Combining Texts

All the ideas for 'Academica', 'Constructibility and Mathematical Existence' and 'Carnap and Logical Truth'

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

20 ideas

2. Reason / C. Styles of Reason / 1. Dialectic
2661 Dialectic is speech cast in the form of logical argument [Cicero]
3. Truth / A. Truth Problems / 1. Truth
2673 There cannot be more than one truth [Cicero]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
8758 We could talk of open sentences, instead of sets [Chihara, by Shapiro]
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]
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]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
13681 Logical consequence is marked by being preserved under all nonlogical substitutions [Quine, by Sider]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
2669 Dialectic assumes that all statements are either true or false, but self-referential paradoxes are a big problem [Cicero]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
13829 If logical truths essentially depend on logical constants, we had better define the latter [Hacking on Quine]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
9003 Set theory was struggling with higher infinities, when new paradoxes made it baffling [Quine]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
10265 Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro]
8759 We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
9004 If set theory is not actually a branch of logic, then Frege's derivation of arithmetic would not be from logic [Quine]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
10264 Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro]
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
9006 Commitment to universals is as arbitrary or pragmatic as the adoption of a new system of bookkeeping [Quine]
10. Modality / A. Necessity / 6. Logical Necessity
9001 Frege moved Kant's question about a priori synthetic to 'how is logical certainty possible?' [Quine]
12. Knowledge Sources / A. A Priori Knowledge / 7. A Priori from Convention
9005 Examination of convention in the a priori begins to blur the distinction with empirical knowledge [Quine]
12. Knowledge Sources / B. Perception / 1. Perception
2664 If we have complete healthy senses, what more could the gods give us? [Cicero]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
2665 How can there be a memory of what is false? [Cicero]
13. Knowledge Criteria / D. Scepticism / 3. Illusion Scepticism
20800 Every true presentation can have a false one of the same quality [Cicero]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
2672 Virtues must be very detached, to avoid being motivated by pleasure [Cicero]