Gabriel Sandu
University of Helsinki,
Finland
SOME REMARKS ON PHILOSOPHY AND LOGIC
In the paper I will show how certain philosophical presuppositions
on the nature of some of our basic logical concepts, have an impact on the
resulting logical systems, or for the solution to some of well known
logical puzzles.
In the Begriffsschrift (1879), Frege was looking for a common
predicate of all judgments, something corresponding to the English
predicate “is a fact”. The particularity of this predicate is that it only
serves to turn content into a judgment. I take Frege to say that “is a fact”
applies to content, without making any contribution to it. The counterpart
of “is a fact” in Frege’s ideography is “⊢”.
By introducing the notion of content into logic, Frege split with
the algebraic tradition of Boole, and Schröder . In Foundations of
mathematics (1925) Ramsey continues this tradition and does something
similar for “is true”: truth applies to content (in the form of belief). Thus
the truth of someone’s (say A’s) belief is to be analyzed as: “it is a belief
that p and p.” Similarly, in certain contexts, “She spoke truly” is to be
analyzed as “She said that p and p.”
Tarski breaks partially with Frege and Ramsey and takes sentences
as truth-bearers. His T-schema initiates also the inferential conception of
truth. In addition to regular or standard sentential naming procedures
(inverted commas) Tarski also introduces structural descriptions. The
derivation of the liar paradox in natural languages employs both devices.
Tarski’s ideas led, through the work of Kripke to truth-value gaps and
trivalent logic. I will take some of the reactions to Tarski’s solution to
the paradoxes to be a revolt against his (partial) elimination of content
from logic. Some of the more recent solutions to the paradoxes (Charles
Parson, Stephen Read) advocate, as we will see, a conception of truth
according to which the truth predicate applies either to propositions or to
what a sentence “says”. As a result, there is no need for truth-value gaps.
Perhaps nowhere is the dispute between the two conceptions better
spelled out that in the following passage:
Truth, as we ordinarily understand the notion, is a property of
things like claims, testimony, assertions, beliefs, statements, or
propositions. It is not a property of sentences. But the decision to use
sentences as the bearers of truth has proven to be a useful fiction, a good
way of getting a certain amount of logic done without bogging down in
extralogical questions about the nature of the bearers of truth. But the
fiction is harmless only in cases we can unambiguously associate a claim
about the world with each sentence, or where the slippage between
different claims made by different uses of a sentence is negligible for the
purposes at hand. (Barwise and Etchmendy 1987).
An interesting elaboration of this claim is to be found in Frapolli
(2013). In the paper I will deepen the debate between the two traditions
and also extend it to bear on the debate between Davidson and Quine on
the interpretation of belief statements and the possibility of modal logic.
References:
1. M. J. Frapolli, The Nature of Truth, Springer, 2013.
2. Ch. Parsons, Mathematics in Philosophy, Cornell University Press,
1983.
3. S. Read, The truth schema and the Liar, in S. Rahman, T. Tulenheimo,
and E. Genot (eds), Unity, Truth, and The Liar, Springer, 2008, Chapter1.
4. J. Barwise and J. Etchmendy, The Liar: An Essay in Truth and
Circularity, Oxford University Press, 1987.