Combining Texts

All the ideas for 'Logicism and Ontological Commits. of Arithmetic', '(Nonsolipsistic) Conceptual Role Semantics' and 'The Foundations of Mathematics'

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34 ideas

2. Reason / A. Nature of Reason / 6. Coherence
Reasoning aims at increasing explanatory coherence [Harman]
Reason conservatively: stick to your beliefs, and prefer reasoning that preserves most of them [Harman]
3. Truth / F. Semantic Truth / 2. Semantic Truth
Truth in a model is more tractable than the general notion of truth [Hodes]
Truth is quite different in interpreted set theory and in the skeleton of its language [Hodes]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
Infinity: there is an infinity of distinguishable individuals [Ramsey]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
We have a theory of logic (implication and inconsistency), but not of inference or reasoning [Harman]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Higher-order logic may be unintelligible, but it isn't set theory [Hodes]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey]
Identity is a level one relation with a second-order definition [Hodes]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
I might accept P and Q as likely, but reject P-and-Q as unlikely [Harman]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense' [Hodes]
5. Theory of Logic / L. Paradox / 1. Paradox
Contradictions are either purely logical or mathematical, or they involved thought and language [Ramsey]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
Mathematics is higher-order modal logic [Hodes]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
Arithmetic must allow for the possibility of only a finite total of objects [Hodes]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
It is claimed that numbers are objects which essentially represent cardinality quantifiers [Hodes]
Numerical terms can't really stand for quantifiers, because that would make them first-level [Hodes]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey]
7. Existence / D. Theories of Reality / 3. Reality
Reality is the overlap of true complete theories [Harman]
7. Existence / D. Theories of Reality / 7. Fictionalism
Talk of mirror images is 'encoded fictions' about real facts [Hodes]
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
I just confront the evidence, and let it act on me [Ramsey]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
A belief is knowledge if it is true, certain and obtained by a reliable process [Ramsey]
15. Nature of Minds / A. Nature of Mind / 6. Anti-Individualism
There is no natural border between inner and outer [Harman]
We can only describe mental attitudes in relation to the external world [Harman]
15. Nature of Minds / B. Features of Minds / 5. Qualia / c. Explaining qualia
The way things look is a relational matter, not an intrinsic matter [Harman]
18. Thought / D. Concepts / 5. Concepts and Language / a. Concepts and language
Concepts in thought have content, but not meaning, which requires communication [Harman]
19. Language / A. Nature of Meaning / 6. Meaning as Use
Take meaning to be use in calculation with concepts, rather than in communication [Harman]
The use theory attaches meanings to words, not to sentences [Harman]
19. Language / A. Nature of Meaning / 7. Meaning Holism / c. Meaning by Role
Meaning from use of thoughts, constructed from concepts, which have a role relating to reality [Harman]
Some regard conceptual role semantics as an entirely internal matter [Harman]
The content of thought is relations, between mental states, things in the world, and contexts [Harman]
19. Language / F. Communication / 3. Denial
If one proposition negates the other, which is the negative one? [Harman]
19. Language / F. Communication / 6. Interpreting Language / a. Translation
Mastery of a language requires thinking, and not just communication [Harman]