Topoï : Epistemology of Mathematics

The next volume of Topoï has several articles about the epistemology of Mathematics : innateness of mathematical concepts, intuition of mathematical objects, mathematical knowledge. Worth reading for all interested in Philosophy of Mathematics and mathematical cognition !

The Epistemological Argument against Mathematical Platonism

I found a few weeks ago this call for proposals :

"Call for Proposals:
Just the Arguments: 100 of the Most Important Arguments in Western Philosophy

Wiley-Blackwell is pleased to announce a call for proposals for Just the Arguments: 100 of the Most Important Arguments in Western Philosophy, edited by Michael Bruce and Steven Barbone. The completed text will be a survey and presentation of 100 of the most important arguments in Western philosophy, wherein experts will write brief encyclopedia-like entries presenting arguments in their essence, including a representative quotation, explication of the context and aim of the argument, and the argument’s logical form. "

An philosophical encyclopedia like this one is a very interesting manual for students, amateurs and professional in Philosophy. I am willing to answer this call. Here is my contribution. Any comments are welcome.

A description of the call for proposal can be found here.

Coconut-carrying Octopus

Julian K. Finn (Victoria Museum, Australia), Tom Tregenza (University of Exeter, UK), and Mark D. Norman (Victoria Museum, Australia) have found that invertrabae can show cognitive sophistication by filming octopuses using a tool. Here are the summary of the paper, videos about the phenomenon, and a link to the fullpaper.

SUMMARY :

"The use of tools has become a benchmark for cognitive sophistication. Originally regarded as a defining feature of our species, tool-use behaviours have subsequently been revealed in other primates and a growing spectrum of mammals and birds. Among invertebrates, however, the acquisition of items that are deployed later has not previously been reported. We repeatedly observed soft-sediment dwelling octopuses carrying around coconut shell halves, assembling them as a shelter only when needed. Whilst being carried, the shells offer no protection and place a requirement on the carrier to use a novel and cumbersome form of locomotion — ‘stilt-walking’."

As it is shown in the videos (see at the end of the post), they are one-coconut-carrying and two-coconuts-carrying octopuses. Instance of coconut's use is : sheltering against unknown intruder in the field (the octopus flees in the half of the empty coconut to escape the human observer).

VIDEOS :



Another video on the BBC website (with commentaries about the paper and remarks by biologists, including the authors of the paper) : Octopus snatches coconut and runs.

Other videos can be found on Current Biology, in the online version of the paper : Julian K. Finn1, Tom Tregenza, and Mark D. Norman, "Defensive tool use in a coconut-carrying octopus", Current Biology, Volume 19, Issue 23, R1069-R1070, 15 December 2009. (Full-text.)

A Survey of philosophers' views

The PhilPapers Survey was a survey of professional philosophers and others on their philosophical views, carried out in November 2009. The Survey was taken by 3226 respondents, including 1803 philosophy faculty members and/or PhDs and 829 philosophy graduate students. The preliminary results can be found on "Preliminary results". Others results are coming soon. Materials can be downloaded on this page.

Work done by David Chalmers and David Bourget.

Aristotelian Society and Mind Association : Call for Papers for the 2010 Conference

The call for papers reads as following :

"CALL FOR PAPERS

2010 JOINT SESSION OF THE ARISTOTELIAN SOCIETY AND THE MIND ASSOCIATION. UNIVERSITY COLLEGE, DUBLIN, 9TH –11TH JULY

The Joint Session is the annual conference of The Aristotelian Society held in conjunction with The Mind Association. It is the largest and primary conference for philosophers in the UK. There is a wide subject base and international speaker profile.



OPEN SESSIONS

A number of parallel sessions on Saturday and Sunday afternoons will be available for the presentation of papers not previously published. There will be a considerable number of these sessions available, allowing room for many submissions to be included. The intention is to accommodate all philosophical material suitable for presentation to a professional audience, so far as time and space in the programme allow, and not to operate a selective policy.

Each presentation should last no more than 20 minutes, so that a further 10-15 minutes may be allowed for discussion. Presented papers should aim to introduce material involving recent research. There are no restrictions on the areas of philosophy which papers may address. Philosophers whose papers are included in this part of the programme must be or become subscribing members of one of the organising societies.

Those wishing to make a presentation should submit by e-mail attachment a copy of their paper (no more than 2000 words), together with a 250-word abstract, to jointsession@ucd.ie by 1st February 2010. Decisions on whether papers have been accepted will be made by the end of March 2010. Authors wishing for an earlier response should submit papers as early as possible.

Papers accepted for the Open Sessions will not be published in the Supplementary Volume of the Aristotelian Society (unlike papers invited for the plenary programme of the conference); and expenses will not be paid.



POSTGRADUATE SESSIONS

Two parallel sessions on the Saturday afternoon will be devoted to short presentations by graduate students (or those who have recently obtained a postgraduate degree). Each student should speak for 20 minutes, allowing 10 minutes for discussion.

Students wishing to participate should send their paper, preferably by attachment in Word 98 or higher, otherwise in two hard copies, by 1st February 2010 to: The Executive Secretary, The Aristotelian Society, Room 281, Stewart House, Russell Square, London WC1B 5DN. Email: mail@aristoteliansociety.org.uk.

The paper should be about 2000 words but no more than 2500 words, including notes and bibliography, and should begin with a brief abstract. It should be typewritten in 12-point text, single-spaced throughout (i.e. including references and quotations), on one side of white A4 paper. All pages should be numbered and have margins of 1 inch or more. Papers containing symbols liable to distortion in transmission should be submitted as hard copies; otherwise electronic copy is welcome.

Please ensure that there are no self-identifying references in the text. Submissions should be accompanied by a separate page containing the title of the paper, the name of the author, institution and status, and email and postal addresses.

Authors are advised to consult supervisors about what may be suitable for presentation to a largely professional audience. Given the tight word-limit, they are advised to give as much space as they can to the statement of their own ideas.

The papers will be sent to referees, and a maximum of eight will be selected for presentation at the Joint Session. The programme will be settled in May 2010.

The selected authors will have their conference fee and accommodation expenses (but not their travel costs) paid by the Mind Association and the Aristotelian Society.

Some papers may subsequently be considered for publication in the Proceedings of the Aristotelian Society.


Nobody should submit a paper for both the Postgraduate and the Open Sessions, and only one paper may be submitted per individual. However, graduate students whose submission for the Postgraduate Sessions is unsuccessful may subsequently be advised that their paper has been accepted for the Open Sessions. Conference costs will not be paid by the organisers.



INVITED SPEAKERS

Inaugural Address – Anthony Duff

Symposia:

Rowland Stout and Mitch Green

Robert Audi and Jonathan Dancy

Miranda Fricker and Michael Brady

Dean Zimmerman and Penelope Mackie

Tim Maudlin and Cian Dorr

Peter Simons and Fraser McBride



For information about the Aristotelian Society & the Joint Session see: http://www.aristoteliansociety.org.uk

Phil Joyce
Executive Administrator
The Aristotelian Society
email: mail@aristoteliansociety.org.uk
website: http://www.aristoteliansociety.org.uk
Tel: +44 (0) 20 7862 8685

The Aristotelian Society is a charity registered in the UK. Registered address: Room 281, Stewart House, Russell Square, London, WC1B 5DN. Reg charity no. 254021."

Studia Logica : Call for Papers about Trends in Philosophy of Mathematics

It reads as following :

"Call for Papers

Special Issue of Studia Logica on the Philosophy of Mathematics

Guest editors: André Fuhrmann, Ivan Kasa and Manfred Kupffer

For a special issue of Studia Logica, we invite papers that contribute to and try to advance current debates in the Philosophy of Mathematics. Accepted papers will be published together with selected proceedings from this year's conference Trends in the Philosophy of Mathematics, which has taken place in Frankfurt, Sep.1-4, 2009. Authors are invited to submit an anonymized paper, including an abstract, and a separate title-page including name, affiliation, title of the paper, and contact information. Submissions should be in PDF format. Please submit your paper no later than December 1st, 2009 by email to trends@uni-frankfurt.de

André Fuhrmann
Ivan Kasa
Manfred Kupffer

Goethe-University Frankfurt am Main"

However, the deadline for the special issue of Studia Logica has been moved to January 15th,2010.

Marc Jeannerod en librairie

Le bal des ardents, une librairie lyonnaise, organise le 2/12/2009 une rencontre avec Marc Jeannerod,spécialiste en sciences cognitives, à l'occasion de la sortie de son dernier opus : Le Cerveau volontaire, aux éditions Odile Jacob. Plus de précisions sur le site du bal des ardents.

Bad News for Kant's Aesthetic

At the Catholic University of Louvain, 28-30 April, will take place a workshop about Aesthetic (title : "L'art en valeurs")

Since Florian Cova and myself are working on objectivism in Aesthetic, we have submitted our work for the workshop. And it has been accepted ! Here is the summary of our work : Le sens commun peut-il fonder l'objectivisme esthétique ?

Death of Claude Levi-Strauss

It is announced there (french) and there (english).

Quinean dogma : analyticity and syntheticity

A discussion of the famous "Two Dogmas of Empiricism" written by Quine (republished in From a Logical point of View).

(Version française)


The two dogmas are the following :

1. There exists a fixed and determined criterion for the distinction between analytic propositions and synthetic propositions.
2. Reductionnism is true. (Reductionnism is a interpretation of verificationism. Verificationism is the thesis that the meaning of a proposition is the method by which the proposition is confirmed or infirmed ; reductionism is the method by immediate experience that infirms or confirms a proposition.)
   

According to Quine, the two dogmas are correlated. Take the proposition "2+2=4". It is true whatever are the circumstances but nothing empirical can confirm or infirm it (it can only be exemplified). For Empiricism, as Quine understand it, this proposition has no meaning and contains only a linguistic part. Here is the theory of signification of Empiricism according to Quine : synthetic propositions are constituted by linguistic and factual aspects, as analytic propositions are constituted only by a linguistic aspect. If a proposition is meaningful, then it is a synthetic proposition. If the proposition has no specific meaning, and it is true whatever are the circumstances or false whatever are the circumstances, then it is an analytic proposition. Analyticity and syntheticity depend on the method of verification for every proposition taken individually.

How Quine addresses these dogmas ? Quine's reasoning is not easy to follow, but I think that the steps are the following. Here the first step of the reasoning. The topic is analytic propositions.

Step 1 :

1) Empiricists states that analyticity is the fact for a proposition to be true in virtue of the signification of the logical terms ("no", "every",...) of the proposition. (For ex., a proposition of the form "No x is non-x" is always true, whatever is the interpretation of the variable "x". Hereafter this type of proposition is named "class a".)
2) Empiricists (Carnap) states that there exists a class of proposition (class b) which are analytic in virtue of there logical components and of the meaning of the extra-logical components, and which can be reduced to propositions of class a. E.g. if y is synonymous of x, then the substitution of y to x, in the class a proposition P "No x is no-x", which permits us to form a class b proposition Q "No x is no-y", permits to form Q, which has the same meaning as P and which is analytic. When we say that a class b proposition Q is a synonymous interpretation of a class a proposition P, we mean that they have necessarily the same meaning and that Q is necessarily analytic.
3) But there are no plausible explanation (contradiction, definition, interchangeability salva veritate) of synonymy that can secure the fact that the substitution of extra-logical components that has been described preserves meaning and analyticity.
4) Thus Empiricists cannot states that there exist a class b propositions which must necessarily be analytic.

End of the first step. The capital consequence of this step is scepticism towards the theory of verification and its capacity to resolve the analyticity problem. Indeed, since analyticity and the theory of verification are two sides of the same coin, then, since we have established that signification is not sufficient to preserve analyticity, then the theory of verification may have not the means to explain analyticity.

Purpose of the second step : showing that there is no determined criterium between analytic propositions and synthetic propositions. Quine is wondering if the fact that an analytic statement is "analytic for" a given language may be true, such that the statement "the proposition S is analytic for language X", where S and X are variables whose field is limited to artificial languages, is true. Quine made a trial with a type of semantic rule, rejects it, then did a test with another rule. I followed literally his progress.

Step 2

1) Let us suppose that L' is an artificial language which has a semantical rule R which purpose is to discriminate the set of analytic propositions and the set of synthetic statements, that is to say to tell us that such statements are analytic and only those, and such statements are synthetic and only those.
2) But the rule R allows us only to recognize which statements are the analytical and which ones are the synthetic propositions, without defining analyticity. In other words, there is an ostensive definition of analyticity ("this set of statements") in L ', but not an intensional definition or a definition of the meaning of "analytic" in "analytic for L'" .
3) Since one has a sufficient intuitive knowledge of analyticity to assume that all analytic propositions in L ' belong to a subset of all true propositions in L', then we can perhaps say that a proposition S is analytic iff S is not only true, but true according to a semantical rule T which says that such statements belong to the set of all true propositions.
4) Now the status of "semantic rule T" can not be attributed to any statement that says that statements of a certain class are true, because all true statements consistent with T would be analytic. We must assume that the status of "semantic rule T" can only be attributed to certain classes of these truths. Yet all true statements can claim the status of "semantical rule T" since no true statement does intrinsically possess the property of being " the semantical rule T". In other words, the notion of "semantical rule T" is relative to an order of exposure of a given language. Therefore, if the notion of "semantical rule T" is the criterion to define analyticity, then all statements may claim the status of analytic proposition and classes of analytic propositions are relative to the order selected to describe L'.
5) Therefore, since there is no semantical rule that can establish a determined distinction between analytic and synthetic propositions, then analyticity is not a property that pertain "essentially" to a class of propositions.


End of the second step. Basically Quine has shown that there is no intrinsically fixed criterion for discriminating analytical propositions. Yet we remember that Quine argues that the second dogma of Logical Empiricism is the thesis of reductionism as an interpretation of the theory of verification. Quine does not abandon the theory of verification as a theory of signification, but he wants to refute reductionism as an interpretation of the theory of verification. This is the step 3 of his reasoning.


Step 3

1) If reductionism is true, then the meaning of a proposition is the immediate experience -which is the method of verification- that confirms or infirms this proposition.
2) If immediate experience as a method of verification is true, then an analytic proposition is the extreme case in which the proposition is confirmed (or infirmed) whatever are the immediate experiences, and a synthetic proposition is the case in which the meaning of a given proposition is established in respect of an isolated immediate experience alone and is confirmed or infirmed only relatively to this immediate experience.
3) If the thesis that the meaning of an isolated synthetic proposition is established by an immediate experience alone is true, then there are rules that correlate such isolated immediate experiences with their corresponding proposition.
4) But there is no rule that can make this correlation.
5) So reductionism is not true.


What are the consequences of this demonstration? 1) It is not possible to define analyticity as what is always empirically verifiable. 2) The division between the factual component and the linguistic component of a proposition is not as good as we thought. Indeed, we do not have at our disposal a criterion that can discriminate what makes a proposition a true proposition and the logical component. 3) There is no clear distinction between proposition based on facts and others not based on facts. In other words, there is no clear separation between natural science and metaphysics (in the sense of "speech that claims to be scientific but is not based on facts ").


I suppose that Quine is making another reasoning in the last part of his paper that is implied by his holism and that can be presented in the following manner :



Step 4


1) The entire body of our scientifical beliefs is a logically structured totality (our knowledge is true if and only if all our scientifical beliefs are true together : the logical operator between all propositions held true is a conjunction).
2) A conflict between experience and our beliefs leads to adjustments in the entire "field" of our beliefs (the truth values are redistributed).
3) Empiricists's theories are refuted by experiences and theoretical examination.
4) So scepticism upon all of the statements held true by Empiricists must be maintained until a satisfactory and complete redistribution of truth values is done.

Question: is Quine just stating an absolute truth? No! Here are some ways to address his reasoning.

The first way, the least interesting, is to notice that anyway, before 1950, Carnap, the leading advocate of verificationism, had abandoned the defense of reductionism. At that time Empiricism was already in an advanced revisionist phase because of/thanks to Carl Hempel.To put it in a nutshell, it means that Quine's paper is about an obsolete topic.

The second way is more interesting than the first . We can address the premise 3 of the first argument, which asserts that there is no plausible explanation of synonymy. Indeed, Quine's criticism is based on the distinction between extensional and intensional languages, ta distinction he has developed from the 1940s (see especially the chapter "Reference and Modality" in From a Logical Point of View). A language is extensional iff, a) when A and B are two terms or formulas of this language and A contains B, b) if B' has the same extension as B, c) if A' is the result of replacing B by B', d) then the extension of A' is the same as the extension of A. A language is intensional if it fails to meet these conditions. An extensional language has a limit. Take the proposition T : "All the rabbits and only the rabbits are necessarily rabbits. " T is an analytic proposition, even if it has no strict definition of" necessarily ". If we say "rabbit" and "domestic hare" are synonyms then we say that the proposition T ' "All the rabbits and only rabbits are necessarily domestic hare" is analytic. The adverb "necessarily" is the origin of the problem : what is the aspect of "necessarily" that can garantee us that T and T' have the same meaning, that the extension is the same in T and in T'. The problem is that if we answer that we know the meaning of necessity, then we already know what analyticity is. So the argument is circular. What we can do is criticizing Quine for rejecting completely intensional languages! Has he ever ask if there can be an answer to the question of whether there is a determined distinction between analytic and synthetic propositions in intensional languages? No!

Another way would be to say that Quine confuses analyticity and a priori in some parts of his paper (step 3 of my presentation). Indeed, in the first section of his article, he proposes the following definition of analytic propositions "a statement is analytic when it is true in virtue of meanings" (Part 1: Perspectives on the analyticity). But later, analytical statements are "true in all circumstances" (Part 6: Empiricism without dogmas). The first definition of analyticity given by Quine fits the definition of analyticity in semantical terms, but the second is very remote from this fitness. Using the experience to distinguish what is independant from experience and what is dependent of it permits to discriminate (and not define) a priori and a posteriori, but not to discriminate analyticity and syntheticity, let alone define it. (On a priori and analyticity, see also the recent post by Florian Cova on the a priori and the debates it has provoked.)


A fourth way would be to distinguish between metaphysical analyticity and epistemic analyticity: "According to the metaphysical concept, a sentence is analytic if it owes its truth entirely to its meaning and without any contribution from the 'facts'. By contrast, I took a sentence to be epistemically analytic if grasp of its meaning can suffice for justified belief in the truth of the proposition express it. "wrote Paul Boghossian in his article" Epistemic Analyticity: A Defense ". This article and "Analyticity Reconsidered" are available on his homepage.

A fifth way would be to address the premises 1-2 of the fourth step of my presentation, that is to say, Quine's holism. But that will probably the topic of my next post !


Do you see other weakness in Quine's reasoning ? Or do you think my presentation does not do justice to Quine's paper ? Or do you think that we must defend Quine's paper ?

W. V. O. Quine, "Two Dogmas of Empiricism", Philosophical Review, 60/1 (Jan. 1951) ; 20-43.

W. V. O. Quine (1953), From a Logical Point of View. Nine Logico-Philosophical Essays. Harvard University Press.