Combining Texts

All the ideas for 'fragments/reports', 'Elucidation of some points in E.Schrder' and 'Grundgesetze der Arithmetik 2 (Basic Laws)'

expand these ideas     |    start again     |     specify just one area for these texts


17 ideas

1. Philosophy / D. Nature of Philosophy / 4. Divisions of Philosophy
Six parts: dialectic, rhetoric, ethics, politics, physics, theology [Cleanthes, by Diog. Laertius]
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 / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
A class is an aggregate of objects; if you destroy them, you destroy the class; there is no empty class [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 / 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]
17. Mind and Body / A. Mind-Body Dualism / 8. Dualism of Mind Critique
Bodies interact with other bodies, and cuts cause pain, and shame causes blushing, so the soul is a body [Cleanthes, by Nemesius]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
The soul suffers when the body hurts, creates redness from shame, and pallor from fear [Cleanthes]
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]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
The ascending scale of living creatures requires a perfect being [Cleanthes, by Tieleman]