Combining Texts

All the ideas for 'Frege philosophy of mathematics', 'Inverted Earth' and 'De Ente et Essentia (Being and Essence)'

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42 ideas

2. Reason / D. Definition / 5. Genus and Differentia
If definitions must be general, and general terms can't individuate, then Socrates can't be defined [Aquinas, by Cover/O'Leary-Hawthorne]
The definitions expressing identity are used to sort things [Aquinas]
2. Reason / D. Definition / 7. Contextual Definition
A contextual definition permits the elimination of the expression by a substitution [Dummett]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
A prime number is one which is measured by a unit alone [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
A number is a multitude composed of units [Dummett]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The identity of a number may be fixed by something outside structure - by counting [Dummett]
Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Set theory isn't part of logic, and why reduce to something more complex? [Dummett]
7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing
If affirmative propositions express being, we affirm about what is absent [Aquinas]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy [Dummett]
7. Existence / D. Theories of Reality / 2. Realism
Realism is just the application of two-valued semantics to sentences [Dummett]
8. Modes of Existence / B. Properties / 8. Properties as Modes
Properties have an incomplete essence, with definitions referring to their subject [Aquinas]
8. Modes of Existence / D. Universals / 6. Platonic Forms / d. Forms critiques
If the form of 'human' contains 'many', Socrates isn't human; if it contains 'one', Socrates is Plato [Aquinas]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
Nominalism assumes unmediated mental contact with objects [Dummett]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
The existence of abstract objects is a pseudo-problem [Dummett]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
Abstract objects nowadays are those which are objective but not actual [Dummett]
It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett]
'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett]
9. Objects / A. Existence of Objects / 2. Abstract Objects / d. Problems with abstracta
Abstract objects need the context principle, since they can't be encountered directly [Dummett]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
The principle of diversity for corporeal substances is their matter [Aquinas, by Cover/O'Leary-Hawthorne]
9. Objects / D. Essence of Objects / 1. Essences of Objects
It is by having essence that things exist [Aquinas]
9. Objects / D. Essence of Objects / 2. Types of Essence
Specific individual essence is defined by material, and generic essence is defined by form [Aquinas]
9. Objects / D. Essence of Objects / 4. Essence as Definition
The definition of a physical object must include the material as well as the form [Aquinas]
9. Objects / D. Essence of Objects / 5. Essence as Kind
Essence is something in common between the natures which sort things into categories [Aquinas]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
A simple substance is its own essence [Aquinas]
9. Objects / F. Identity among Objects / 2. Defining Identity
Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett]
Frege introduced criteria for identity, but thought defining identity was circular [Dummett]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
Definition of essence makes things understandable [Aquinas]
15. Nature of Minds / B. Features of Minds / 5. Qualia / b. Qualia and intentionality
The Inverted Earth example shows that phenomenal properties are not representational [Block, by Rowlands]
18. Thought / D. Concepts / 4. Structure of Concepts / i. Conceptual priority
Maybe a concept is 'prior' to another if it can be defined without the second concept [Dummett]
An argument for conceptual priority is greater simplicity in explanation [Dummett]
18. Thought / E. Abstraction / 1. Abstract Thought
Abstract terms are acceptable as long as we know how they function linguistically [Dummett]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
There is no reason why abstraction by equivalence classes should be called 'logical' [Dummett, by Tait]
We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus' [Dummett]
18. Thought / E. Abstraction / 8. Abstractionism Critique
To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too [Dummett]
19. Language / C. Assigning Meanings / 3. Predicates
The mind constructs complete attributions, based on the unified elements of the real world [Aquinas]
19. Language / C. Assigning Meanings / 5. Fregean Semantics
Fregean semantics assumes a domain articulated into individual objects [Dummett]
26. Natural Theory / C. Causation / 5. Direction of causation
A cause can exist without its effect, but the effect cannot exist without its cause [Aquinas]
27. Natural Reality / C. Space / 3. Points in Space
Why should the limit of measurement be points, not intervals? [Dummett]