Stephen Yablo | |
|---|---|
.jpg) Yablo in 2022 | |
| Born | (1957-09-30)30 September 1957 (age 68) Toronto, Canada |
| Spouse | Sally Haslanger |
| Education | |
| Education | University of Toronto(B.Sc.) University of California, Berkeley(Ph.D.) |
| Doctoral advisor | Donald Davidson |
| Philosophical work | |
| Era | Contemporary philosophy |
| Region | Western philosophy |
| School | Analytic |
| Doctoral students | Carolina Sartorio |
| Main interests | Philosophical logic,philosophy of language,philosophy of mathematics,philosophy of mind |
| Notable ideas | Yablo's paradox |
Stephen Yablo (/ˈjæbloʊ/;[1] born 1957) is a Canadian-born American philosopher. He is the Emeritus David W. Skinner Professor of Philosophy at theMassachusetts Institute of Technology (MIT) and taught previously at theUniversity of Michigan, Ann Arbor.[2] He specializes in thephilosophy of logic,philosophy of mind,metaphysics,philosophy of language, andphilosophy of mathematics.
He was born inToronto, on 30 September 1957, to a Polish father Saul Yablo and Romanian-Canadian mother Gloria Yablo (née Herman), bothJewish.[3] He is married to fellow MIT philosopherSally Haslanger.
His Ph.D. is fromUniversity of California, Berkeley, where he worked withDonald Davidson andGeorge Myro. In 2012, he was elected a Fellow of theAmerican Academy of Arts and Sciences.
Yablo has published a number of influential papers in philosophy of mind, philosophy of language, and metaphysics, and gave theJohn Locke Lectures at Oxford in 2012, which formed the basis for his bookAboutness, which one reviewer described as "an important and far-reaching book that philosophers will be discussing for a long time."[4]
In papers published in 1985[5] and 1993,[6] Yablo showed how to create a paradox similar to theliar paradox, but withoutself-reference. Unlike the liar paradox, which uses a single sentence,Yablo's paradox uses an infinite list of sentences, each referring to sentences occurring later in the list. Analysis of the list shows that there is no consistent way to assign truth values to any of its members. Since everything on the list refers only to later sentences, Yablo claims that his paradox is "not inany way circular". However,Graham Priest disputes this.[7][8]
Consider the followinginfinite set of sentences:
For anyn, the propositionSn is of universally quantified form, expressing an unending number of claims (each the negation of a statement with a larger index). As a proposition, anySn also expresses thatSn + 1 is not true, for example.
For any pair of numbersn andm withn < m, the propositionSn subsumes all the claims also made by the laterSm. As this holds for all such pairs of numbers, one finds that allSn imply anySm withn < m. For example, anySn impliesSn + 1.
Claims made by any of the propositions ("the next statement is not true") stand in contradiction with an implication we can also logically derive from the lot (the validity of the next statement is implied by the current one). This establishes that assuming anySn leads to a contradiction. And this just means that allSn are proven false.
But allSn being false also exactly validates the very claims made by them. So we have the paradox that each sentence in Yablo's list is both not true and true.
For any, thenegation introduction principle ofpropositional logic negates. So no consistent theory proves that one of its propositions equivalent to itself. Metalogically, it means any axiom of the form of such an equivalence is inconsistent. This is one formal pendant of the liar paradox.
Similarly, for any unary predicate and if is anentiretransitive relation, then by a formal analysis as above,predicate logic negates theuniversal closure of
On the natural numbers, for taken to be equality "", this also follows from the analysis of the liar paradox. For taken to be the standard order "", it is still possible to obtain anon-standard model of arithmetic for theomega-inconsistent theory defined by adjoining all the equivalences individually.[9]
