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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.

Speakpigeon
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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 Nov 21 '23 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 Nov 21 '23 at 12:34
  • The theme in the comments above is that 'universal' is not defined. – J D Nov 21 '23 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 Nov 21 '23 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 Nov 22 '23 at 10:55
  • @PaulTanenbaum "What, precisely, is your understanding" My own view is that if correct reasoning is logical reasoning, then logic may be universal in the sense that there is no restriction on the subject matter of logical reasoning. Logic applies to potentially any problem whatever. 2. "in what ways does it fall short" It doesn't. What does is the academic view of logic. It is inconsistent with the universalism of logic. – Speakpigeon Nov 23 '23 at 10:58
  • My point is that if you find the argument inconclusive, then it hasn’t convinced you that logic is not universal, so you must put some stock in the arguments of those who say it is. But how can you not know any sense in which it would be, given that you have read and not rejected arguments to the effect that it is? – Paul Tanenbaum Nov 23 '23 at 11:41

3 Answers3

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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.

Jo Wehler
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  • logic is from logos; using strict science to approach logic is emasculation of reality. – Ioannis Paizis Nov 21 '23 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 Nov 21 '23 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 Nov 21 '23 at 17:19
  • @Ioannis Paizis I made an addition concerning the term "sicence"; I do not know if there exists one common umbrella term in English. – Jo Wehler Nov 21 '23 at 18:14
  • @Speakpigeon I clarified my use of the term "science".- ad 3. There is not much ado about the law of identity "A=A". It is part of the axiom that equality is an equivalence relation. Therefore equality has to be a reflexive relation. - ad 4. I do not understand your comment about dialethic logic; please explain. – Jo Wehler Nov 21 '23 at 19:31
  • @JoWehler "not much ado about the law of identity" It is accepted as a law of logic and seems as universal as could be: absolutely every thing is identical to itself. 2. "clarified my use of the term "science"." Doesn't help. Humanities are philosophy, literature, and art! Not what we mean by "science". 3. "structural sciences" Structural sciences describe the general structures of the real world. Logic itself doesn't seem to say anything about the "real world". Maybe you have an example of that? 4. *"dialethic logic . . . have been axiomatized" So? Does this prove it is logic? – Speakpigeon Nov 22 '23 at 10:50
  • @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 Nov 22 '23 at 15:00
  • @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 Nov 22 '23 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.

Ioannis Paizis
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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 Nov 21 '23 at 17:34
  • By accepting it as it is: reversed. – Ioannis Paizis Nov 21 '23 at 17:46
  • Please explain. – Speakpigeon Nov 21 '23 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 Nov 21 '23 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 Nov 22 '23 at 10:33
  • @Speakpigeon, Since the liar's paradox does not refer or complement to something else, to something that can be evaluated as true of false, as long as it is self contained, it does not contribute any value (true or false) to anything. So - to my definition of logic - no connection can be made: we have a pause here, but not a contradiction; but if the liar refers to something, ex. "I want an apple", then what follows (from logic) is that he doen't really want one. So, the paradox is a paradox technically only (by name) and not in the context of logic as a serialized process of reasoning. – Ioannis Paizis Nov 22 '23 at 11:36
  • "a close relationship with reasoning." The usual reasoning concerning the Liar proposed in the academic literature is as follows: If it is true, then it is false; If it is false, then it is true. So, either there is no "close" relationship with logic, or, if you think there is one, how do you propose to reason about the !liar? – Speakpigeon Nov 22 '23 at 17:03
  • @Speakpigeon, if you click the link, you can read my analysis on reasoning. As an intermediate conclusion : the starting point of reasoning is "why something is the way it is" : in this way the paradox is identified as such, ie. a paradox and reasoning is done about it. – Ioannis Paizis Nov 22 '23 at 17:18
  • @Speakpigeon, indeed if a machine was to reason it would stack in an internal loop inside the liar paradox, but we are not machines, so we can identify it as such and proceed forward. logic is not a strict machine nor a software, it contains the programmer too. – Ioannis Paizis Nov 22 '23 at 18:01
  • @Speakpigeon: For posterity: the Liar's paradox is an interpretation of a general category-theoretic statement, Lawvere's fixed-point theorem; see Lawvere's paper, Yanofsky's explanatory paper, and Yanofsky's lecture. We have completely made sense of it. – Corbin Nov 24 '23 at 19:18
  • @Corbin This must be interesting to mathematicians. It may prove something about the Liar and other paradoxes, but the question is not a mathematical one but of reasoning logically. To say that the Liar is a logical paradox just means that logicians cannot make any logical sense of it. Everybody, I guess, gets that the sentence "This statement is false" taken self-referentially is nonsense, and as one of the papers says, calls for trouble, yet no logician in 2,500 years (not 3000 years as one of your papers says) was able to produce a logical reasoning resolving the paradox. But thanks. – Speakpigeon Nov 25 '23 at 17:37
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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"...

xerx593
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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 Nov 21 '23 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 Nov 21 '23 at 17:07