Combining Philosophers

All the ideas for Alistair Mitchell, Richard Wollheim and Jos L. Zalabardo

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35 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo]
A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
Determinacy: an object is either in a set, or it isn't [Zalabardo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / l. Axiom of Specification
Specification: Determinate totals of objects always make a set [Zalabardo]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
A first-order 'sentence' is a formula with no free variables [Zalabardo]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo]
Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / b. Basic connectives
Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo]
We can do semantics by looking at given propositions, or by building new ones [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth
We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
'Logically true' (|= φ) is true for every truth-assignment [Zalabardo]
Logically true sentences are true in all structures [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo]
Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
If a set is defined by induction, then proof by induction can be applied to it [Zalabardo]
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
Classes rarely share properties with their members - unlike universals and types [Wollheim]
14. Science / C. Induction / 3. Limits of Induction
Maybe induction is only reliable IF reality is stable [Mitchell,A]
15. Nature of Minds / C. Capacities of Minds / 4. Objectification
We often treat a type as if it were a sort of token [Wollheim]
21. Aesthetics / A. Aesthetic Experience / 2. Aesthetic Attitude
Interpretation is performance for some arts, and critical for all arts [Wollheim]
A love of nature must precede a love of art [Wollheim]
21. Aesthetics / B. Nature of Art / 1. Defining Art
A criterion of identity for works of art would be easier than a definition [Wollheim]
21. Aesthetics / B. Nature of Art / 2. Art as Form
If beauty needs organisation, then totally simple things can't be beautiful [Wollheim]
21. Aesthetics / B. Nature of Art / 4. Art as Expression
Some say art must have verbalisable expression, and others say the opposite! [Wollheim]
It is claimed that the expressive properties of artworks are non-physical [Wollheim]
21. Aesthetics / B. Nature of Art / 6. Art as Institution
Style can't be seen directly within a work, but appreciation needs a grasp of style [Wollheim]
The traditional view is that knowledge of its genre to essential to appreciating literature [Wollheim]
21. Aesthetics / B. Nature of Art / 7. Ontology of Art
If artworks are not physical objects, they are either ideal entities, or collections of phenomena [Wollheim]
The ideal theory says art is an intuition, shaped by a particular process, and presented in public [Wollheim]
The ideal theory of art neglects both the audience and the medium employed [Wollheim]
A musical performance has virtually the same features as the piece of music [Wollheim]
21. Aesthetics / B. Nature of Art / 8. The Arts / a. Music
An interpretation adds further properties to the generic piece of music [Wollheim]
21. Aesthetics / C. Artistic Issues / 3. Artistic Representation
A drawing only represents Napoleon if the artist intended it to [Wollheim]