Focus instead on the question: how does this help with the problem we are concerned with? The book is one of the most significant intellectual achievements of the past decades, but it is not clear what, exactly, it accomplishes. The final section offers our own resolution which, however, runs against the foundationalist spirit of the Scottish neo-logicist program. The nature of vagueness: Humpty Dumpty gets his due ; 2. For response-dependence to come into the picture at all, 4 must be true. And what of propositions for which no proof is possible? Logical relativism is a pluralism according to which validity and logical consequence are relative to something. In line with the philosophical account, however, the notion of super-truth does not play a central role in the development of validity.
And I will keep on doing so. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in. In each case, the philosophical picture is developed by extending and modifying the original account. A different concern regarding Shapiro's appeal to response-dependence is that it is not fully clear just what the claim of response-dependence is supposed to amount to. The ultimate goalof the technical aspects of the work is to delimit a plausible notion of logical consequence, and to explore what happens with the sorites paradox.
In line with the philosophical account, however, the notion of super-truth does not play a central role in the development of validity. I suggested above that the scarcity of explicit arguments in Shapiro's book is due to the fact that he thinks the attractiveness of the resulting theory is argument enough. There is no need to blame the phenomenon on any one of those aspects. He argues that the question of meaning shift is itself context-sensitive and interest-relative. Refinements and extensions I: so-called 'higher-order vagueness' ; 6.
It is a commonplace that the extensions of vague terms vary with such contextual factors as the comparison class and paradigm cases. According to one, logic is exempt from, or lies outside the scope of, the attack on the analytic-synthetic distinction. Does the electronic version of the book completely replace the paper version? So ante rem structuralist is a form of ante rem realism concerning universals. She would then avoid embracing the radical iii , but at the seeming 'cost' of denying that the seeming disagreement really is genuine. Consider the following claims one can make about borderline sentences: i Borderline sentences are somehow 'unsettled' or 'open' -- whatever fixes the meanings of the expressions of our language hasn't fixed determinate truth-values for them.
Chapter one lays out the basic elements of the proposed theory of vagueness. It is a commonplace that the extensions of vague terms vary with such contextual factors as the comparison class and paradigm cases. Shapiro takes Wright to subscribe to the open texture thesis he describes. In order to develop the argument fully, the author presents a detailed description of higher-order logic, including a comprehensive discussion of its semantics. So it is not clear what is the relation between it and Shapiro's other theses. We show that the second-order axiom of comprehension applied to non-instantiated properties and the standard first-order existential instantiation and universal elimination principles are essential for the derivation of key results, specifically a theorem of infinity, but have not been shown to be epistemically innocent. A central thesis is that in some cases, a competent speaker of the language can go either way in the borderline area of a vague predicate without sinning against the meaning of the words and the non-linguistic facts.
That everyone agrees on the principle does not mean that everyone in fact can respect it. Crispin Wright introduced into the sorites literature the idea that speakers can permissibly go either way with respect to borderline cases. A proponent of ii can explain instances of seemingly permissible disagreement by saying that the speakers in fact do not assert contradictory propositions. This advances Boolos's longstanding interest in the foundations of set theory. In each case, the philosophical picture is developed by extending and modifying the original account.
Chapter five deals with the problem of higher-order vagueness. Later chapters deal with what passes for higher-order vagueness - vagueness in the tions of 'determinacy' and 'borderline' - and with vague singular terms, or objects. It is also here that the response-dependence comes in. What do mathematical statements mean? Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences. Compare: 1 Speaker judgments help determine that 'F' is true of a. Shapiro devotes a chapter to higher-order vagueness. This distinction is tied to Shapiro's understanding of determinate truth: a sentence is determinately true as used in a given context if and only if its meaning plus the external factors of this context determine it as true.
This paper produces a more Aristotelian theory, eschewing the existence of points and the use of infinite sets or pluralities. I have myself blurred the distinction here, sometimes using 'F' to stand in for a predicate, sometimes using it to stand in for a name of a predicate. I explore some alternatives, relating the developed view to the intuitive, pre-theoretic notion of truth. Finally, after describing how to nominalize our theory, we close with comparisons with earlier efforts related to our own. Best of all, if after reading an e-book, you buy a paper version of Vagueness in Context.