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Logic is generally regarded as dealing with laws of thought.
Then question rises whether the range of the laws of thought could be determined within the range of laws of thought

My question is not that so general
and I don't think this could be properly held in this line
but concrete; i.e.

"Wherein lies the difference of logic and psychology"

"Wherein lies the difference of logic and mathematics"
[I personally believe symbolic logic is mathematics and could not be discerned from it although the impetus of it could have been risen from laws of thought but it is not essentially different from the fact that mathemtics could arise from technical necessity]

These may throw a light into the above question.

김세현
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  • Pure deductive logic is a universal topic. That is every rational subject includes some deductive reasoning. This does not mean everything IS LOGIC. Mathematicians have borrowed many ideas from deductive logic with a twist. That is the context is different from the subjects. Deductive logic That I was taught was to reduce deceptive reasoning. This is not so for math. Mathematicians don't care if propositions are true and are focused only on validity. The purpose of symbolic logic is a shorthand form of deductive logic not math. Concepts don't all carry over between math and logic. – Logikal Mar 16 '18 at 19:53
  • You mean; _errors_ are also universal.
    What I mean with that phrase is not about the purpose but that symbolic logic and mathematics are _epistemologically_ (or even logically) indiscernible.     – 김세현 Mar 16 '18 at 20:15
  • Do you mean logical errors or fallacies? Yes they would be repeatable patterns. The intent of deductive reasoning in philosophy differs from math even thought they share some symbolization. Math only cares about validity. When I learned logic it was about soundness as sound arguments must be valid anyway. – Logikal Mar 16 '18 at 20:43
  • Okay then it is somewhat similar to the difference of mathematics and physics; Logics has some psychological factor of expecting something _more_ than the mere process of reasoning. Although there may, I believe, be no essential difference with respect to reasoning – 김세현 Mar 16 '18 at 21:06
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    I would not say logic itself has other topics. I would say the other way around as logic is universal and applies to all topics that are rational. I. Everyday life yes psychology, rhetoric and math are usually the topics that come up frequently. Many people are taught math is logic which I find deceptive. – Logikal Mar 16 '18 at 21:11
  • I mean _logics_ is mathematics rather than mathematics is logics or both are exactly same; what people think when they say so is that mathematics is logic _al_ rather than mathematics is logics. What I want to say is that logics is mathematical; they largely depends on geometry. Dealing with Informal fallacies is certainly not mathematics. – 김세현 Mar 16 '18 at 21:23
  • I disagree. Math has some deductive reasoning and not all of the other stuff. There is a distinct topic of Mathematical Logic which is popular today. This differs from Aristotelian logic. – Logikal Mar 16 '18 at 21:26
  • That type of logic is specifically called Mathematical Logic which is also called new logic as opposed to classical logic. – Logikal Mar 16 '18 at 21:40
  • Rational usually expreases TRUE propositions that justify a position or belief. The reason something is rational is because there is a true explanation for that original thing. – Logikal Mar 16 '18 at 21:58
  • Content and form was what I was taught. Mathematical logic claims not to care about content and only focusses on validity which is FORM. – Logikal Mar 16 '18 at 22:30
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    For #2 see [my answer on this overlapping question](https://philosophy.stackexchange.com/a/49571/2297). – Dennis Mar 17 '18 at 03:11
  • 'Logics has some psychological factor of expecting something more than the mere process of reasoning.' (Should be 'Logic', not 'Logics'.) Logic has no such expectation; those who use it might have but that is a fact about them, not about logic. – Geoffrey Thomas Mar 17 '18 at 09:32
  • How is it logically possible for Logic to have an expectation ? It is not a conscious entity. – Geoffrey Thomas Mar 17 '18 at 09:42
  • It is a matter of condition of significance; you can't speak of what you don't know or what is meaningless although logic itself could become quite void afterwards – 김세현 Mar 17 '18 at 10:17
  • Logic is **not** about the "laws of thought". Logic is about the validity of arguments. See [Aristotle's logic](https://plato.stanford.edu/entries/aristotle-logic/#SubLogSyl). It is more linked to language. – Mauro ALLEGRANZA Mar 17 '18 at 11:25
  • Psychology is an *empirical* science; logic is formal. – Mauro ALLEGRANZA Mar 17 '18 at 11:26
  • If it is formal the criterion of truth left to be used is nothing but laws of thought, validity and laws of thought becoming almost synonymous. I mean; if you want to say the way of filling the content, then "soundness" is more appropriate – 김세현 Mar 17 '18 at 22:04
  • For some references, see [What is logic?](http://philosophy.hku.hk/think/logic/whatislogic.php) – Mauro ALLEGRANZA Mar 18 '18 at 10:53

1 Answers1

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▻ LOGIC AND PSYCHOLOGY

Logic is not concerned with the laws of thought. Psychology was excluded from logic long ago.

Logic is concerned with relations between sentences or propositions. For instance, the two proposition :

All whales are mammals

All whales are water-creatures

imply the propositions :

Some water-creatures are mammals.

This implications holds regardless of what propositions pass through anybody's mind. A machine could be produce this conclusion. No-one has to think it through. The implication between propositions is independent of what goes on in anyone's head.

Where psychology enters the picture is not through implication but through inference - when someone reasons from data or assumptions. If you remember that your friend's birthday is on the first day of summer, you check online and discover that the first day of summer is 19 April, you check the calender and work out that the first day of summer is five weeks away, then realise that this is how far away your friend's birthday is, you have come to a conclusion - got a result - through a process of inference.

▻ LOGIC AND MATHEMATICS

This is a far more tangled matter, difficult to elaborate. I omit it because you seem to have already made up your mind - you have recorded a belief - about the relationship between symbolic logic and mathematics and others can in any case throw more light on this than I can.

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Geoffrey Thomas
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  • That does somewhat assume that "whales" is a nonempty class of things (which I grant it is not). – Veedrac Mar 17 '18 at 15:28
  • @Veedrac. To logic, does it matter whether a class is non-empty or not? I could have sia – Geoffrey Thomas Mar 17 '18 at 15:57
  • Your post is truncated. The issue is that "some X are Y" means "there exists an X which is a Y", which can only be true if there exists an X. – Veedrac Mar 17 '18 at 16:04
  • @Veedrac. To logical implication, does it matter whether a class is non-empty or not? 'All centaurs are half man and half horse' implies 'Some centaurs are half man and half horse'. Does the ontological status of centaurs matter ? Is the implication nullified because centaurs are an empty class ? I don't ask any of this aggressively ! If I have made a logical mistake, I'm eager to be set right. Best - Geoffrey. – Geoffrey Thomas Mar 17 '18 at 16:25
  • "All X are Y" means "everything that is an X is also a Y". It does not imply that an X exists, and it does not imply that "some X are Y". It does mean that "if an X exists, then some X are Y". – Veedrac Mar 17 '18 at 16:28
  • It's worth noting that it's entirely reasonable to talk about implications on things that don't exist as physically realized objects; one can say "some circles have radius 1" without ever having a physical thing that corresponds to a circle of radius 1. But one would be incorrect to say "some circles that are not circles have radius 1", since the class of circles that aren't circles is empty. – Veedrac Mar 17 '18 at 16:34
  • @Veedrac. I see, yes okay : if 'some' involves existential quantification, then there can't be implication from the null-class. But that means that there is nothing wrong with my original example about whales. However, your comment about 'some' and existential quantification is obviously very helpful and illuminating. I'm resistant to the idea that 'some' does necessarily involve existential quantification. I'm clearly working from an older logic. – Geoffrey Thomas Mar 17 '18 at 16:36
  • @Veedrac. 'But one would be incorrect to say "some circles that are not circles have radius 1", since the class of circles that aren't circles is empty.' Clearly so but all I assumed was what you allow : 'that it's entirely reasonable to talk about implications on things that don't exist as physically realized objects'. Great ! You've made things clear - Geoffrey – Geoffrey Thomas Mar 17 '18 at 16:42
  • I struggle with your first sentence since Aristotle's logic seems designed to model the way we (usually intend to) think and to do it successfully. . . –  May 15 '18 at 11:32
  • @PeterJ. I didn't have Aristotle's logic in mind, though I admit my example would fit it. I was thinking of eg the truth of a conditional in modern logic if the antecedent is false and the consequent true. We do not reason in this way; it is (I assume) valid logic but completely alien to the psychology of inference. I see logic as holding between or within propositions, statements or sentences as in 1st order propositional and predicate logic ; psychology doesn't enter into logic. I see inference as a reasoning process done by humans who do not use e.g. the paradoxes of material implication. – Geoffrey Thomas May 15 '18 at 12:58
  • @PeterJ. 'Logic' is a word of many meanings. I don't deny that it can be used to cover inference = the psychological process or reasoning, and the propositional and predicate calculus. Really all I am saying, which strikes me as obvious, is that as calculus it is not inference and as inference it is not calculus. – Geoffrey Thomas May 15 '18 at 13:06
  • @GeoffreyThomas - Fair enough. I'm not up to speed on modern logic being happy with the old-fashioned sort. . –  May 16 '18 at 08:31
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    @PeterJ. Tell you a secret - me, too. Since Frege, logic has acquired new strengths but few of these are of use beyond certain technical applications. And they certainly do not aid ordinary reasoning. No-one reasons in practical life that a conditonal is true if its antecedent is false and its consequent true. It's this thought that animated my answer. Best - GT – Geoffrey Thomas May 16 '18 at 09:13