Combining Philosophers

All the ideas for Saunders MacLane, Bernard Linsky and Kent Bach

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38 ideas

2. Reason / D. Definition / 7. Contextual Definition
Contextual definitions eliminate descriptions from contexts [Linsky,B]
2. Reason / D. Definition / 8. Impredicative Definition
'Impredictative' definitions fix a class in terms of the greater class to which it belongs [Linsky,B]
4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
Free logic at least allows empty names, but struggles to express non-existence [Bach]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC could contain a contradiction, and it can never prove its own consistency [MacLane]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
Reducibility says any impredicative function has an appropriate predicative replacement [Linsky,B]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
In first-order we can't just assert existence, and it is very hard to deny something's existence [Bach]
5. Theory of Logic / E. Structures of Logic / 3. Constants in Logic
In logic constants play the role of proper names [Bach]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
Proper names can be non-referential - even predicate as well as attributive uses [Bach]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
Millian names struggle with existence, empty names, identities and attitude ascription [Bach]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / a. Descriptions
An object can be described without being referred to [Bach]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
Definite descriptions can be used to refer, but are not semantically referential [Bach]
Definite descriptions, unlike proper names, have a logical structure [Linsky,B]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / c. Theory of definite descriptions
Definite descriptions theory eliminates the King of France, but not the Queen of England [Linsky,B]
5. Theory of Logic / I. Semantics of Logic / 5. Extensionalism
Extensionalism means what is true of a function is true of coextensive functions [Linsky,B]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
The task of logicism was to define by logic the concepts 'number', 'successor' and '0' [Linsky,B]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
Higher types are needed to distinguished intensional phenomena which are coextensive [Linsky,B]
Types are 'ramified' when there are further differences between the type of quantifier and its range [Linsky,B]
The ramified theory subdivides each type, according to the range of the variables [Linsky,B]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Did logicism fail, when Russell added three nonlogical axioms, to save mathematics? [Linsky,B]
For those who abandon logicism, standard set theory is a rival option [Linsky,B]
8. Modes of Existence / B. Properties / 11. Properties as Sets
Construct properties as sets of objects, or say an object must be in the set to have the property [Linsky,B]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / b. Invariantism
How could 'S knows he has hands' not have a fixed content? [Bach]
If contextualism is right, knowledge sentences are baffling out of their context [Bach]
Sceptics aren't changing the meaning of 'know', but claiming knowing is tougher than we think [Bach]
19. Language / B. Reference / 1. Reference theories
Fictional reference is different inside and outside the fiction [Bach]
We can refer to fictional entities if they are abstract objects [Bach]
You 'allude to', not 'refer to', an individual if you keep their identity vague [Bach]
19. Language / B. Reference / 4. Descriptive Reference / b. Reference by description
What refers: indefinite or definite or demonstrative descriptions, names, indexicals, demonstratives? [Bach]
If we can refer to things which change, we can't be obliged to single out their properties [Bach]
We can think of an individual without have a uniquely characterizing description [Bach]
It can't be real reference if it could refer to some other thing that satisfies the description [Bach]
Since most expressions can be used non-referentially, none of them are inherently referential [Bach]
Just alluding to or describing an object is not the same as referring to it [Bach]
19. Language / B. Reference / 5. Speaker's Reference
Context does not create reference; it is just something speakers can exploit [Bach]
'That duck' may not refer to the most obvious one in the group [Bach]
What a pronoun like 'he' refers back to is usually a matter of speaker's intentions [Bach]
Information comes from knowing who is speaking, not just from interpretation of the utterance [Bach]
19. Language / F. Communication / 5. Pragmatics / a. Contextual meaning
People slide from contextual variability all the way to contextual determination [Bach]