3 philosophy papers (2 published and 1 to be published)

1 chapter accepted and published:

• Pain, N. (2011), Mathematical Platonism, in Bruce, M. & Barbone, S. (eds), Just the Arguments: 100 of the Most Important Arguments in Western Philosophy, Oxford: Blackwell, 373-375.

 






 
1 paper accepted and published:

• Pain, N. (2011), Le coût de l'argument de l'indispensabilité des mathématiques, Répha, 3.

1 paper accepted and to be published:

• Cova, F. & Pain, N. (2012), Can folk aesthetics ground aesthetic realism (draft)? The Monist.

CALL FOR PAPERS: From Practice to Results in Logic and Mathematics

Philosophia Scientiae invites contributions for the following special topic: From Practice to Results in Logic and Mathematics. Thematic issue of Philosophia Scientiae 16/1 (February 2012)

Guest editors: Valeria Giardino, Amirouche Moktefi, Sandra Mols, and Jean Paul Van Bendegem

Submission Deadline: March 20, 2011 (extended deadline)
Acceptance Notification: June 1st, 2011

The PratiScienS research group, in collaboration with Prof. Jean Paul Van Bendegem, invites the submission of articles for a thematic issue of the journal Philosophia Scientiae dedicated to the role of practices in the establishment of results in logic and mathematics.

We look for papers on how the concrete practices of mathematicians and logicians may influence the results of their enquiries and, more broadly, the definition of what counts as proof. We are also interested in papers proposing a methodological reflection on the difficulties that a critical analysis of such practices in logic and mathematics implies, and on issues related to the development of the appropriate exploratory conceptual tools. Case studies are welcome, though authors should make explicit what they consider as practices and how their papers are related to the practice-focused theme of this issue of Philosophia Scientiae.

We are also strongly interested in papers linking the issue’s theme with that at the core of PratiScienS, that is, the issue of practices in their relations with the construction and validation of scientific knowledge. Therefore, we are also looking for this special issue for papers discussing practices and results in logic and mathematics in relation with PratiScienS’s main research topics: the "Wimsatt-like" concept of robustness, the role of tacit aspects, and the contingency vs. inevitability issue, as in the case of mathematics and logic.

Manuscripts should be submitted in English or French, and prepared for anonymous peer review. Abstracts in French and English (200-300 words) should be included.

Guidelines for authors are to be found on the journal’s website.

Papers should be sent by e-mail to Valeria Giardino: Valeria.Giardino@ens.fr

For more information on the PratiScienS group, its research themes and its activities, please visit its website.

Mathematics and cognition

The topic of the last issue of Trends in Cognitive Sciences is mathematical capacities ! Numeral and spatial capacities. Here is the table of content.

En l'honneur de Gerhard Heinzmann

Pierre Edouard Bour, Manuel Rebuschi, Laurent Rollet are the editors of a book published for celebrating Gerhard Heinzmann's works. Here is the description :

This Festschrift is published on the occasion of Gerhard Heinzmann's 60th birthday. Its title "Construction" refers to Heinzmann's philosophical options (intuitionism, dialogical pragmatism, constructivism), as well as to his exceptional involvement in the building of many scientific enterprises and new scientific institutions. Sixty authors contributed to the volume, and the gathered essays witness the various centers of interest and intellectual achievements of Heinzmann. They are organized in five sections: (1) Henri Poincaré; (2) History and Philosophy of Mathematics; (3) History and Philosophy of Logic; (4) Pragmatism; and (5) Miscellaneous.

Contributors :
Evandro Agazzi, Michael Astroh, Hervé Barreau, Thomas Bénatouïl, Denis Bonnay, Hélène Bouchilloux, Pierre Edouard Bour, Michel Bourdeau, Christophe Bouriau, Christiane Chauviré, Michael Detlefsen, Pascal Engel, Dominique Fagnot, Virginie Fiutek, Didier Galmiche, Paul Gochet, Jeremy Gray, Marcel Guillaume, Jaakko Hintikka, Bertram Kienzle, Ralf Krömer, Jacques Lambert, Dominique Larchey-Wendling, Philippe Lombard, Kuno Lorenz, Igor Ly, Ulrich Majer, Mathieu Marion, Alexandre Métraux, Michel Meulders, Philippe Nabonnand, Michel Paty, Roger Pouivet, Joelle Proust, Shahid Rahman , Narahari Rao , Manuel Rebuschi, Laurent Rollet, Séverine Rollet, Giuseppina Ronzitti, Philippe de Rouilhan, Helge Rückert, Fabien Schang, Anne-Françoise Schmid, François Schmitz, Elisabeth Schwartz, Hourya Sinaceur, Antonia Soulez, Claudine Tiercelin, Richard Tieszen, Frédérick Tremblay, Tero Tulenheimo, Johan van Benthem, Louis Vax, Denis Vernant, Joseph Vidal-Rosset, Henk Visser, Klaus Volkert, Gudrun Vuillemin, Scott Walter.

Pierre Edouard Bour, Manuel Rebuschi Laurent Rollet (ed.) (2010). Construction. Festschrift for Gerhard Heinzmann. College Publications.

Full table of content.

Leviathan & Poincaré

A terrific discovery in Paleontology (Nature) : the fossil of the skull of a whale (3 m. long), very alike to the skeleton of a sperm whale in size and in appearance. This whale seemed to be a very aggressive predator : a massive jaw with huge teeth, teeth on the upper and lower jaws, probably 17m. long. The team call this whale : Leviathan melvillei. Watch the nice video and read the article. A summary of both can be found at the BBC.

Note also a very important step in Mathematics : the conjecture de Poincaré is now considered a theorem, thanks to G. Perelman. See  Pour la Science.

MAJ (3/07/2010) : Perelman did not accept the prize associated with the solving of the problem. See : Brilliant & reclusive Russian Mathematician doesn't need your money.

The Geometry of Visual Space and the Nature of Visual Experience, by Farid Masrour

Next Tuesday, June 29th at the Colloquium du DEC, (12h à 13h3O – Salle Paul Lapie – 29 rue d’Ulm – 1er étage) : The Geometry of Visual Space and the Nature of Visual Experience, Farid Masrour (Assistant Professor, NYU).

Abstract :

Empirical research shows that we see bent lines as straight, we see an object oriented along the depth axis as having a different size than a same-sized object oriented along the horizontal axis, as a result objects seem to change their shape as they rotate in space. Our visual experiences seems to systematically falsify some of the basic principles that are required to make sense of fundamental geometrical notions such as straight lines, distances and planes. This paper argues that these results have significant philosophical implications about the nature of our perceptual experience. In particular, I shall argue that they put pressure on accounts that regard our visual experiences as constituted by relations to external facts, as well as those accounts that assimilate our visual experience to pictures.

Second Paris-Nancy PhilMath Workshop

November 17-19, 2010, Paris

This is the second in an annual series of workshops on the philosophy of mathematics organized by a team of scholars from Paris, Nancy and elsewhere in France. The three-day meeting will feature both invited and contributed talks. The invited speakers, who have confirmed their participation, are:

- Patricia Blanchette (Notre Dame University)
- Jacques Bouveresse (Collège de France, Paris)
- John Burgess (Princeton University)
- Gabrielle Crocco (University of Provence, Aix-Marseille)
- Gilles Dowek (Ecole Polytechnique, Paris)
- Ignasi Jané (University of Barcelona)

Call for papers

Submissions of full-text papers are invited in the philosophy of mathematics for presentation at the workshop as one of six contributed talks. The languages of the workshop are English and French. Presentations should be no longer than 45 minutes, and will be followed by 30 minutes of discussion. In particular younger scholars and graduate students working on their dissertations are encouraged to submit, as the workshop provides them with an opportunity to discuss their work with experts from around the world. The deadline for submission is August 31st. Receipt of submissions will be acknowledged by email. The Program Committee will evaluate all papers and announce its decisions by the end of September. The papers should be sent by email in DOC, RTF, or PDF format to the following address: Marco.Panza@univ-paris1.fr

Steering Committee: M. van Atten, D. Bonnay, G. Crocco, J. Dubucs, S. Gandon, G. Heinzmann, P. Mancosu, S. Shapiro, I. Smadja.

Program Committee: A. Arana, M. Detlefsen, B. Halimi, P. Nabonnand, M. Panza, J.-J. Szczeciniarz, S. Walsh

Local Organizing Committee: M. Panza, P. Cardon, M. Detlefsen, A. Rodin, J.-J. Szczeciniarz.

Schedule

Call for papers: June 10st

Deadline for submission of papers: August 31st

Notification of acceptance: September 30st

Support: Chaire d’excellence ANR (senior) Michael Detlefsen.

Paraconsistent Foundations of Mathematics : a weblog.

Paraconsistent Foundations for Mathematics is a new blog created for a new project at the University of Melbourne. The project is under the direction of Pr. Graham Priest, Ass. Pr. Greg Restall, and a research associate Francesco Berto. Zach Weber is the author of the blog. I am looking forward to read the next posts !

(Introduction to Paraconsistent Logic.)

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.

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.

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.