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There is what seems to me an inconclusive debate in the academic literature concerning the idea that logic is universal, but in what sense exactly would logic be universal?

One example of a claim that logic is universal was that of Bertrand Russell:

Logic is, broadly speaking, distinguished by the fact that its propositions can be put into a form in which they apply to anything whatever.

To go a bit further, if correct reasoning is logical reasoning, logic may be universal in the sense that there is no restriction on the subject matter of logical reasoning. Logical reasoning applies to potentially any problem whatever.

This is one possible interpretation.

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    Do you have in mind universal meaning universally applicable, or universally used by all people, or whether there is a universal logic that underpins all systems of logic, or something else?
    – Bumble
    Commented Nov 21, 2023 at 12:01
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    Which "universal"? For Frege-Russell's universalist conception the debate pretty much concluded with the demise of logicism after Gödel and Tarski, a universalist logic is inconsistent. For Ryle's sense of topic-neutral see SEP, Topic neutrality.
    – Conifold
    Commented Nov 21, 2023 at 12:34
  • The theme in the comments above is that 'universal' is not defined.
    – J D
    Commented Nov 21, 2023 at 18:27
  • If the debate in the academic literature truly seems inconclusive to you, then can you really have no idea of an exact sense in which logic would be universal? What, precisely, is your understanding, and in what ways does it fall short of the completeness you seek?
    – Paul Tanenbaum
    Commented Nov 21, 2023 at 20:46
  • @Bumble "Do you have in mind . . ." I am asking what you may have in mind. What does it possibly mean according to you when philosophers say that logic is universal.
    – Speakpigeon
    Commented Nov 22, 2023 at 10:55

3 Answers 3

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Logic is a science - the word taken as an umbrella term for structural sciences and the humanities - about structural relations like mathematics as emphasized by Bourbaki. And like mathematics, also in logic there exist several different axiomatized calculus.

All natural sciences, all humanities and also general human thinking follow a calculus of logic. In general, it is a calculus of 2-valued logic: Statements are either true or false. In particular, no statement is true and false.

Nevertheless there exist axiomatized systems of many-valued logic. And also theories with a probabilistic or fuzzy truth value. Moreover we have forms of logic with different kinds of modality like temporal logic, deontic logic (obligation, permission, prohibition) or modal logic (real, possible, necessary). All these domain specific logics have been axiomatized.

The only candidate for a universal logical law is IMO the law of non-contradiction. But even here, dialethic logic discusses how to deal with contradictions.

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  • logic is from logos; using strict science to approach logic is emasculation of reality.
    – Ioannis Paizis
    Commented Nov 21, 2023 at 16:55
  • of course you can talk about logic in the scientific context, but restricting logic only in this context by definition is a limitation of its scope; philosophy and science are not the same things.
    – Ioannis Paizis
    Commented Nov 21, 2023 at 17:04
  • @JoWehler "Logic is a science about structural relations" Can you explain? What makes us so sure that our logic is correct? 2. "All sciences (...) follows a calculus of logic." Ah, but if logic itself is a science, as you just claimed, this is circular, and so bad logic. Any idea how you could resolve this? 3. "is IMO the law of non-contradiction" What about the law of identity? 4. "dialethic logic" So because some dudes invent a theory and call it "logic" it makes the law of contradiction not universal? Whoa. There is something wrong in your conception of logic.
    – Speakpigeon
    Commented Nov 21, 2023 at 17:19
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    @Speakpigeon I forwarded your comment concerning the law of identity to Wittgenstein. Here is his answer from Tractatus logico-philosophicus, 5.5303: "Roughly speaking: to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing.” :-)
    – Jo Wehler
    Commented Nov 22, 2023 at 15:00
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    @Speakpigeon ad 3) I mean that logic and mathematics are structural sciences in the sense of "formal sciences", in the same sense that Bourbaki characterizes mathematics as dealing with structures like algebraic, topological and order structures - of course not in the sense that logic and mathematics describe the structure of the real world. ad 4) I have the same question like you.
    – Jo Wehler
    Commented Nov 22, 2023 at 16:26
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Logic, in its most general form, can be defined as the process of making connections among concepts. Obviously, these connections must have a meaning, but the meaning can't always be objective. It all depends on the concepts; for numbers it is objective, for happiness or strategy it is subjective. I understand logic - as a process - to be universal and concepts as things that can be communicated in a universal level. So I consider logic as a universal framework under which communication can be established.

Addition

Since logic can have many connotations - if considered outside a formal system - I assume a close relationship with reasoning.

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  • "I consider logic as a universal framework" So it must apply to the Liar? How would you explain the logic of the Liar? If it is true, then it is false; If it is false, then it is true?!
    – Speakpigeon
    Commented Nov 21, 2023 at 17:34
  • By accepting it as it is: reversed.
    – Ioannis Paizis
    Commented Nov 21, 2023 at 17:46
  • Please explain.
    – Speakpigeon
    Commented Nov 21, 2023 at 17:55
  • The liar paradox is a universal paradox: it's always a paradox or can be recognised as such. Note that I do not treat logic as a formal system in my answer but in its most general aspect.
    – Ioannis Paizis
    Commented Nov 21, 2023 at 18:06
  • "The liar paradox is . . . always a paradox or can be recognised as such." Sure, but how does that make it meaningful? Logicians still today cannot make any logical sense of it! And I don't think you can either. Essentially, this means that one way or the other, our logic doesn't apply to the Liar, which makes our logic not universal. Any solution?
    – Speakpigeon
    Commented Nov 22, 2023 at 10:33
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Logic is applicable (i.e. correct):

  • At any (also "no") location (in whole space)
  • at any (also the "no") "point in time" (in whole time)

The (no-) location makes logic "universal"(ubiquitous).

The (no-) time makes logic "eternal"...

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    As it’s currently written, your answer is unclear. Please edit to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers in the help center.
    – Meanach
    Commented Nov 21, 2023 at 12:27
  • @xerx593 "ubiquitous" Surely not. Ubiquitous means "present everywhere". not applicable everywhere. 2. "Logic is applicable (...) At any (also "no") location" This is contradictory. "Applicable at no location" means that it is not applicable anywhere. 3. Can you give an example of an application at what you call "no location"?
    – Speakpigeon
    Commented Nov 21, 2023 at 17:07

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