Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Counterparts and Identity' and 'Grundgesetze der Arithmetik 2 (Basic Laws)'

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18 ideas

2. Reason / D. Definition / 2. Aims of Definition
Later Frege held that definitions must fix a function's value for every possible argument [Frege, by Wright,C]
2. Reason / D. Definition / 7. Contextual Definition
We can't define a word by defining an expression containing it, as the remaining parts are a problem [Frege]
2. Reason / D. Definition / 11. Ostensive Definition
Only what is logically complex can be defined; what is simple must be pointed to [Frege]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
To say there could have been people who don't exist, but deny those possible things, rejects Barcan [Stalnaker, by Rumfitt]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
Cardinals say how many, and reals give measurements compared to a unit quantity [Frege]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Real numbers are ratios of quantities [Frege, by Dummett]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
A number is a class of classes of the same cardinality [Frege, by Dummett]
Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett]
Only applicability raises arithmetic from a game to a science [Frege]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
The first demand of logic is of a sharp boundary [Frege]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
Unlike Lewis, I defend an actualist version of counterpart theory [Stalnaker]
If possible worlds really differ, I can't be in more than one at a time [Stalnaker]
If counterparts exist strictly in one world only, this seems to be extreme invariant essentialism [Stalnaker]
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
The modern account of real numbers detaches a ratio from its geometrical origins [Frege]
18. Thought / E. Abstraction / 8. Abstractionism Critique
If we abstract the difference between two houses, they don't become the same house [Frege]
19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
Extensional semantics has individuals and sets; modal semantics has intensions, functions of world to extension [Stalnaker]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]