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All the ideas for 'Frege philosophy of mathematics', 'Kinds of Minds' and 'Barcan Formulae'

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40 ideas

2. Reason / D. Definition / 7. Contextual Definition
A contextual definition permits the elimination of the expression by a substitution [Dummett]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
Barcan:nothing comes into existence; Converse:nothing goes out; Both:domain is unchanging [Vervloesem]
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 / 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 / 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 / 1. Mind / e. Questions about mind
Minds are hard-wired, or trial-and-error, or experimental, or full self-aware [Dennett, by Heil]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / a. Consciousness
Sentience comes in grades from robotic to super-human; we only draw a line for moral reasons [Dennett]
15. Nature of Minds / B. Features of Minds / 5. Qualia / a. Nature of qualia
What is it like to notice an uncomfortable position when you are asleep? [Dennett]
16. Persons / B. Nature of the Self / 6. Self as Higher Awareness
Being a person must involve having second-order beliefs and desires (about beliefs and desires) [Dennett]
17. Mind and Body / C. Functionalism / 6. Homuncular Functionalism
We descend from robots, and our intentionality is composed of billions of crude intentional systems [Dennett]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
There is no more anger in adrenaline than silliness in a bottle of whiskey [Dennett]
17. Mind and Body / E. Mind as Physical / 3. Eliminativism
Maybe there is a minimum brain speed for supporting a mind [Dennett]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
The materials for a mind only matter because of speed, and a need for transducers and effectors [Dennett]
18. Thought / B. Mechanics of Thought / 4. Language of Thought
The predecessor and rival of the language of thought hypothesis is the picture theory of ideas [Dennett]
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 / b. Concepts are linguistic
Concepts are things we (unlike dogs) can think about, because we have language [Dennett]
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 / 5. Fregean Semantics
Fregean semantics assumes a domain articulated into individual objects [Dummett]
25. Social Practice / F. Life Issues / 3. Abortion
Most people see an abortion differently if the foetus lacks a brain [Dennett]
27. Natural Reality / C. Space / 3. Points in Space
Why should the limit of measurement be points, not intervals? [Dummett]
27. Natural Reality / G. Biology / 2. Life
Maybe plants are very slow (and sentient) animals, overlooked because we are faster? [Dennett]