Combining Texts

All the ideas for 'Function and Concept', 'Davidson on himself' and 'Grundgesetze der Arithmetik 2 (Basic Laws)'

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40 ideas

2. Reason / A. Nature of Reason / 5. Objectivity
Truth and objectivity depend on a community of speakers to interpret what they mean [Davidson]
There are no ultimate standards of rationality, since we only assess others by our own standard [Davidson]
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 / A. Syllogistic Logic / 2. Syllogistic Logic
Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
First-level functions have objects as arguments; second-level functions take functions as arguments [Frege]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
Relations are functions with two arguments [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 / 6. Logicism / a. Early logicism
Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [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]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
Frege takes the existence of horses to be part of their concept [Frege, by Sommers]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
Frege allows either too few properties (as extensions) or too many (as predicates) [Mellor/Oliver on Frege]
9. Objects / A. Existence of Objects / 3. Objects in Thought
The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place [Frege]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
The first demand of logic is of a sharp boundary [Frege]
15. Nature of Minds / A. Nature of Mind / 1. Mind / a. Mind
There are no such things as minds, but people have mental properties [Davidson]
17. Mind and Body / D. Property Dualism / 1. Reductionism critique
If the mind is an anomaly, this makes reduction of the mental to the physical impossible [Davidson]
17. Mind and Body / D. Property Dualism / 2. Anomalous Monism
Obviously all mental events are causally related to physical events [Davidson]
There are no strict psychophysical laws connecting mental and physical events [Davidson]
Mental entities do not add to the physical furniture of the world [Davidson]
17. Mind and Body / D. Property Dualism / 3. Property Dualism
The correct conclusion is ontological monism combined with conceptual dualism [Davidson]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
Absence of all rationality would be absence of thought [Davidson]
18. Thought / C. Content / 6. Broad Content
Our meanings are partly fixed by events of which we may be ignorant [Davidson]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
Concepts are the ontological counterparts of predicative expressions [Frege, by George/Velleman]
An assertion about the concept 'horse' must indirectly speak of an object [Frege, by Hale]
A concept is a function whose value is always a truth-value [Frege]
18. Thought / D. Concepts / 4. Structure of Concepts / a. Conceptual structure
Unlike objects, concepts are inherently incomplete [Frege, by George/Velleman]
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 / B. Reference / 5. Speaker's Reference
I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false [Frege]
19. Language / D. Propositions / 6. Propositions Critique
Propositions explain nothing without an explanation of how sentences manage to name them [Davidson]
19. Language / F. Communication / 4. Private Language
Thought is only fully developed if we communicate with others [Davidson]
19. Language / F. Communication / 6. Interpreting Language / c. Principle of charity
There is simply no alternative to the 'principle of charity' in interpreting what others do [Davidson]
25. Social Practice / E. Policies / 5. Education / c. Teaching
Without a teacher, the concept of 'getting things right or wrong' is meaningless [Davidson]
26. Natural Theory / C. Causation / 9. General Causation / b. Nomological causation
Cause and effect relations between events must follow strict laws [Davidson]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
The Ontological Argument fallaciously treats existence as a first-level concept [Frege]