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All the ideas for 'Grundgesetze der Arithmetik 2 (Basic Laws)', 'fragments/reports' and 'Propositions'

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30 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]
2. Reason / E. Argument / 1. Argument
Arguers often turn the opponent's modus ponens into their own modus tollens [Merricks]
3. Truth / F. Semantic Truth / 2. Semantic Truth
'Snow is white' only contingently expresses the proposition that snow is white [Merricks]
4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
Simple Quantified Modal Logc doesn't work, because the Converse Barcan is a theorem [Merricks]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
The Converse Barcan implies 'everything exists necessarily' is a consequence of 'necessarily, everything exists' [Merricks]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Sentence logic maps truth values; predicate logic maps objects and sets [Merricks]
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]
9. Objects / E. Objects over Time / 12. Origin as Essential
In twinning, one person has the same origin as another person [Merricks]
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 / A. Nature of Meaning / 1. Meaning
I don't accept that if a proposition is directly about an entity, it has a relation to the entity [Merricks]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
A sentence's truth conditions depend on context [Merricks]
19. Language / D. Propositions / 1. Propositions
Propositions are standardly treated as possible worlds, or as structured [Merricks]
'Cicero is an orator' represents the same situation as 'Tully is an orator', so they are one proposition [Merricks]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
Propositions are necessary existents which essentially (but inexplicably) represent things [Merricks]
True propositions existed prior to their being thought, and might never be thought [Merricks]
The standard view of propositions says they never change their truth-value [Merricks]
19. Language / D. Propositions / 3. Concrete Propositions
Propositions can be 'about' an entity, but that doesn't make the entity a constituent of it [Merricks]
Early Russell says a proposition is identical with its truthmaking state of affairs [Merricks]
19. Language / D. Propositions / 5. Unity of Propositions
Unity of the proposition questions: what unites them? can the same constituents make different ones? [Merricks]
We want to explain not just what unites the constituents, but what unites them into a proposition [Merricks]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
Critolaus redefined Aristotle's moral aim as fulfilment instead of happiness [Critolaus, by White,SA]