Combining Philosophers

Ideas for Eubulides, Francis de Vitoria and Jos L. Zalabardo

expand these ideas     |    start again     |     choose another area for these philosophers

display all the ideas for this combination of philosophers


15 ideas

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]
5. Theory of Logic / L. Paradox / 1. Paradox
If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
If you say truly that you are lying, you are lying [Eubulides, by Dancy,R]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R]