Question 1We have been clarifying some of Wittgenstein’s syntactacal and semantical vocabulary: “structure”, “(picture) element” are the chief examples of the former. (I’m putting “form” aside since we’re still working on that.) “Depict”, “ represent” and “stand (proxy) for” are the chief examples of the latter. Describe the syntax and semanics of the sentence “Heloise loves Abelard” using this vocabulary. (A short para. should be enough.)
Question 2 TLP 2.17: “What a picture must have in common with reality…if it is to be possible to depict it is its pictorial form”. Why is this surprising, given that Wittgenstein’s talk of pictures or models is supposed to be highly general? (Answer in one or two sentences.)
Question 3: The logic text book we are using offers the following “definition” of the existential quantifier:
To tell whether or not a sentence of the form ∃x(…x…x…) is true: Remove the initial existential quantifier. Pretend that the variable it was binding is a name letter. If there is something that the pretend constant could stand for such that the sentence you now have is true, then the original sentence is true; otherwise it is false. [ch. 3, s. 4, p. 8]
“Pretend that the variable…is a name” sounds a bit strange. Presumably the point is that the variable is (a) like a name in that it is assigned to an object, but (b) unlike a name in that it is not assigned to a particular object once and for all. So we can restate the definition this way:
a sentence of the form ∃x(…x…x…) is true just in case the formula (…x…x…) is true relative to some assignment of the variable x to an object.
Wittgenstein offers the following explanation of“∼∃x(…x…x…):
5.52 If ξ has as its values all the values of a function fx for all values of x, then
N(ξ) = ∼(∃x). f x.
In general, ξ is used as a propositional variable—a variable whose values are propositions. The bar over the variable indicates that the order of the terms doesn’t matter. (See 5.501.) In 5.52, it is stipulated that ξ has as its values all the propositions that are the values of the propositional function fx. So roughly 5.52 tells you to:
(i) take all the names available: a, b, c, d, e,…
(ii) then form from them the propositions fa, fb, fc, fd, fe,.. (these propositions are the values of the propositional function fx for the arguments a, b, c, d…)
(iii) and, finally, form the joint negation: N(fa, fb, fc, fd…) = ∼fa &∼fb &∼fc &∼fd…
Roughly Wittgenstein is defining ∼(∃x). fx as N(ξ) = ∼fa &∼fb &∼fc &∼fd…
Question 3: (a) Given the logic textbook definition, does the truth value of
It is not the case that there are craters on the dark side of the moon caused by collisions with asteroids
depend on what names we have for objects?
(b) Given Wittgenstein’s definition, does the truth value of this same sentence depend on what names we have for objects?
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