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Saturday, November 15, 2014

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>>LF2. (∃x)Fx & Mp & (∃y)Fy & ~Mp

Actually I am not so sure of this as an interpretation, for it does not capture the 'another person called "Peter"' bit. In classical logic, the constants are not essentially ambiguous, as they are in English.

Right. I made a change.

>>Right. I made a change.

To this:

LF2. (∃x)(∃y)(Fx & Fy & ~(x = y)) & Mp & ~Mp

I still suspect this is incorrect, but I am not an expert. The reason is that in predicate logic (unlike ordinary language) there is no semantic connection between 'being called Peter' and the use of the logical constant for Peter. Thus your formalisation does not imply Ex Fx and Mx. I may be wrong (although pretty sure).

Let's focus on (LF1). I assumed that 'x is called "Peter"' is interchangeable salva significatione with 'x = Peter.' That seems like a harmless assumption. Or can you show that it isn't?

Another assumption I clearly stated above:

>>My analysis assumes that in the original sentence(s) the first USE (not mention) of 'Peter' is replaceable salva significatione by 'he,' and that the antecedent of 'he' is the immediately preceding expression 'Peter.' And the same for the second USE (not mention) of 'Peter.'<<

That seems harmless as well.

No one who understands English will understand 'There is a man named "Peter" and Peter is a musician' as meaning that there are two men being referred to.

I understand your point, but my question is about classical predicate logic. I am 99% certain that classical logic is not allowed to 'see through' the predicate to the assignment of the constant. I agree we can do this in ordinary language. I.e. in English "'this person is called "Peter"' is interchangeable salva significatione with 'this person = Peter.' "

I don't think this holds in classical i.e. formal logic. Of course we can assign the constant 'Peter' to something, but the assignation is not itself a proposition of the calculus. I think Frege himself makes this point.

But this is not a speculative question. Only appeals to authority are valid here.

Well, do the authorities (Frege, Russell, Quine, chiefly) address this question head on? If yes, please cite them.

Is it your point that in MPL (modern predicate logic) it is expressly denied that one can move from

x is called 'N'
to
x = N
?

Or is it your point that nothing in MPL sanctions this move and that the move needs sanction?

And why is this a logical question, strictly speaking, and not a question of the translation of O.L. into logical symbols?

I believe, in the sense of being fairly certain, that it is ill-formed.

On the authorities, Frege says in S&R that if one asserts "Kepler died in misery" then the sense of the sentence does not contain the thought that the name 'Kepler' designates anything. Otherwise we would have to represent the negation not as "Kepler did not die in misery" but as "Kepler did not die in misery OR the name 'Kepler' has no reference".

He is arguing this on the general principle that logic cannot have propositions which assert things about the meaning of those propositions. Tarski made a similar argument. Also Buridan produced many paradoxes caused by doing the same kind of thing.

>>And why is this a logical question, strictly speaking, and not a question of the translation of O.L. into logical symbols?

It is simply about the well-formedness of the predicate calculus.

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