Combining Texts

All the ideas for 'The Case against Closure (and reply)', 'Knowledge First (and reply)' and 'Grundgesetze der Arithmetik 1 (Basic Laws)'

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27 ideas

5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
Frege considered definite descriptions to be genuine singular terms [Frege, by Fitting/Mendelsohn]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Real numbers are ratios of quantities, such as lengths or masses [Frege]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright]
Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
My Basic Law V is a law of pure logic [Frege]
11. Knowledge Aims / A. Knowledge / 7. Knowledge First
We don't acquire evidence and then derive some knowledge, because evidence IS knowledge [Williamson]
Knowledge is prior to believing, just as doing is prior to trying to do [Williamson]
Belief explains justification, and knowledge explains belief, so knowledge explains justification [Williamson]
A neutral state of experience, between error and knowledge, is not basic; the successful state is basic [Williamson]
Internalism about mind is an obsolete view, and knowledge-first epistemology develops externalism [Williamson]
Knowledge-first says your total evidence IS your knowledge [Williamson]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / b. Direct realism
Surely I am acquainted with physical objects, not with appearances? [Williamson]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / c. Knowledge closure
Closure says if you know P, and also know P implies Q, then you must know Q [Dretske]
We needn't regret the implications of our regrets; regretting drinking too much implies the past is real [Dretske]
Knowing by visual perception is not the same as knowing by implication [Dretske]
Reasons for believing P may not transmit to its implication, Q [Dretske]
The only way to preserve our homely truths is to abandon closure [Dretske]
P may imply Q, but evidence for P doesn't imply evidence for Q, so closure fails [Dretske]
We know past events by memory, but we don't know the past is real (an implication) by memory [Dretske]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
A concept is a function mapping objects onto truth-values, if they fall under the concept [Frege, by Dummett]
Frege took the study of concepts to be part of logic [Frege, by Shapiro]
19. Language / C. Assigning Meanings / 2. Semantics
How does inferentialism distinguish the patterns of inference that are essential to meaning? [Williamson]
Internalist inferentialism has trouble explaining how meaning and reference relate [Williamson]
Inferentialist semantics relies on internal inference relations, not on external references [Williamson]
19. Language / C. Assigning Meanings / 7. Extensional Semantics
Truth-conditional referential semantics is externalist, referring to worldly items [Williamson]