Combining Texts

All the ideas for 'The Gettier Problem', 'Varieties of Ontological Dependence' and 'Grundgesetze der Arithmetik 2 (Basic Laws)'

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21 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 / 4. Real Definition
Real definitions don't just single out a thing; they must also explain its essence [Koslicki]
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]
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 / 4. Axioms for Number / a. Axioms for numbers
It is more explanatory if you show how a number is constructed from basic entities and relations [Koslicki]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege]
A number is a class of classes of the same cardinality [Frege, by Dummett]
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]
7. Existence / C. Structure of Existence / 1. Grounding / b. Relata of grounding
The relata of grounding are propositions or facts, but for dependence it is objects and their features [Koslicki]
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 / D. Essence of Objects / 2. Types of Essence
Modern views want essences just to individuate things across worlds and times [Koslicki]
9. Objects / D. Essence of Objects / 4. Essence as Definition
For Fine, essences are propositions true because of identity, so they are just real definitions [Koslicki]
We need a less propositional view of essence, and so must distinguish it clearly from real definitions [Koslicki]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / b. Gettier problem
A Gettier case is a belief which is true, and its fallible justification involves some luck [Hetherington]
14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
A good explanation captures the real-world dependence among the phenomena [Koslicki]
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
The modern account of real numbers detaches a ratio from its geometrical origins [Frege]
We can abstract to a dependent entity by blocking out features of its bearer [Koslicki]
18. Thought / E. Abstraction / 8. Abstractionism Critique
If we abstract the difference between two houses, they don't become the same house [Frege]