Combining Texts

All the ideas for 'Frege's Theory of Numbers', 'Grundgesetze der Arithmetik 2 (Basic Laws)' and 'World and Essence'

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24 ideas

2. Reason / D. Definition / 2. Aims of Definition
13886 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
9845 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
10019 Only what is logically complex can be defined; what is simple must be pointed to [Frege]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
9886 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
9889 Real numbers are ratios of quantities [Frege, by Dummett]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17447 Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
10020 Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege]
10553 A number is a class of classes of the same cardinality [Frege, by Dummett]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
9887 Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett]
8751 Only applicability raises arithmetic from a game to a science [Frege]
9. Objects / A. Existence of Objects / 4. Impossible objects
16435 Plantinga proposes necessary existent essences as surrogates for the nonexistent things [Plantinga, by Stalnaker]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
14655 The 'identity criteria' of a name are a group of essential and established facts [Plantinga]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
14658 'Being Socrates' and 'being identical with Socrates' characterise Socrates, so they are among his properties [Plantinga]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
9891 The first demand of logic is of a sharp boundary [Frege]
9. Objects / D. Essence of Objects / 2. Types of Essence
14656 Does Socrates have essential properties, plus a unique essence (or 'haecceity') which entails them? [Plantinga]
9. Objects / D. Essence of Objects / 9. Essence and Properties
14654 Properties are 'trivially essential' if they are instantiated by every object in every possible world [Plantinga]
14653 X is essentially P if it is P in every world, or in every X-world, or in the actual world (and not ¬P elsewhere) [Plantinga]
14660 If a property is ever essential, can it only ever be an essential property? [Plantinga]
14661 Essences are instantiated, and are what entails a thing's properties and lack of properties [Plantinga]
9. Objects / F. Identity among Objects / 5. Self-Identity
14657 Does 'being identical with Socrates' name a property? I can think of no objections to it [Plantinga]
10. Modality / A. Necessity / 4. De re / De dicto modality
14652 'De re' modality is as clear as 'de dicto' modality, because they are logically equivalent [Plantinga]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
14659 We can imagine being beetles or alligators, so it is possible we might have such bodies [Plantinga]
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
9890 The modern account of real numbers detaches a ratio from its geometrical origins [Frege]
18. Thought / E. Abstraction / 8. Abstractionism Critique
11846 If we abstract the difference between two houses, they don't become the same house [Frege]