Combining Philosophers

Ideas for Horsten,L/Pettigrew,R, Hermarchus and Alfred Tarski

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24 ideas

5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
10152 Set theory and logic are fairy tales, but still worth studying [Tarski]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
10048 There is no clear boundary between the logical and the non-logical [Tarski]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
13337 A language: primitive terms, then definition rules, then sentences, then axioms, and finally inference rules [Tarski]
5. Theory of Logic / A. Overview of Logic / 9. Philosophical Logic
18739 Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
18812 Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match [Tarski, by Rumfitt]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10694 Logical consequence is when in any model in which the premises are true, the conclusion is true [Tarski, by Beall/Restall]
10479 Logical consequence: true premises give true conclusions under all interpretations [Tarski, by Hodges,W]
13344 X follows from sentences K iff every model of K also models X [Tarski]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
19192 The truth definition proves semantic contradiction and excluded middle laws (not the logic laws) [Tarski]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
18759 Identity is invariant under arbitrary permutations, so it seems to be a logical term [Tarski, by McGee]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
18741 Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
10823 A name denotes an object if the object satisfies a particular sentential function [Tarski]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
18756 Tarski built a compositional semantics for predicate logic, from dependent satisfactions [Tarski, by McGee]
19313 Tarksi invented the first semantics for predicate logic, using this conception of truth [Tarski, by Kirkham]
13335 Semantics is the concepts of connections of language to reality, such as denotation, definition and truth [Tarski]
13336 A language containing its own semantics is inconsistent - but we can use a second language [Tarski]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
13339 A sentence is satisfied when we can assert the sentence when the variables are assigned [Tarski]
13340 Satisfaction is the easiest semantical concept to define, and the others will reduce to it [Tarski]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
13343 A 'model' is a sequence of objects which satisfies a complete set of sentential functions [Tarski]
16323 The object language/ metalanguage distinction is the basis of model theory [Tarski, by Halbach]
18744 Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew]
5. Theory of Logic / K. Features of Logics / 2. Consistency
13341 Using the definition of truth, we can prove theories consistent within sound logics [Tarski]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
8940 Tarski avoids the Liar Paradox, because truth cannot be asserted within the object language [Tarski, by Fisher]
19187 The Liar makes us assert a false sentence, so it must be taken seriously [Tarski]