Combining Texts

All the ideas for 'fragments/reports', 'Sources of Knowledge of Mathematics' and 'Semantic Necessity'

unexpand these ideas     |    start again     |     specify just one area for these texts

---

8 ideas

5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic

14620	Theories in logic are sentences closed under consequence, but in truth discussions theories have axioms [Fine,K]
	Full Idea: It is customary in logic to take a theory to be a set of sentences closed under logical consequence, whereas it is common in discussions of theories of truth to take a theory to be an axiomatized theory.
	From: Kit Fine (Semantic Necessity [2010], n8)

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

9545	Late in life Frege abandoned logicism, and saw the source of arithmetic as geometrical [Frege, by Chihara]
	Full Idea: Near the end of his life, Frege completely abandoned his logicism, and came to the conclusion that the source of our arithmetical knowledge is what he called 'the Geometrical Source of Knowledge'.
	From: report of Gottlob Frege (Sources of Knowledge of Mathematics [1922]) by Charles Chihara - A Structural Account of Mathematics Intro n3
	A reaction: We have, rather crucially, lost touch with the geometrical origins of arithmetic (such as 'square' numbers), which is good news for the practice of mathematics, but probably a disaster for the philosophy of the subject.

9. Objects / C. Structure of Objects / 6. Constitution of an Object

6019	If someone squashed a horse to make a dog, something new would now exist [Mnesarchus]
	Full Idea: If, for the sake of argument, someone were to mould a horse, squash it, then make a dog, it would be reasonable for us on seeing this to say that this previously did not exist but now does exist.
	From: Mnesarchus (fragments/reports [c.120 BCE]), quoted by John Stobaeus - Anthology 179.11
	A reaction: Locke would say it is new, because the substance is the same, but a new life now exists. A sword could cease to exist and become a new ploughshare, I would think. Apply this to the Ship of Theseus. Is form more important than substance?

10. Modality / C. Sources of Modality / 1. Sources of Necessity

14530	The role of semantic necessity in semantics is like metaphysical necessity in metaphysics [Fine,K, by Hale/Hoffmann,A]
	Full Idea: Fine's paper argues that the notion of semantic necessity has a role to play in understanding the nature and content of semantics comparable to the role of metaphysical necessity in metaphysics.
	From: report of Kit Fine (Semantic Necessity [2010]) by Bob Hale/ Aviv Hoffmann - Introduction to 'Modality' 2

19. Language / C. Assigning Meanings / 2. Semantics

14618	Semantics is either an assignment of semantic values, or a theory of truth [Fine,K]
	Full Idea: On one view, a semantics for a given language is taken to be an assignment of semantic values to its expressions; according to the other, a semantics is taken to be a theory of truth for that language.
	From: Kit Fine (Semantic Necessity [2010], Intro)
	A reaction: The first is Frege, the second Tarski via Davidson, says Fine. Fine argues against these as the correct alternatives, and says the distinction prevents us understanding what is really going on. He votes for semantics as giving 'semantic requirements'.

14621	Semantics is a body of semantic requirements, not semantic truths or assigned values [Fine,K]
	Full Idea: Semantics should be conceived as a body of semantic requirements or facts - and not as a body of semantic truths, or as an assignment of semantic values.
	From: Kit Fine (Semantic Necessity [2010], 5)
	A reaction: The 'truths' view is Tarski, and the 'values' view is Frege. You'll have to read the Fine paper to grasp his subtle claim.

19. Language / C. Assigning Meanings / 7. Extensional Semantics

14622	Referential semantics (unlike Fregeanism) allows objects themselves in to semantic requirements [Fine,K]
	Full Idea: What distinguishes the referential position in semantics from Fregeanism is that it makes use of de re semantic facts, in which it is required of an object itself that it enter into certain semantic requirements.
	From: Kit Fine (Semantic Necessity [2010], 5)
	A reaction: I have a repugnance to any sort of semantics that involves the objects themselves, even when dealing with proper names. If I talk of 'Napoleon', no small Frenchman is to be found anywhere in my sentences.

19. Language / E. Analyticity / 4. Analytic/Synthetic Critique

14619	The Quinean doubt: are semantics and facts separate, and do analytic sentences have no factual part? [Fine,K]
	Full Idea: The source of the Quinean scepticism about analytic and synthetic is, first, scepticism over whether we can factor truth into a semantic and a factual component, and (second) if we can, is the factual component ever null?
	From: Kit Fine (Semantic Necessity [2010], 1)
	A reaction: You certainly can't grasp 'bachelors are unmarried men' if you haven't grasped the full Woosterian truth about men and marriage. But I could interdefine four meaningless words, so that you could employ them in analytic sentences.