to have a mustache. However, not all men have mustaches. In this example, proposition (2) is wrong, yet the conclusion based on both propositions happens to be correct.

Example 1

Consider the following propositions :

  1. Heidi is a man.

  2. All men have breasts.

The logical conclusion of propositions (1) and (2) would be that Heidi has breasts.

Now, Heidi indeed does happen to have breasts. However, she isn't a man. Neither do all men have breasts. In this example, both proposition (1) and (2) are wrong, yet the conclusion based on those propositions happens to be correct.

Example 3

  1. Sven is a man.

  2. Some men have mustaches

You cannot conclude based on propositions (1) and (2) that Sven has a mustache. Drawing that conclusion based only on those two propositions would be a logical error. However, it just happens to be the case that Sven has a mustache.

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John Slegers
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In the popular example of "Schrödinger's cat" (see citation below), both polemic states of being alive and dead are accepted as true. Schrödinger presents a situation that, despite the seemingly inherent fact that if one is alive they are not dead (and vice versa), in the mathematical interpretation of a physical experiment you can have a "justified true belief" for both possibilities simultaneously. It is only until one opens the box that one becomes true and the other false.

This epistemological issue exists in the relationship to "Truth" and "Knowledge". While A and "not-A" cannot both be observably true, they can theoretically (mathematically) exist simultaneously given a closed system without an observer. This same issue is brought to light with similar thought experiments.

A man stands in a field full of barn facades. In the field there is one real (non-facade) barn. The man, under the impression that all the barns are real, points to the real barn and says, "That is a barn".

Though the man has a "true belief", the justification of that belief complicates the matter, because he has a false sense of the accuracy of his choice. However it does not in the end diminish the accuracy of his statement. Therefore, even with a fallacious premise ("the man believing all the barns were real") the truth of his statement remains intact. Just as the truth of the cat being simultaneous dead and alive remains intact, until an observer opens the box. These are examples of Logical Truths despite false premises.

...ridiculous cases [like, a] cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter, there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer that shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.

~ Erwin Schrödinger, Die gegenwärtige Situation in der Quantenmechanik (The present situation in quantum mechanics), Naturwissenschaften (translated by John D. Trimmer in Proceedings of the American Philosophical Society)

Link to Wikipedia

Eliot G York
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  • This still seems really poorly balanced in terms of what's needed to answer vs. how much you write... – virmaior May 30 '16 at 10:15
  • @virmaior you can edit it if you would like. I am unsure how 8 sentences is excessive. – Eliot G York May 31 '16 at 22:00
  • for me, the *"truth"* issue regarding Schrodinger's cat is that of choosing between the [Copenhagen interpretation of quantum mechanics](https://en.wikipedia.org/wiki/Copenhagen_interpretation) vs. that of the [Many Worlds interpretation](https://en.wikipedia.org/wiki/Many-worlds_interpretation). – robert bristow-johnson Jun 03 '16 at 17:23
  • @alampert22 I'm not sure how I can edit something that I would never write ... – virmaior Jun 06 '16 at 07:36
  • @virmaior if it's "poorly balanced", perhaps you could edit it and improve the balance? It would help me understand the constructive criticism. – Eliot G York Jun 06 '16 at 07:44
  • Try this, read the question `can something be true if it does not follow logic?`, then read each sentence in your answer. delete any sentence that isn't inside of a paragraph that answers this question. Then at the end add a brief thing saying you think quantum superposition is like this. At least when I do this, it seems unbalanced. As in the details on super positions are long, but the details on how that answers the question are shorter. – virmaior Jun 06 '16 at 08:03
  • @virmaior thanks I'll take a look in the morning. – Eliot G York Jun 06 '16 at 08:12
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What kind of logic? There are many logical systems, devised by human beings to think about and understand different kids of phenomena or experience. For example, the two valued Aristotelian logic. That logic is inadequate to understand the sub-atomic phenomena of quantum physics. Even though sub-atomic phenomena are real, they seem illogical to Aristotelian mind.

Marino Klisovich
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here is a religious perspective:

"...Jews demand signs and Greeks search for wisdom, but we preach Christ crucified, a stumbling block to Jews and foolishness to Gentiles, ..."

there appears to be something goofy about seeking the salvation of humankind in that of sacrifice. just doesn't seem logical.

robert bristow-johnson
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  • Your answer appears to assume the truth of the quoted text. How do you justify this? – nwr Jun 03 '16 at 17:00
  • that's sorta the nature of holding to a religious belief. persons of faith detect or discern truths (or maybe better said "**Truth**") in *"things hoped for* [and of] *of things not seen."* and for non-believers, that is considered foolishness. what differentiates the different religions is what those "things" are. and, to some degree, it's the invisible "things" that's what differentiates believers in God from believers in something else (e.g. a Multiverse). believing in God may seem like foolishness to some and believing in other universes may seem like foolishness to others. – robert bristow-johnson Jun 03 '16 at 17:10
  • That's "certainly" true. – nwr Jun 03 '16 at 17:22
  • i'm just a little curious. where is the word *"certainly"* being quoted from? – robert bristow-johnson Jun 03 '16 at 17:25
  • I used the quotes to highlight that, while I believe it to be true and would say in conversation "that's certainly true", it is not strictly a certain truth. – nwr Jun 03 '16 at 17:31
  • cool. (8 chars of text). – robert bristow-johnson Jun 03 '16 at 17:32
  • At least one user doesn't think this is a good answer. Can you unpack how it is a *philosophical* answer – virmaior Jun 06 '16 at 07:37
  • it's just that in the context of faith, "truth" might be something that transcends human construction like logic. the latter is more superficial, ostensible, the former is deeper. – robert bristow-johnson Jun 06 '16 at 10:16
  • Err, edit the answer to improve it rather than tell me in the comments why you think it works.. – virmaior Jun 06 '16 at 10:28