Combining Texts

Ideas for 'fragments/reports', 'The Concept of Truth for Formalized Languages' and 'works'

unexpand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

---

6 ideas

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]
	Full Idea: Tarski showed that the only binary relations invariant under arbitrary permutations are the universal relation, the empty relation, identity and non-identity, thus giving us a reason to include '=' among the logical terms.
	From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Vann McGee - Logical Consequence 6
	A reaction: Tarski was looking for a criterion to distinguish logical from non-logical terms, since his account of logical validity depended on it. This idea lies behind whether a logic is or is not specified to be 'with identity' (i.e. using '=').

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]
	Full Idea: To say that the name x denotes a given object a is the same as to stipulate that the object a ... satisfies a sentential function of a particular type.
	From: Alfred Tarski (The Concept of Truth for Formalized Languages [1933], p.194)

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]
	Full Idea: Tarski discovered how to give a compositional semantics for predicate calculus, defining truth in terms of satisfaction, and showing how satisfaction for a complicated formula depends on satisfaction of the simple subformulas.
	From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Vann McGee - Logical Consequence 4
	A reaction: The problem was that the subformulas may contain free variables, and thus not be sentences with truth values. 'Satisfaction' can handle this, where 'truth' cannot (I think).

19313	Tarksi invented the first semantics for predicate logic, using this conception of truth [Tarski, by Kirkham]
	Full Idea: Tarski invented a formal semantics for quantified predicate logic, the logic of reasoning about mathematics. The heart of this great accomplishment is his theory of truth. It has been called semantic 'theory' of truth, but Tarski preferred 'conception'.
	From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Richard L. Kirkham - Theories of Truth: a Critical Introduction 5.1

5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models

16323	The object language/ metalanguage distinction is the basis of model theory [Tarski, by Halbach]
	Full Idea: Tarski's distinction between object and metalanguage forms the basis of model theory.
	From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Volker Halbach - Axiomatic Theories of Truth 11

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]
	Full Idea: In Tarski's account of truth, self-reference (as found in the Liar Paradox) is prevented because the truth predicate for any given object language is never a part of that object language, and so a sentence can never predicate truth of itself.
	From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Jennifer Fisher - On the Philosophy of Logic 03.I
	A reaction: Thus we solve the Liar Paradox by ruling that 'you are not allowed to say that'. Hm. The slightly odd result is that in any conversation about whether p is true, we end up using (logically speaking) two different languages simultaneously. Hm.