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All the ideas for 'Logical Consequence', 'Concepts' and 'The Foundations of Mathematics (2nd ed)'

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32 ideas

1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
Naturalistic philosophers oppose analysis, preferring explanation to a priori intuition [Margolis/Laurence]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 8. Material Implication
A step is a 'material consequence' if we need contents as well as form [Beall/Restall]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Models are mathematical structures which interpret the non-logical primitives [Beall/Restall]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall]
8. Modes of Existence / A. Relations / 4. Formal Relations / b. Equivalence relation
An 'equivalence' relation is one which is reflexive, symmetric and transitive [Kunen]
12. Knowledge Sources / D. Empiricism / 2. Associationism
Modern empiricism tends to emphasise psychological connections, not semantic relations [Margolis/Laurence]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
Body-type seems to affect a mind's cognition and conceptual scheme [Margolis/Laurence]
18. Thought / B. Mechanics of Thought / 4. Language of Thought
Language of thought has subject/predicate form and includes logical devices [Margolis/Laurence]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
Concepts are either representations, or abilities, or Fregean senses [Margolis/Laurence]
18. Thought / D. Concepts / 3. Ontology of Concepts / a. Concepts as representations
A computer may have propositional attitudes without representations [Margolis/Laurence]
Do mental representations just lead to a vicious regress of explanations [Margolis/Laurence]
18. Thought / D. Concepts / 3. Ontology of Concepts / b. Concepts as abilities
Maybe the concept CAT is just the ability to discriminate and infer about cats [Margolis/Laurence]
The abilities view cannot explain the productivity of thought, or mental processes [Margolis/Laurence]
18. Thought / D. Concepts / 4. Structure of Concepts / a. Conceptual structure
Concept-structure explains typicality, categories, development, reference and composition [Margolis/Laurence]
18. Thought / D. Concepts / 4. Structure of Concepts / c. Classical concepts
Classically, concepts give necessary and sufficient conditions for falling under them [Margolis/Laurence]
The classical theory explains acquisition, categorization and reference [Margolis/Laurence]
Typicality challenges the classical view; we see better fruit-prototypes in apples than in plums [Margolis/Laurence]
It may be that our concepts (such as 'knowledge') have no definitional structure [Margolis/Laurence]
18. Thought / D. Concepts / 4. Structure of Concepts / d. Concepts as prototypes
People don't just categorise by apparent similarities [Margolis/Laurence]
Many complex concepts obviously have no prototype [Margolis/Laurence]
Prototype theory categorises by computing the number of shared constituents [Margolis/Laurence]
Complex concepts have emergent properties not in the ingredient prototypes [Margolis/Laurence]
The prototype theory is probabilistic, picking something out if it has sufficient of the properties [Margolis/Laurence]
18. Thought / D. Concepts / 4. Structure of Concepts / f. Theory theory of concepts
The theory theory of concepts says they are parts of theories, defined by their roles [Margolis/Laurence]
The theory theory is holistic, so how can people have identical concepts? [Margolis/Laurence]
18. Thought / D. Concepts / 4. Structure of Concepts / g. Conceptual atomism
Maybe concepts have no structure, and determined by relations to the world, not to other concepts [Margolis/Laurence]
18. Thought / D. Concepts / 5. Concepts and Language / c. Concepts without language
People can formulate new concepts which are only named later [Margolis/Laurence]