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What is logic?

One can imagine Turing, Godel or Post writing a paper on logic. What provides the "validity" to the content they write? One proper answer to this question is the a priori "understanding" embedded in their mind. Mind, then, is in a strict sense, a priori in this case. Language is an apparatus to present logic, it cannot be that logic is about language. Logic may not be strictly equated with formal logic: the latter is in some sense a proper subset of logic -for mind again is a priori to the formal system under discussion. It appears what logicians talk about in their papers, in a deep sense, isn't about symbols, arithmetic or even mathematics in the end. They aren't talking about anything ! One then may even say, crudely, they are outlining fragments of "understanding". That may be complicated, thereby requiring a full paper, but the fact remains.

So is logic then an exact theory of mind -an exposition of the a priori thought? How can we characterise relationship between logic and "a priori" nature of mind?

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  • Logic is about inference, deduction, proof. All human "practices" grounded in language: they are formal and thus we can use formal languages to provide mathematical models for them. Jun 15 at 18:21
  • @MauroALLEGRANZA How would you characterise relationship between logic and "a priori" nature of mind?
    – Ajax
    Jun 15 at 18:51
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Your question is a topic in the philosophy of logic. A great deal has been written on it and there are many different points of view. You might like to read my answer to this related question.

In broad-brush terms, some consider logic to be about conceptual relationships. Others, that it is concerned with what is a priori knowable. Others, with what is necessarily true. Others hold that logic is fundamentally linguistic in nature and should be understood in terms of meanings, or substitutivity of terms, or grammatical forms. There are several variations on each of these, and often a criterion is included that logic is topic-neutral, i.e. it does not depend on information that is specific to a particular subject matter.

Since you ask specifically about the relationship between logic and a priori knowledge, some further considerations are:

  • It is dubious to place much weight on how humans actually think. Studies by cognitive psychologists show that people are not very good at logic, and are especially bad at reasoning with uncertainties. Appealing to natural selection as a justification for logic is also questionable. Humans survived being eaten by sabre-toothed tigers by climbing trees and using weapons, not by beating them at poker.

  • Most logicians (though not all) consider logic to be normative, so logic is not so much about how people reason, but about how they ought to.

  • There are many logics, and there is no general agreement on whether there should be a single 'correct' logic, and if so, which it would be. Classical logic is by far the most commonly used, but it has many limitations and is not universally accepted. Many logicians use non-classical logics, and some are pluralists about logic.

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  • "Appealing to natural selection as a justification for logic is also questionable. Humans survived being eaten by sabre-toothed tigers by climbing trees and using weapons, not by beating them at poker." Seriously? You think logic is about playing poker? Jun 16 at 12:51
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What is logic?

In simple words, logic is a set of formal rules that seem to describe the behavior of the world. For example, if A=B and B=C, so, logically A=C. Such logical rule is just the formalization of a description of the world.

What provides the "validity" to the content they write?

Your own experience. Someone might state that A=B and B=C, so, logically A=C, but that might be false for you, so you can say that the rule is not valid. But most of us have deduced such behavior from experience and accepted the rule.

One proper answer to this question is the a priori "understanding" embedded in their mind.

That is not a valid answer, without specifying the sources of a priori knowledge. Otherwise, you are saying that "A priori knowledge, that is, some knowledge, that mysteriously raises in our mind, holds the rule that gives validity to KG's Theorem".

So is logic then an exact theory of mind -an exposition of the a priori thought?

Could be, depending on the sources of a priori that you base your acceptance of a priori knowledge upon.

How can we characterise relationship between logic and "a priori" nature of mind?

Hold right there! That is a HUGE problem. Kant's Critique of Pure Reason (in my opinion, the most profound proposition in all history of philosophy), is entirely consecrated to address such issue.

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The brain builds a predictive model out of its experiences in order to save energy. Logic is the the consciously directed continuation of that process. Using patterns and input to build other patterns of what we might expect. It is all grounded by experience. And the brain notices patterns within experience and tries to predict. We can then test some things empirically/experimentally and update our patterns/model/logic.

I am coming from an empiricist perspective and using some neuroscience that David Eagleman talks about https://youtu.be/5ok2ejw8d8c?t=3144 (need to watch more of the whole talk to see his fuller depiction of the brain). Everything we know about the world comes from senses that feed into the brain.

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One can imagine Turing, Godel or Post writing a paper on logic. What provides the "validity" to the content they write?

Turing and Gödel have been brought up in mathematical logic and so would have been unlikely to write about anything else, certainly not logic.

There are only two possible meanings for the notion of validity. Either it is valid because it is factual, or it is valid because it is logical, and of course possibly both.

So Gödel writing about mathematical logic would have been logical because this is what human beings do, and he would have been factual in starting from the a priori of mathematical logic, such as for example the truth-functionality of the conditional. Of course, the a priori of mathematical logic are essentially irrelevant to logic itself, but there would be no conflict there because of these two independent forms of validity.

One proper answer to this question is the a priori "understanding" embedded in their mind. Mind, then, is in a strict sense, a priori in this case. (...) So is logic then an exact theory of mind -an exposition of the a priori thought? How can we characterise relationship between logic and "a priori" nature of mind?

Logic does not work as an understanding. Rather, it is a brain process to arrive at a conclusion given certain premises. As such, we are essentially ignorant of the process itself since we are ignorant as to how our own brain works.

So logic is a priori, but it is not a priori knowledge. It is just something our brain does, like vision and memory.

Language is an apparatus to present logic, it cannot be that logic is about language.

No, language is used to communicate ideas between brains. Initially only shouts and grunts but it has evolved subsequently to become the very sophisticated language we can use today.

As a means to communicate ideas, language can be used to submit our reasonings to other people.

Our logical reasonings, strictly speaking, are about the various fictional worlds represented in our verbal communication.

Logic may not be strictly equated with formal logic:

Indeed, not strictly and in fact not at all. Formal logic is the discipline in which people try to articulate formal models of logic.

the latter is in some sense a proper subset of logic

Certainly not. See above.

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  • When you say "logic is a priori" and "something our brain does" do you mean that brains show logical reasoning prior to language? And if so are you talking strictly about deductive logic, or forms of mental inference that blend aspects of what in language we identify as deduction and induction?
    – Hypnosifl
    Jun 16 at 17:07
  • @Hypnosifl 1. I am talking about deductive logic, the logic of human deductive reasoning - 2. Brains show a logical capacity, in evidence in what we say and do, and introspectively in how we think. If I imagine Wilbur and Wilfred in the kitchen, then I will inevitably be imagining Wilfred in the kitchen. - 3. Our logical capacity appeared not only before human language but before humans. It is inherited directly from species ancestors of the human species. Logical reasoning is something else. It is the application of our logical capacity to the fictional world described in verbal statements. Jun 16 at 17:37
  • We can say that if a pre-linguistic being (an animal, a baby) is imagining Wilbur and Wilfred in the kitchen, a component of that imagined image must correspond to the proposition we would label "Wilfred in the kitchen". But are you saying the being itself has some self-awareness of the fact that it's imagining Wilfred in the kitchen as distinct from the image in its mind of Wilbur and Wilfred in the kitchen? Can you imagine a brain or artificial neural net whose behavior shows it recognizes an image of W&W in the kitchen but doesn't understand this entails Wilfred in the kitchen?
    – Hypnosifl
    Jun 16 at 17:51
  • @Hypnosifl You are overinterpreting what I said. Come back to what I said. I don't want to expound further. Jun 17 at 10:08
  • You're free not to respond, but for anyone else reading this discussion, my basic point is that saying that our "logical capacity" is pre-linguistic and "inherited directly from species ancestors" seems meaningless/unfalsifiable unless you can explain what it would mean to have a hypothetical brain that lacks this logical capacity as one of its mental abilities (all you showed in the kitchen example is that if we describe its behaviors and internal processes in language, all the propositions about it would still respect the rules of logic, this says nothing about its own abilities).
    – Hypnosifl
    Jun 17 at 15:52

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