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All the ideas for 'Frege philosophy of mathematics', '(Nonsolipsistic) Conceptual Role Semantics' and 'Abstract Objects: a Case Study'

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47 ideas

2. Reason / A. Nature of Reason / 6. Coherence
Reasoning aims at increasing explanatory coherence [Harman]
Reason conservatively: stick to your beliefs, and prefer reasoning that preserves most of them [Harman]
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 / 1. Overview of Logic
We have a theory of logic (implication and inconsistency), but not of inference or reasoning [Harman]
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]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
I might accept P and Q as likely, but reject P-and-Q as unlikely [Harman]
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 / c. Neo-logicism
Mathematics is both necessary and a priori because it really consists of logical truths [Yablo]
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]
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo]
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]
Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo]
We are thought to know concreta a posteriori, and many abstracta a priori [Yablo]
7. Existence / D. Theories of Reality / 2. Realism
Realism is just the application of two-valued semantics to sentences [Dummett]
7. Existence / D. Theories of Reality / 3. Reality
Reality is the overlap of true complete theories [Harman]
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 / 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]
15. Nature of Minds / A. Nature of Mind / 6. Anti-Individualism
There is no natural border between inner and outer [Harman]
We can only describe mental attitudes in relation to the external world [Harman]
15. Nature of Minds / B. Features of Minds / 5. Qualia / c. Explaining qualia
The way things look is a relational matter, not an intrinsic matter [Harman]
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 / D. Concepts / 5. Concepts and Language / a. Concepts and language
Concepts in thought have content, but not meaning, which requires communication [Harman]
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 / A. Nature of Meaning / 6. Meaning as Use
Take meaning to be use in calculation with concepts, rather than in communication [Harman]
The use theory attaches meanings to words, not to sentences [Harman]
19. Language / A. Nature of Meaning / 7. Meaning Holism / c. Meaning by Role
Meaning from use of thoughts, constructed from concepts, which have a role relating to reality [Harman]
Some regard conceptual role semantics as an entirely internal matter [Harman]
The content of thought is relations, between mental states, things in the world, and contexts [Harman]
19. Language / C. Assigning Meanings / 5. Fregean Semantics
Fregean semantics assumes a domain articulated into individual objects [Dummett]
19. Language / F. Communication / 3. Denial
If one proposition negates the other, which is the negative one? [Harman]
19. Language / F. Communication / 6. Interpreting Language / a. Translation
Mastery of a language requires thinking, and not just communication [Harman]
27. Natural Reality / C. Space / 3. Points in Space
Why should the limit of measurement be points, not intervals? [Dummett]