comments on Michael De's "Essentialism, Reference and Quantified Modal Logic"
There were lots of typos in the comments that were presented in html here and there were problems rendering '' with some browsers on some platforms. I've created a .pdf document that contains a corrected, updated version of the comments on Michael De's "Essentialism, Reference and Quantified Modal Logic." and placed it here.
posted by Jesse Butler @ 8:50 AM
2 Comments:
Hey, interesting blog! Thanks for the comments and remarks. I'll try to answer all of the questions as best I can.
"First, how are we to understand the predicate abstract [λ.x(x > 7)]?"
Intuitively, it denotes the class of things (say natural numbers) whose members are greater than 7. In particular, [λ.x(x > 7)](t) is true iff t>7. Sentences with abstracted predicates in which there are no modal operator occurrences in the abstracted predicates are evaluable classically (which is why it is basically pointless to have abstraction in a first-order language without modal operators, unless e.g. you want to make explicit certain scope distinctions).
On the other hand, M,a|= [λ.x([]x > 7)](t) (where M is a model and a a point in M) iff for all b such that Rab, M,b|= []x>7[s] where s: x --> I^M(t,a) is a function taking x to the value of t in M at a; i.e. s(x) is an object assignment to x in M.
"Second, if we reject Quine's claim that de re modal claims make sense only if the particular res is considered under some description, how are we to answer whether a particular cyclist who is also a mathematician is necessarily two-legged?"
According to Marcus (with whom I agree), this is a non-issue because these sorts of properties cannot hold necessarily of anything. If they did they would hold necessarily of everything, in which case they wouldn't be essentialist then anyway (because they would violate her principles (8) and (9)) as you note above. So the answer to the question "Is S necessarily two-legged?" is always "No", and likewise for similar properties.
Your puzzlement expressed in section 2, I think, is due to my poor choice of wording which you quote at length above. In the first sentence, what is "the same" is how we handle non-rigid terms whether they be descriptions or proper names. What is not the same is how they and rigid terms are handled. You're right--the referent of a non-rigid term will vary from world-to-world (otherwise it wouldn't be non-rigid, or just so coincidentally in a given model) but if the modal operator occurs in the predicate abstract (for simplicity, let's ignore other cases), to put it in your terms, when we evaluate the sentence by looking at the other accessible worlds, the referent of the non-rigid term will have been fixed by the interpretation. Having been fixed, we look at the relevant accessible worlds where it exists and see whether it satisfies the formula. E.g. to evaluate [λy.[]A(y)](ιxP(x)) in an interpretation I at w, the referent I(ixP(x),w) of the description is fixed and then we look at all worlds w' such that Rww' and see whether I(ixP(x),w), if it exists there, satisfies A(y).
"One claim is that the property expressed by this predicate abstract need not be essentialist because it is syntactically complex. I'm still a bit unclear on the details of the reasoning. It seems that only predicates of the syntactical form F(x) are candidates for essential ones. Why is this so?"
Traditionally the view has been that essential properties just are (identical to) necessary ones. Recently this has been challenged on account of examples like "being such that p or ~p" which doesn't seem to be essential to a thing because it doesn't tell us anything about a thing's essence. So people have given up the equivalence of necessary properties with essential ones, but I think it's a mistake, or at least a mistake if one gives only this as a reason. We can still maintain the equivalence if properties are genuine monadic ones, for there is no such property necessarily had by everything. Counterexamples given which rely on abstracted predicates show to be inequivalent to monadic ones and thereby fail to be genuine counterexamples. Also it just strikes me as strange to grant that relational properties can be essential to things because essential properties should be about only the individual to which they're essential. (I know that argument is circular or stipulative.)
I look forward to meeting you at the conference.
Cheers,
Michael
Hey, interesting blog! Thanks for the comments and remarks. I'll try to answer all of the questions as best I can.
"First, how are we to understand the predicate abstract [λ.x(x > 7)]?"
Intuitively, it denotes the class of things (say natural numbers) whose members are greater than 7. In particular, [λ.x(x > 7)](t) is true iff t>7. Sentences with abstracted predicates in which there are no modal operator occurrences in the abstracted predicates are evaluable classically (which is why it is basically pointless to have abstraction in a first-order language without modal operators, unless e.g. you want to make explicit certain scope distinctions).
On the other hand, M,a|= [λ.x([]x > 7)](t) (where M is a model and a a point in M) iff for all b such that Rab, M,b|= []x>7[s] where s: x --> I^M(t,a) is a function taking x to the value of t in M at a; i.e. s(x) is an object assignment to x in M.
"Second, if we reject Quine's claim that de re modal claims make sense only if the particular res is considered under some description, how are we to answer whether a particular cyclist who is also a mathematician is necessarily two-legged?"
According to Marcus (with whom I agree), this is a non-issue because these sorts of properties cannot hold necessarily of anything. If they did they would hold necessarily of everything, in which case they wouldn't be essentialist then anyway (because they would violate her principles (8) and (9)) as you note above. So the answer to the question "Is S necessarily two-legged?" is always "No", and likewise for similar properties.
Your puzzlement expressed in section 2, I think, is due to my poor choice of wording which you quote at length above. In the first sentence, what is "the same" is how we handle non-rigid terms whether they be descriptions or proper names. What is not the same is how they and rigid terms are handled. You're right--the referent of a non-rigid term will vary from world-to-world (otherwise it wouldn't be non-rigid, or just so coincidentally in a given model) but if the modal operator occurs in the predicate abstract (for simplicity, let's ignore other cases), to put it in your terms, when we evaluate the sentence by looking at the other accessible worlds, the referent of the non-rigid term will have been fixed by the interpretation. Having been fixed, we look at the relevant accessible worlds where it exists and see whether it satisfies the formula. E.g. to evaluate [λy.[]A(y)](ιxP(x)) in an interpretation I at w, the referent I(ixP(x),w) of the description is fixed and then we look at all worlds w' such that Rww' and see whether I(ixP(x),w), if it exists there, satisfies A(y).
"One claim is that the property expressed by this predicate abstract need not be essentialist because it is syntactically complex. I'm still a bit unclear on the details of the reasoning. It seems that only predicates of the syntactical form F(x) are candidates for essential ones. Why is this so?"
Traditionally the view has been that essential properties just are (identical to) necessary ones. Recently this has been challenged on account of examples like "being such that p or ~p" which doesn't seem to be essential to a thing because it doesn't tell us anything about a thing's essence. So people have given up the equivalence of necessary properties with essential ones, but I think it's a mistake, or at least a mistake if one gives only this as a reason. We can still maintain the equivalence if properties are genuine monadic ones, for there is no such property necessarily had by everything. Counterexamples given which rely on abstracted predicates show to be inequivalent to monadic ones and thereby fail to be genuine counterexamples. Also it just strikes me as strange to grant that relational properties can be essential to things because essential properties should be about only the individual to which they're essential. (I know that argument is circular or stipulative.)
I look forward to meeting you at the conference.
Cheers,
Michael
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