Ideas from 'Carnap and Logical Truth' by Willard Quine [1954], by Theme Structure

[found in 'Ways of Paradox and other essays' by Quine,Willard [Harvard 1976,0-674-94837-8]].

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5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
In order to select the logic justified by experience, we would need to use a lot of logic
                        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.
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
Elementary logic requires truth-functions, quantifiers (and variables), identity, and also sets of variables
                        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 / B. Logical Consequence / 1. Logical Consequence
Logical consequence is marked by being preserved under all nonlogical substitutions
                        Full Idea: Quine's view of logical consequence is that it is when there is no way of uniformly substituting nonlogical expressions in the premises and consequences so that the premises all remain true but the consequence now becomes false.
                        From: report of Willard Quine (Carnap and Logical Truth [1954], p.103) by Theodore Sider - Logic for Philosophy 1.5
                        A reaction: One might just say that the consequence holds if you insert consistent variables for the nonlogical terms, which looks like Aristotle's view of the matter.
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
If logical truths essentially depend on logical constants, we had better define the latter
                        Full Idea: Quine said a logical truth is a truth in which only logical constants occur essentially, ...but then a fruitful definition of 'logical constant' is called for.
                        From: comment on Willard Quine (Carnap and Logical Truth [1954]) by Ian Hacking - What is Logic? §02
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
Set theory was struggling with higher infinities, when new paradoxes made it baffling
                        Full Idea: Unlike elementary logic, the truths of set theory are not obvious. Set theory was straining at the leash of intuition ever since Cantor discovered higher infinites; and with the added impetus of the paradoxes of set theory the leash snapped.
                        From: Willard Quine (Carnap and Logical Truth [1954], II)
                        A reaction: This problem seems to have forced Quine into platonism about sets, because he felt they were essential for mathematics and science, but couldn't be constructed with precision. So they must be real, but we don't quite understand them.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
If set theory is not actually a branch of logic, then Frege's derivation of arithmetic would not be from logic
                        Full Idea: We might say that set theory is not really logic, but a branch of mathematics. This would deprive 'includes' of the status of a logical word. Frege's derivation of arithmetic would then cease to count as a derivation from logic: for he used set theory.
                        From: Willard Quine (Carnap and Logical Truth [1954], II)
                        A reaction: Quine has been making the point that higher infinities and the paradoxes undermine the status of set theory as logic, but he decides to continue thinking of set theory as logic. Critics of logicism frequently ask whether the reduction is to logic.
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
Commitment to universals is as arbitrary or pragmatic as the adoption of a new system of bookkeeping
                        Full Idea: One's hypothesis as to there being universals is at bottom just as arbitrary or pragmatic a matter as one's adoption of a new brand of set theory or even a new system of bookkeeping.
                        From: Willard Quine (Carnap and Logical Truth [1954], x)
                        A reaction: This spells out clearly the strongly pragmatist vein in Quine's thinking.
10. Modality / A. Necessity / 6. Logical Necessity
Frege moved Kant's question about a priori synthetic to 'how is logical certainty possible?'
                        Full Idea: When Kant's arithmetical examples of a priori synthetic judgements were sweepingly disqualified by Frege's reduction of arithmetic to logic, attention moved to the less tendentious and logically prior question 'How is logical certainty possible?'
                        From: Willard Quine (Carnap and Logical Truth [1954], I)
                        A reaction: A nice summary of the story so far, from someone who should know. This still leaves the question open of whether any synthetic truths can be derived from the logical certainties which are available.
12. Knowledge Sources / A. A Priori Knowledge / 7. A Priori from Convention
Examination of convention in the a priori begins to blur the distinction with empirical knowledge
                        Full Idea: In trying to make sense of the role of convention in a priori knowledge, the very distinction between a priori and empirical begins to waver and dissolve.
                        From: Willard Quine (Carnap and Logical Truth [1954], VI)
                        A reaction: This is the next stage in the argument after Wittgenstein presents the apriori as nothing more than what arises from truth tables. The rationalists react by taking us back to the original 'natural light of reason' view. Then we go round again...