Combining Texts

All the ideas for 'Grundgesetze der Arithmetik 2 (Basic Laws)', 'On the Syllogism IV' and 'Finkish dispositions'

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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]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
De Morgan started the study of relations and their properties [De Morgan, by Walicki]
De Morgan found inferences involving relations, which eluded Aristotle's syllogistic [De Morgan, by Hart,WD]
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]
8. Modes of Existence / B. Properties / 6. Categorical Properties
The distinction between dispositional and 'categorical' properties leads to confusion [Lewis]
8. Modes of Existence / C. Powers and Dispositions / 3. Powers as Derived
All dispositions must have causal bases [Lewis]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / c. Dispositions as conditional
A 'finkish' disposition is real, but disappears when the stimulus occurs [Lewis]
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 / B. Possibility / 9. Counterfactuals
Backtracking counterfactuals go from supposed events to their required causal antecedents [Lewis]
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]