Combining Texts

All the ideas for 'Philosophy of Mathematics', 'A World of Dispositions' and 'Speaking of Objects'

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15 ideas

2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
We can only see an alien language in terms of our own thought structures (e.g. physical/abstract) [Quine]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
"No entity without identity" - our ontology must contain items with settled identity conditions [Quine, by Melia]
8. Modes of Existence / B. Properties / 12. Denial of Properties
There is no proper identity concept for properties, and it is hard to distinguish one from two [Quine]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / e. Dispositions as potential
All structures are dispositional, objects are dispositions sets, and events manifest dispositions [Fetzer]
9. Objects / A. Existence of Objects / 2. Abstract Objects / b. Need for abstracta
Our conceptual scheme becomes more powerful when we posit abstract objects [Quine]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
I prefer 'no object without identity' to Quine's 'no entity without identity' [Lowe on Quine]
9. Objects / C. Structure of Objects / 1. Structure of an Object
All events and objects are dispositional, and hence all structural properties are dispositional [Fetzer]
19. Language / F. Communication / 6. Interpreting Language / b. Indeterminate translation
You could know the complete behavioural conditions for a foreign language, and still not know their beliefs [Quine]
Translation of our remote past or language could be as problematic as alien languages [Quine]
26. Natural Theory / B. Natural Kinds / 2. Defining Kinds
Kinds are arrangements of dispositions [Fetzer]
26. Natural Theory / D. Laws of Nature / 3. Laws and Generalities
Lawlike sentences are general attributions of disposition to all members of some class [Fetzer]