View source for Stephen Yablo

{{short description|Canadian-born American philosopher}}
{{Use mdy dates|date=December 2024}}{{Infobox philosopher
| region           = [[Western philosophy]]
| era              = [[Contemporary philosophy]]
| image            = Stephen Yablo Howison Lecture (cropped).jpg
| caption          = Yablo in 2022 
| name             = Stephen Yablo
| birth_date  = {{birth date and age|1957|09|30|df=y}}
| birth_place = [[Toronto]], Canada
| education        = [[University of Toronto]] <small>([[Bachelor of Science|B.Sc.]])</small><br />[[University of California, Berkeley]] <small>([[Ph.D.]])</small>
| school_tradition = [[Analytic philosophy|Analytic]]
| notable_ideas    = Yablo's paradox
| spouse           = [[Sally Haslanger]]
| main_interests   = [[Philosophical logic]], [[philosophy of language]], [[philosophy of mathematics]], [[philosophy of mind]]
| doctoral_advisor = [[Donald Davidson (philosopher)|Donald Davidson]]
| doctoral_students = [[Carolina Sartorio]]
}}

'''Stephen Yablo''' (born 1957) is a Canadian-born American philosopher. He is the Emeritus David W. Skinner Professor of Philosophy at the [[Massachusetts Institute of Technology]] (MIT) and taught previously at the [[University of Michigan, Ann Arbor]].<ref>{{Cite web |title=Yablo |url=http://www.mit.edu/~yablo/cv.pdf |website=www.mit.edu}}</ref> He specializes in the [[philosophy of logic]], [[philosophy of mind]], [[metaphysics]], [[philosophy of language]], and [[philosophy of mathematics]].

==Life and career==
He was born in [[Toronto]], on 30 September 1957, to a Polish father Saul Yablo and Romanian-Canadian mother Gloria Yablo (née Herman), both [[Jewish]].<ref>{{Cite web |last=Tremain |first=Shelley |author-link=Shelley Lynn Tremain |date=2018-08-15 |title=Dialogues on Disability: Shelley Tremain Interviews Stephen Yablo |url=https://philosophycommons.typepad.com/disability_and_disadvanta/2018/08/dialogues-on-disability-shelley-tremain-interviews-stephen-yablo.html |archive-url=http://web.archive.org/web/20210127004452/https://philosophycommons.typepad.com/disability_and_disadvanta/2018/08/dialogues-on-disability-shelley-tremain-interviews-stephen-yablo.html |archive-date=2021-01-27 |access-date=2024-12-20 |website=Discrimination and Disadvantage}}</ref> He is married to fellow MIT philosopher [[Sally Haslanger]].

His Ph.D. is from [[University of California, Berkeley]], where he worked with [[Donald Davidson (philosopher)|Donald Davidson]] and [[George Myro]]. In 2012, he was elected a Fellow of the [[American Academy of Arts and Sciences]]. 

==Philosophical work==

Yablo has published a number of influential papers in philosophy of mind, philosophy of language, and metaphysics, and gave the [[John Locke Lectures]] at Oxford in 2012, which formed the basis for his book ''Aboutness'', which one reviewer described as "an important and far-reaching book that philosophers will be discussing for a long time."<ref>{{Cite web|url=https://ndpr.nd.edu/news/50261-aboutness/|title = Aboutness| date=10 September 2014 | last1=Morton | first1=Adam }}</ref>

===Yablo's paradox===
In papers published in 1985<ref>{{cite journal | author=S. Yablo |url=https://www.researchgate.net/publication/226983444 |title=Truth and reflection|journal=[[Journal of Philosophical Logic]] |volume=14 |issue=2 |year=1985 |pages=297–348 |doi=10.1007/BF00249368 |s2cid=36735626 }}</ref> and 1993,<ref>{{cite journal|author=S. Yablo|url=https://www.mit.edu/~yablo/pwsr.pdf |title=Paradox Without Self-Reference |journal=[[Analysis (journal)|Analysis]] |volume=53 |issue=4 |year=1993 |pages=251–252 |doi=10.1093/analys/53.4.251 }}</ref> Yablo showed how to create a paradox similar to the [[liar paradox]], but without [[self-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 in ''any'' way circular". However, [[Graham Priest]] disputes this.<ref>{{cite journal | author=G. Priest |title=Yablo's paradox |journal=[[Analysis (journal)|Analysis]] |volume=57 |issue=4 |year=1997 |pages=236–242 |doi=10.1093/analys/57.4.236 | citeseerx=10.1.1.626.8312 }}</ref><ref>{{cite journal | author=J. Beall |url=http://ferenc.andrasek.hu/papersybprx/jcbeal_is_yablo_non_circular.pdf |title=Is Yablo's paradox non-circular? |journal=[[Analysis (journal)|Analysis]] |volume=61 |issue=3 |year=2001 |pages=176–187 |doi=10.1093/analys/61.3.176 }}</ref>

=== Statement ===
Consider the following [[infinite set]] of sentences:
: ''S''<sub>1</sub>: For each ''i'' > 1, ''S<sub>i</sub>'' is not true.
: ''S''<sub>2</sub>: For each ''i'' > 2, ''S<sub>i</sub>'' is not true.
: ''S''<sub>3</sub>: For each ''i'' > 3, ''S<sub>i</sub>'' is not true.
: ...

=== Analysis ===
For any ''n'', the proposition ''S''<sub>''n''</sub> is of universally quantified form, expressing an unending number of claims (each the negation of a statement with a larger index). As a proposition, any ''S''<sub>''n''</sub> also expresses that ''S''<sub>''n + 1''</sub> is not true, for example.

For any pair of numbers ''n'' and ''m'' with ''n < m'', the proposition ''S''<sub>''n''</sub> subsumes all the claims also made by the later ''S''<sub>''m''</sub>. As this holds for all such pairs of numbers, one finds that all ''S''<sub>''n''</sub> imply any ''S''<sub>''m''</sub> with ''n < m''. For example, any ''S''<sub>''n''</sub> implies ''S''<sub>''n + 1''</sub>.

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 any ''S''<sub>''n''</sub> leads to a contradiction. And this just means that all ''S''<sub>''n''</sub> are proven false. 

But all ''S''<sub>''n''</sub> 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.

==== First-order logic ====
For any <math>P</math>, the [[negation introduction]] principle of [[propositional logic]] negates <math>P\leftrightarrow \neg P</math>. 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 <math>Q</math> and if <math>R</math> is an [[Total relation|entire]] [[transitive relation]], then by a formal analysis as above, [[predicate logic]] negates the [[Universal quantification|universal closure]] of
:<math>Q(n) \leftrightarrow \forall i. \big(R(i, n)\to \neg Q(i)\big)</math>
On the natural numbers, for <math>R</math> taken to be equality "<math>=</math>", this also follows from the analysis of the liar paradox. For <math>R</math> taken to be the standard order "<math>></math>", it is still possible to obtain an [[omega-inconsistent]] [[non-standard model of arithmetic]] for the theory defined by adjoining all the equivalences individually.<ref>[https://www.impan.pl/~kz/truthseminar/KetlandSyntheseYablo.pdf Yablo’s Paradox and ω-Inconsistency, Ketland]</ref>

==Books==
*''Thoughts (Philosophical Papers, volume 1)'' (Oxford University Press, 2009)
*''Things (Philosophical Papers, volume 2)'' (Oxford University Press, 2010)
*''Aboutness'' (Princeton University Press, 2014).

==References==
{{Reflist}}

==External links==
* {{cite IEP |url-id=par-liar |title=Liar Paradox}}
* {{cite IEP |url-id=yablo-pa |title=Yablo's Paradox}}
*[https://www.mit.edu/~yablo/pwsr.pdf "Paradox Without Self-Reference"] - ''Analysis'', vol. 53 (1993), pp.&nbsp;251–52
*[https://www.mit.edu/~yablo/mc.pdf "Mental Causation"] - ''The Philosophical Review'', vol. 101, issue 2 (1992), pp.&nbsp;245–280
*[https://www.mit.edu/%7Eyablo/gf.pdf "Go Figure: A Path Through Fictionalism"]
*[https://www.3ammagazine.com/3am//about-aboutness/ Interview] at [[3:AM Magazine]]
*[http://www.whatisitliketobeaphilosopher.com/#/stephen-yablo/ Interview] at ''What is it like to be a philosopher''?

{{Philosophy of language}}
{{Paradoxes}}
{{Authority control}}

{{DEFAULTSORT:Yablo, Stephen}}
[[Category:Analytic philosophers]]
[[Category:American logicians]]
[[Category:Philosophers of mathematics]]
[[Category:Philosophers of mind]]
[[Category:Philosophers of language]]
[[Category:Living people]]
[[Category:Fellows of the American Academy of Arts and Sciences]]
[[Category:University of Michigan faculty]]
[[Category:Year of birth missing (living people)]]
[[Category:Self-referential paradoxes]]