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All the ideas for 'Frege's Theory of Numbers', 'Naturalism in Mathematics' and 'Philosophy of Mind'

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64 ideas

1. Philosophy / G. Scientific Philosophy / 1. Aims of Science
There is no such thing as 'science'; there are just many different sciences [Heil]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
'Forcing' can produce new models of ZFC from old models [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
Axiom of Reducibility: propositional functions are extensionally predicative [Maddy]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
'Propositional functions' are propositions with a variable as subject or predicate [Maddy]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
Completed infinities resulted from giving foundations to calculus [Maddy]
Cantor and Dedekind brought completed infinities into mathematics [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
Infinity has degrees, and large cardinals are the heart of set theory [Maddy]
For any cardinal there is always a larger one (so there is no set of all sets) [Maddy]
An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
Theorems about limits could only be proved once the real numbers were understood [Maddy]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
The extension of concepts is not important to me [Maddy]
In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
Frege solves the Caesar problem by explicitly defining each number [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Making set theory foundational to mathematics leads to very fruitful axioms [Maddy]
Unified set theory gives a final court of appeal for mathematics [Maddy]
Set theory brings mathematics into one arena, where interrelations become clearer [Maddy]
Identifying geometric points with real numbers revealed the power of set theory [Maddy]
The line of rationals has gaps, but set theory provided an ordered continuum [Maddy]
Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
Maybe applications of continuum mathematics are all idealisations [Maddy]
Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy]
7. Existence / C. Structure of Existence / 3. Levels of Reality
A higher level is 'supervenient' if it is determined by lower levels, but has its own natural laws [Heil]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy]
8. Modes of Existence / B. Properties / 5. Natural Properties
Functionalists in Fodor's camp usually say that a genuine property is one that figures in some causal laws [Heil]
8. Modes of Existence / B. Properties / 6. Categorical Properties
A stone does not possess the property of being a stone; its other properties make it a stone [Heil]
8. Modes of Existence / B. Properties / 7. Emergent Properties
Complex properties are not new properties, they are merely new combinations of properties [Heil]
Complex properties are just arrangements of simple properties; they do not "emerge" as separate [Heil]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
From the property predicates P and Q, we can get 'P or Q', but it doesn't have to designate another property [Heil]
8. Modes of Existence / B. Properties / 13. Tropes / b. Critique of tropes
The supporters of 'tropes' treat objects as bundles of tropes, when I think objects 'possess' properties [Heil]
9. Objects / E. Objects over Time / 9. Ship of Theseus
If you can have the boat without its current planks, and the planks with no boat, the planks aren't the boat [Heil]
10. Modality / E. Possible worlds / 1. Possible Worlds / c. Possible worlds realism
You can't embrace the formal apparatus of possible worlds, but reject the ontology [Heil]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / a. Idealism
Idealism explains appearances by identifying appearances with reality [Heil]
15. Nature of Minds / A. Nature of Mind / 1. Mind / e. Questions about mind
Different generations focus on either the quality of mind, or its scientific standing, or the content of thought [Heil]
15. Nature of Minds / A. Nature of Mind / 3. Mental Causation
If minds are realised materially, it looks as if the material laws will pre-empt any causal role for mind [Heil]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / a. Consciousness
Whatever exists has qualities, so it is no surprise that states of minds have qualities [Heil]
15. Nature of Minds / B. Features of Minds / 4. Intentionality / a. Nature of intentionality
Propositional attitudes are not the only intentional states; there is also mental imagery [Heil]
15. Nature of Minds / B. Features of Minds / 4. Intentionality / b. Intentionality theories
The widespread externalist view says intentionality has content because of causal links of agent to world [Heil]
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy]
16. Persons / C. Self-Awareness / 4. Errors in Introspection
Error must be possible in introspection, because error is possible in all judgements [Heil]
17. Mind and Body / A. Mind-Body Dualism / 2. Interactionism
If causation is just regularities in events, the interaction of mind and body is not a special problem [Heil]
17. Mind and Body / B. Behaviourism / 2. Potential Behaviour
Disposition is a fundamental feature of reality, since basic particles are capable of endless possible interactions [Heil]
17. Mind and Body / B. Behaviourism / 4. Behaviourism Critique
No mental state entails inevitable behaviour, because other beliefs or desires may intervene [Heil]
17. Mind and Body / C. Functionalism / 3. Psycho-Functionalism
Hearts are material, but functionalism says the property of being a heart is not a material property [Heil]
17. Mind and Body / C. Functionalism / 8. Functionalism critique
If you are a functionalist, there appears to be no room for qualia [Heil]
17. Mind and Body / D. Property Dualism / 1. Reductionism critique
Higher-level sciences cannot be reduced, because their concepts mark boundaries invisible at lower levels [Heil]
Higher-level sciences designate real properties of objects, which are not reducible to lower levels [Heil]
17. Mind and Body / D. Property Dualism / 3. Property Dualism
'Property dualism' says mind and body are not substances, but distinct families of properties [Heil]
17. Mind and Body / E. Mind as Physical / 2. Reduction of Mind
Early identity theory talked of mind and brain 'processes', but now the focus is properties [Heil]
17. Mind and Body / E. Mind as Physical / 3. Eliminativism
It seems contradictory to be asked to believe that we can be eliminativist about beliefs [Heil]
17. Mind and Body / E. Mind as Physical / 5. Causal Argument
The appeal of the identity theory is its simplicity, and its solution to the mental causation problem [Heil]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / a. Physicalism critique
Functionalists emphasise that mental processes are not to be reduced to what realises them [Heil]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
'Multiple realisability' needs to clearly distinguish low-level realisers from what is realised [Heil]
Multiple realisability is not a relation among properties, but an application of predicates to resembling things [Heil]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / c. Knowledge argument
A scientist could know everything about the physiology of headaches, but never have had one [Heil]
18. Thought / A. Modes of Thought / 1. Thought
Is mental imagery pictorial, or is it propositional? [Heil]
18. Thought / A. Modes of Thought / 4. Folk Psychology
Folk psychology and neuroscience are no more competitors than cartography and geology are [Heil]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
Truth-conditions correspond to the idea of 'literal meaning' [Heil]
19. Language / A. Nature of Meaning / 7. Meaning Holism / b. Language holism
To understand 'birds warble' and 'tigers growl', you must also understand 'tigers warble' [Heil]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
If propositions are abstract entities, how do human beings interact with them? [Heil]