Combining Philosophers

Ideas for Herodotus, James Joule and Willard Quine

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8 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic

13010	In order to select the logic justified by experience, we would need to use a lot of logic [Boghossian on Quine]
	Full Idea: Quine ends up with the logic that is maximally justified by experience, ...but a large number of the core principles of logic will have to be used to select the logic that is maximally justified by experience.
	From: comment on Willard Quine (Carnap and Logical Truth [1954]) by Paul Boghossian - Knowledge of Logic p.233
	A reaction: In order to grasp some core principles of logic, you will probably need a certain amount of experience. I take logic to be an abstracted feature of reality (unless it is extended by pure fictions). Some basic logic may be hard wired in us.

9020	My logical grammar has sentences by predication, then negation, conjunction, and existential quantification [Quine]
	Full Idea: We chose a standard grammar in which the simple sentences are got by predication, and all further sentences are generated from these by negation, conjunction, and existential quantification.
	From: Willard Quine (Philosophy of Logic [1970], Ch.3)
	A reaction: It is interesting that we 'choose' our logic, apparently guided by an imperative to achieve minimal ontology. Of these basic ingredients, negation and predication are the more mysterious, especially the latter. Quine is a bit of an 'ostrich' about that.

5. Theory of Logic / A. Overview of Logic / 3. Value of Logic

9028	Maybe logical truth reflects reality, but in different ways in different languages [Quine]
	Full Idea: Perhaps the logical truths owe their truth to certain traits of reality which are reflected in one way by the grammar of our language, in another way by the grammar of another language, and in a third way by the grammar and lexicon of a third language.
	From: Willard Quine (Philosophy of Logic [1970], Ch.7)
	A reaction: This explains Quine's subsequent interest in translation, and the interest of his pupil Davidson in charity, and whether there could actually be rival conceptual schemes. I like the link between logical truths and reality, which follows Russell.

5. Theory of Logic / A. Overview of Logic / 6. Classical Logic

9002	Elementary logic requires truth-functions, quantifiers (and variables), identity, and also sets of variables [Quine]
	Full Idea: Elementary logic, as commonly systematized nowadays, comprises truth-function theory (involving 'or', 'and', 'not' etc.), quantifiers (and their variables), and identity theory ('='). In addition, set theory requires classes among values of variables.
	From: Willard Quine (Carnap and Logical Truth [1954], II)
	A reaction: Quine is famous for trying to squeeze properties out of the picture, which would then block higher-order logics (which quantify over properties). Quine's list gives a nice programme for a student of the philosophy of logic to understand.

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic

13639	Quine says higher-order items are intensional, and lack a clearly defined identity relation [Quine, by Shapiro]
	Full Idea: Quine (in 1941) attacked 'Principia Mathematica' because the items in the range of higher-order variables (attributes etc) are intensional and thus do not have a clearly defined identity relation.
	From: report of Willard Quine (Whitehead and the Rise of Modern Logic [1941]) by Stewart Shapiro - Foundations without Foundationalism 1.3

8789	Various strategies try to deal with the ontological commitments of second-order logic [Hale/Wright on Quine]
	Full Idea: Quine said higher-order logic is 'set theory in sheep's clothing', and there is concern about the ontology that is involved. One approach is to deny quantificational ontological commitments, or say that the entities involved are first-order objects.
	From: comment on Willard Quine (Existence and Quantification [1966]) by B Hale / C Wright - Logicism in the 21st Century 8
	A reaction: [compressed] The second strategy is from Boolos. This question seems to be right at the heart of the strategy of exploring our ontology through the study of our logic.

10014	Quine rejects second-order logic, saying that predicates refer to multiple objects [Quine, by Hodes]
	Full Idea: Quine is unwilling to suppose second-order logic intelligible. He holds to Mill's account of the referential role of a predicate: it multiply denotes any and all objects to which it applies, and there is no need for a further 'predicative' entity.
	From: report of Willard Quine (Philosophy of Logic [1970]) by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.130
	A reaction: If we assume that 'quantifying over' something is a commitment to its existence, then I think I am with Quine, because you end up with a massive commitment to universals, which I prefer to avoid.

10828	Quantifying over predicates is treating them as names of entities [Quine]
	Full Idea: To put the predicate letter 'F' in a quantifier is to treat predicate position suddenly as name position, and hence to treat predicates as names of entities of some sort.
	From: Willard Quine (Philosophy of Logic [1970], Ch.5)
	A reaction: It is tricky to distinguish quantifying over predicates in a first-order way (by reifying them), and in a second-order way (where it is not clear whether you are quantifying over a property or a unified set of things.