Reflective Equilibrium and the Principles of Logical Analysis by Peregrin Jaroslav Svoboda Vladimír & Vladimír Svoboda

Author:Peregrin, Jaroslav,Svoboda, Vladimír & Vladimír Svoboda
Language: eng
Format: epub
Publisher: Taylor & Francis (CAM)

6.4 Do Logical Forms Have Truth Conditions?

There might seem to be one more way to reconcile the semantic criterion in the spirit of (TC) with the notion of formalization as aiming at the logical form (not structure). The form contains parameters, uninterpreted symbols, and hence it can be interpreted in various ways. In other words, there are various interpretations of the formula with respect to each of which the formula acquires a truth value. This may invite the following parallel between the formula and the natural language statement, the form of which the formula purports to represent: while the truth value of the statement of the natural language is generally variable and it depends on circumstances/states-of-affairs/possible-worlds, that of the formula is also generally variable and it depends of interpretations (assuming that we take the actual state of the world the statement is supposed to describe as given). Hence, insofar as we are able to consider interpretations as counterparts (explications?) of circumstances/states-of-affairs/possible-worlds, it would seem that we can compare the truth conditions of statements and parametric formulas.

Let us, before continuing, give an example of such an approach. In their ambitious attempt to present a comprehensive account of logical formalization, Baumgartner and Lampert (2008) formulate their semantic criterion in the following way (p. 112):

(ADS) The formalization Φ of a text T is adequate iff (TC′Τ) is satisfied and Φ is at least as similar to T as any other equivalent formula that satisfies (TC′ Τ).16

A text, according to them, is composed of a set of statements; and if A1 ,…, A n are the statements of which T is composed, the criterion (TC′Τ) referred to by (ADS) says (p. 109):

(TC′Τ) The formalization Φ of a text T is correct and complete iff (TC′) is satisfied for all formalizations Φ1 ,…, Φ n of A 1 ,…, A n and for Φ of T, such that Φ is a truth-function of Φ1 ,…, Φ n

The criterion (TC′) referred to by (TC′T in turn says (p. 108):

(TC′) The formalization Φ of a statement S is correct and complete iff relative to all interpretations I of Φ, Φ has the same conditions of truth and falsehood as S has according to the informal judgement.17

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.