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.

  • 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, 2018 at 19:53
  • You mean; errors are also universal. <br/> 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, 2018 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, 2018 at 20:43
  • 2
    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, 2018 at 21:11
  • 1
    For #2 see my answer on this overlapping question.
    – Dennis
    Mar 17, 2018 at 3:11

1 Answer 1



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.


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.

  • That does somewhat assume that "whales" is a nonempty class of things (which I grant it is not).
    – Veedrac
    Mar 17, 2018 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, 2018 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, 2018 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, 2018 at 16:25
  • 1
    @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, 2018 at 9:13

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