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I just looked up the definition of "logical constant" in Wikipedia, and I came across the following definition:

A logical constant is a symbol in symbolic logic that has the same meaning in all models, such as the symbol "=" for "equals".

I don't know what they mean by model, but if you substitute 'mind' for 'model' the resulting definition makes sense to me. Even a fish has access to the meanings of 'not', and 'and'.

I do hold that the elements of logic are universal, in the sense that no one reasoning agent is privileged. The logical connectives in particular have the same meanings in all minds.

So my question is, can we replace the word 'model' by the word 'mind', to define "logical constant"?

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    No, formal logic is not about psychology. Commented May 9 at 15:18
  • @mauro-who made the decision that formal logic is not about psychology?
    – lee pappas
    Commented May 9 at 15:25
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    When we say that the binary predicate symbol = is "constant" we mean that we do not change its meaning (equality) when we change context (interpretation). Commented May 9 at 15:53
  • Who made the decision that formal logic is not about psychology? See Mill's psychologism vs Frege's logicism. Note particularly the recent reevaluations plato.stanford.edu/entries/psychologism/#RecReEva
    – Rushi
    Commented May 9 at 16:12
  • a variable can also have the same meaning for all minds once it has been given a value, so a logical constant is not about minds specifically
    – Nikos M.
    Commented May 9 at 16:17

1 Answer 1

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Logical constants are called "constants" to reflect the fact that they have the same meaning across all logical expressions. Do they also end up having the same meaning in all minds? They certainly end up having the same meaning in the minds of those people who understand the definition! Each logical constant is given a definition, and to understand the definition is precisely to end up having the same meaning in your mind as anyone else who understands the definition.

However, we may understand the definition and see that it is wrong. Thus, to define “A implies B” as A ⊃ B is just wrong. There does not seem to be any problem with the negation ¬A, the conjunction A ∧ B, the disjunction A ∨ B, but defining the implication A → B as ¬A ∨ B is just absurd. This is not limited to propositional logic. Defining "Fx implies Gx" as ∀x(Fx ⊃ Gx) is just as absurd.

Thus, while it is easy to understand the definition of the implication A → B as ¬A ∨ B, thereby ending up with the same meaning in our mind as anyone else who understands the definition, we can see that this definition is just wrong.

We all inevitably have the same meaning in mind as to what the implication is, but defining "Fx implies Gx" as ∀x(Fx ⊃ Gx) is not meant to give the correct definition of the notion of implication that we all have in mind. Rather, ∀x(Fx ⊃ Gx) is a translation that is regarded as expedient. It is a crude and inaccurate model but nobody seems to have anything better to offer, so mathematicians just take it because they have nothing else.

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    I fail to see why the definition (if A then B)=not A or B is absurd. It's meaning comes from observations of reality. I hold up a bowl to a child, and say this thing is the bowl. Then i place all of ome apples and all of some bananas in the bowl and say if the thing is an apple then the thing is in the bowl, and if the thing is a banana then the thing is in the bowl. Then I take out all the bananas and say if the thing is an apple then the thing is in the bowl and if the thing is a banana then the thing is not in the bowl. This communicates the words, not, and.
    – lee pappas
    Commented May 9 at 16:53
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    All of the stuff about how a definition can be "wrong" is incoherent. I have no idea what you are getting at. Commented May 9 at 17:28
  • Then to communicate the meaning of OR, place some bananas in the bowl and say if the thing is in the bowl then the thing is an apple or the thing is a banana. Then to communicate the equivalence if A then B = not A or B, all you have to do is say THE THING IS NOT AN APPLE OR THE THING IS IN BOWL.
    – lee pappas
    Commented May 9 at 17:43
  • @leepappas "It's meaning comes from observations of reality." Presumably, but many false theories come from the observation of reality. For the rest, sorry, I am unable to make sense of it. - 2. "Then to communicate the meaning of OR, place some bananas in the bowl and say if the thing is in the bowl then the thing is an apple or the thing is a banana." And that will be true. Commented May 10 at 10:11
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    @speakpigeon, If it is absurd then it implies a contradiction. How does if A then B= not A or B imply a contradiction? In the example I gave, the word OR was used to describe reality, namely "the thing is not an apple OR the thing is in the bowl". Inclusive OR can now be determined. The child can determine the OR statement means the same thing as, "if the thing is an apple then the thing is in the bowl.". Both statements describe reality equivalently. There is no contradiction.
    – lee pappas
    Commented May 10 at 11:56

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