Combining Texts

All the ideas for 'Frege's Theory of Numbers', 'Quine on Quantifying In' and 'Letters to Leibniz 1'

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4 ideas

5. Theory of Logic / E. Structures of Logic / 1. Logical Form
12220 Is it the sentence-token or the sentence-type that has a logical form? [Fine,K]
     Full Idea: Do we attribute a logical form to a sentence token because it is a token of a type with that form, or do we attribute a logical form to a sentence type because it is a type of a token with that form?
     From: Kit Fine (Quine on Quantifying In [1990], p.110)
     A reaction: Since I believe in propositions (as the unambiguous thought that lies behind a sentence), I take it that logical form concerns propositions, though strict logicians don't like this, for fear that logic spills into psychology.
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
12222 Substitutional quantification is referential quantification over expressions [Fine,K]
     Full Idea: Substitutional quantification may be regarded as referential quantification over expressions.
     From: Kit Fine (Quine on Quantifying In [1990], p.124)
     A reaction: This is an illuminating gloss. Does such quantification involve some ontological commitment to expressions? I feel an infinite regress looming.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17447 Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
     Full Idea: In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal.
     From: report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3
     A reaction: This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'.
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / c. Essence and laws
17009 I won't object if someone shows that gravity consistently arises from the action of matter [Newton]
     Full Idea: If someone explains gravity along with all its laws by the action of some subtle matter, and shows that the motion of the planets and comets will not be disturbed by this matter, I shall be far from objecting.
     From: Isaac Newton (Letters to Leibniz 1 [1693], 1693.10.16)
     A reaction: Important if you think that Newton is the hero of the descriptive regularity theory of laws. Newton probably thought laws came from God, but he wouldn't object to Leibniz's view, that God planted the laws within the matter.