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CfP: Special Issue of Philosophia Scientiae – "The Contingency of Mathematical Proofs and Results?", Deadline: 1 August 2025
CALL FOR PAPERS
[online version of the Call for
Papers:�https://journals.openedition.org/philosophiascientiae/4524]
Philosophia Scienti�invites contributions for the following special topic:
The contingency of mathematical proofs and results?
Exploring the arguments for inevitabilist versus contingentist views about the formal sciences
by comparison with the natural sciences
�
Special Issue of Philosophia Scienti� 31/1 (February 2027)
Guest editors:�
L�na Soler (Univ. Lorraine, AHP, Nancy, France),
Andrew Arana (Univ. Lorraine, AHP, Nancy, France),
Sjoerd Zwart (Univ. Delft, Netherland),
Bart Van Kerkhove (Univ. Brussels, Belgium)
Submission deadline: 1st�August 2025
Notification date: 1st�January 2026
Revision deadline: 1st�March 2026
Final version: 1st�June 2026
Submissionaddresses:�lena.soler@univ-lorraine.fr,�andrew.arana@univ-lorraine.fr,�S.D.Zwart@tudelft.nl,bar
t.van.kerkhove@vub.be�
1. Description
The Special Issue aims at applying to the�formal�sciences an important but still underdeveloped
epistemological question until now applied chiefly to the�natural�sciences: the question of
whether scientific achievements are inevitable or contingent. Roughly, the question
is�formulated at the most general level and using �science� in the broadest sense of the term,
including mathematics and logic: is what we currently identify with our most reliable scientific
knowledge inevitable, i.e., necessary under some conditions? Or could all or part of our
taken-as-valid scientific achievements�conclusions, theories, ontological commitments,
experimental data and approaches, mathematical methods, proofs and theorems, and any other
scientific �results��have been significantly different? The discussion of this question involves
two antagonist positions about taken-as-valid scientific achievements, today currently labelled
�inevitabilism� and �contingentism�. As shorthand we can talk of
the�I/C�(inevitabilist/contingentist) issue.
The�I/C�issue was first introduced in philosophy of science in these terms quite recently by Ian
Hacking. Hacking [1999] coined the �inevitabilist� and �contingentist� labels and isolated
the�I/C�issue as an�autonomous�question�in particular one that should be carefully distinguished
from scientific realism. Hacking [2000] then articulated a more detailed characterization that
subsequently worked as a reference for most thinkers who considered the�I/C�issue. The
corresponding characterization encompasses a well-defined formulation of the general problem,
then almost always used as a starting point by those who contributed to the�I/C�debate: �If the
results�R of a scientific investigation were correct, would any investigation of roughly the
same subject matter, if successful, at least implicitly contain or imply the same results?�.
[Hacking�2000] also delineated some intrinsic difficulties associated with any similar problem
formulation, thereby offering a global theoretical framework to address the issue. Before these
writings from Hacking, the topic of contingency in science was admittedly not absent from the
philosophical, sociological or historical meta-studies on science, but beyond scattered
superficial declarations, only a few works attempted to vindicate a full-blown contingentist
thesis (e.g. [Collins�1981]; [Cushing 1994]; [Pickering 1984, 1995]). In the wake of these
works, especially Hacking�s seminal proposals, others have addressed the�I/C�issue in the last
twenty-five years. The most complete overview available today, with an abundant bibliography,
can be found in [Soler, Trizio & Pickering�2015].
Regarding the�target�of�I/C�discussions in the available literature, the vast majority of the
relevant studies limit themselves to the results of the�empirical�sciences.�Physics is usually
on the front line�notably through the case of empirically equivalent, mutually incompatible
physical theories. Biology progressively became another field of central interest, especially
under the influence of Gregory Radick�s writings [2005, 2008]. Some other empirical disciplines
were also sometimes considered (e.g. psychology in [Bitbol & Petitmengin�2015]). But mathematics
and logic, as for them, were almost always left out of�I/C�discussions.
This motivates the overarching questions of the Special Issue:�Is there anything special about
mathematics and logic that could justify not asking the�I/C�question about them? When we�do�ask
the�I/C�question about them, do we actually find genuinely significant differences with respect
to the case of the natural sciences? To what extent can we replicate or fruitfully accommodate
the types of arguments, the types of strategies for dealing with difficulties, and the types of
answers, that have been articulated about the empirical sciences?
To explain why the formal sciences are usually left out of�I/C�debates, some reasons can be
invoked�though it remains to examine whether they coincide with philosophically acceptable
justifications. Generally speaking, when engaging in�I/C�discussions�whatever the science under
scrutiny, we can become more and more convinced of the widespread, insidious but very powerful
activity of something like an �inevitabilist instinct� [Soler�2015a,�b]. At the heart of the
inevitabilist instinct, lies the strong conviction that well-established scientific results were
essentially inevitable, meaning that the corresponding results had to be reached sooner or later
by any successful science, or more prudently, meaning at least that mutually incompatible
results could not have been�legitimately�validated. The inevitabilist instinct about
taken-as-valid scientific results proves deeply active in most people, including in many
philosophers,�but comparatively, it tends to be much stronger about mathematical and logical
resultsthan about physical, biological, or any other empirical result. The logical-mathematical
realm works, in commonsensical ways of thinking as in many philosophical writings, as the �realm
of necessity� [Bloor�1991]. Relatedly, the idea that our history of mathematics (and logic)
could have turned otherwise and could have led to an alternative mathematics in part
incompatible with ours does not easily come to mind, and a fortiori, is not considered for
discussion.
When scrutinizing the content of many ongoing epistemological debates through the lenses of
the�I/C�framework, as a general trend, it appears that in philosophy of science (including of
the formal sciences and still more strikingly in their case), inevitabilist commitments are
simply taken for granted and often likely not even identified ([Pickering�2015], [Soler�2024]).
Such a trend is particularly noteworthy in debates about scientific realism. In the
corresponding debates, inevitabilist commitments are usually presupposed, not disentangled from
realist claims, and a�fortiori not discussed separately. This is unfortunate given that under
examination, most realist claims include inevitabilist tenets, while the reverse is not
necessarily the case. A related advantage of rethinking the status of scientific knowledge in
the�I/C�framework carefully disentangled from the more familiar realist/antirealist one, is that
we can sidestep the as-problematic-as-unwavering correspondantist intuitions and the
overwhelming difficulties of truth attributions, and be left with a comparatively simpler issue
formulated in terms of the unicity versus the plurality of legitimate scientific options in the
history of science past and present. One of the core questions then becomes: what is the more
plausible or epistemologically fertile position, between estimating that in each decisive stage
of the history of science encompassing a set of mutually conflicting scientific competitors,
(i)�there is�one single optimal�option that should then be�inevitably�selected while all its
inferior rivals should be abandoned, or (ii)�some other competitors, possibly including
competitors incompatible with the one actually selected in the actual history of science, could
have been a legitimate choice as well, so that the option actually selected in the past history
was not inevitable�but contingent�(although not illegitimate for all that)?�
That inevitabilist commitments are not examined for themselves in many epistemological debates
about the empirical and formal sciences is not a philosophically satisfactory situation. Against
this background, a core question of the Special Issue is:�beyond the inevitabilist instinct,
what arguments can be articulated for (or against) the inevitability of mathematical proofs and
results?�The corresponding arguments obviously need to be developed in the framework of a
specified conceptualization of the problem encompassing determined definitions of inevitabilism
and contingentism. Diversified conceptual frameworks and arguments have been proposed by
philosophers, historians and sociologists in relation to the empirical sciences (e.g.
[Radick�2005], [Soler�2008a, b, 2015a, b, 2018], [Soler & Sankey�2008], [Martin�2013],
[Allamel-Raffin & Gangloff 2015], [Kinzel�2015], [Soler, Trizio & Pickering�2015], [Kidd�2016]),
but very few in relation to the formal sciences.�
A small number of striking exceptions can nevertheless be mentioned. They include some rare
remarkable�pioneering�contributions that vindicate a contingentist-like position about
mathematics and logic ([Wittgenstein�1956], [Bloor�1976, 1983, 1991, 1997]). David Bloor, in
particular, can be credited to have provided, as early as the 1970s, a general systematic and
powerful conceptual framework, applicable both to the natural sciences and to mathematics and
logic, that, although primarily couched in the �social� idiom rather in the �contingentist� one,
can straightforwardly be reformulated in�I/C�terms, and is of incredible value for coping with
the�I/C�issue. More recent contributions include [Corfield�2004], [Mancosu�2009], [Hacking 2014,
2015], [Salanskis�2015], [Van Bendegem�2015], and [P�rez-Escobar, Rittberg & Sarikaya�2024].
Today, the field probably the most susceptible to engage in the�I/C�debate about mathematics and
logic, is the relatively new field of the �philosophy of mathematical practice�. Contributors of
this field have often questioned the almost universally held special status of mathematics and
logic (e.g. [Kerkhove & Comijn 2004]), and have frequently been led to make some in passing
remarks that potentially open the door to a contingentist reading of mathematics�even if what
lies behind the door is usually not scrutinized.
Given that mathematics and logic are intuitively expected to be �much less subject� to
contingency than empirical terrains, it is worth examining the grounds of this intuition by
discussing whether, and in what respects,�I/C�questions, arguments, difficulties, and answers
significantly differ when they are directed at the formal sciences instead of at the empirical
ones. The Special Issue invites all kinds of meta-analysis of science to engage in the
elaboration of fertile�I/C�frameworks and arguments for the case of mathematics and logic,
especially in a comparative perspective with the case of the empirical sciences and by
exploiting whenever suitable the cognitive resources that have already been articulated for the
latter.
Particularly sought-after topics
They include, but are not limited to, the following (not independent) fifth topics.
1. Discussing David Bloor�s pioneering but largely ignored �contingentist� conception of
mathematics and logic� And other possible pioneering contributions directly relevant to
the�I/C�debate applied to the formal sciences.
2. Characterizing the typical argumentative strategies and intrinsic difficulties involved in
the vindication of an�I/C�position about mathematics and logic by comparison to the situation in
the natural sciences.
3. Exploring the issue of an alternative mathematics (and logic): can convincing, real or
counterfactual candidates for an alternative mathematics be exhibited? How to cope with the hard
difficulties inherent to the discussion of whether the candidates can do the job?
4. The�I/C�of what, inside of mathematics (or logic)? To what extent should we differentiate the
formulations, arguments, difficulties, and positions according to the mathematical (or logical)
target under consideration?
5. What lessons of the history of mathematics (and logic) regarding the�I/C�philosophical
issue�and reciprocally?
2.�Criteria of acceptance regarding scope
Before starting any reviewing process, the content of the papers will be considered according to
two criteria. First, each contribution should articulate a direct discussion of the�I/C�issue
applied to the formal sciences. Second, the constitutive contributions taken altogether should
ideally address diversified and complementary aspects of the�I/C�issue applied to the formal
sciences. In case the subjects of the received articles are too similar, a preliminary selection
could have to be made in order to satisfy the diversity and complementarity
requirement.�Interested authors should feel free to interact in advance with the guest editors
about the subject of their potential contribution.
Manuscripts must:
� be original, and may not be in the process of being submitted for another publication;
� be written in English or French;
� be prepared for anonymous double-blind evaluation;
� contain an abstract in English (200-300�words) with a space reserved for an additional
abstract in French, or conversely;
� be prepared either in Word or in LATEX (in the standard article class with A4 paper size and
latin modern 12 pt font, i.e. using \documentclass[a4paper,12pt]{article}) after having applied
the stylistic standards of Philosophia Scientiae as specified in the instructions for authors
(see below);
�not exceed 35�000�characters including spaces;
�be sent by August 1st�2025, either in word and PDF (if prepared in word), or in PDF (if
prepared in LATEX), to the email addresses of the guest editors.�
For more details on the article format, notably the citation and bibliography style, please
consult the instructions for authors:�https://journals.openedition.org/philosophiascientiae/633
Bibliography
Allamel-Raffin, Catherine, & Jean-Luc Gangloff.�2015. Some Remarks about the Definitions of
Contingentism and Inevitabilism. In Soler�et al.�2015, 99-116.
Bitbol, Michel, & Claire Petitmengin. 2015. The Science of Mind as It Could Have Been�: About
the Contingency of the (Quasi-) Disappearance of Introspection in Psychology. In Soler�et
al.�2015, 285-316.
Bloor, David. 1976.�Knowledge and Social Imagery. London�: RKP.
Bloor, David. 1983.�Wittgenstein�: A social theory of knowledge.�The Macmillan press ltd.
DOI :�10.1007/978-1-349-17273-3
Bloor, David. 1991.�Knowledge and Social Imagery, 2nd�ed, Chicago�: University of Chicago Press,
1991.
Bloor, David. 1997.�Wittgenstein, Rules and Institutions. London�; New-York�: Routledge.
DOI :�10.1007/978-1-349-17273-3
Collins, Harry. 1981. The Role of the Core-set in Modern Science�: Social Contingency with
Methodological Property in Science.�History of Science�19, no.�1, 6-19.
Corfield, David. 2004.�Towards a Philosophy of Real Mathematics. Cambridge�: Cambridge
University Press.
DOI :�10.1017/CBO9780511487576
Cushing, James T. 1994.�Quantum Mechanics�: Historical Contingency and the Copenhagen Hegemony.
Chicago�: University of Chicago Press.
Hacking, Ian. 1999.�The Social Construction of What�?�Cambridge, MA�: Harvard University Press.
DOI :�10.2307/j.ctv1bzfp1z
Hacking, Ian. 2000. How Inevitable Are the Results of Successful Science�?�Philosophy of
Science, 67, supplement PSA 1998, 58-71.�
DOI :�10.1086/392809
Hacking, Ian. 2014.�Why is There Philosophy of Mathematics at All�?�New York�: Cambridge
University Press.
DOI :�10.1017/CBO9781107279346
Hacking, Ian. 2015. On the Contingency of What Counts as �Mathematics�. In Soler�et al.�2015,
262-282.
Kidd, Ian J. 2016. Inevitability, contingency, and epistemic humility.�Studies in History and
Philosophy of Science, 55, 12-19.
Kinzel, Katherina. 2015. State of the field�: Are the results of science contingent or
inevitable�?�Studies in History and Philosophy of Science Part A,�52, 55-66.
DOI :�10.1016/j.shpsa.2015.05.013
Mancosu, Paolo. 2009. Measuring the size of infinite collections of natural numbers�: was
Cantor�s theory of infinite number inevitable�?�Review of Symbolic Logic�2, 612-46.
DOI :�10.1017/S1755020309990128
Martin, Joseph D. 2013. Is the Contingentist/Inevitabilist Debate a Matter of
Degrees�?�Philosophy of Science, 80(5), December, 919-930.
P�rez-Escobar, J.A., Rittberg, C.J. and Sarikaya, D., 2024. Petrification in Contemporary Set
Theory�: The Multiverse and the Later Wittgenstein.�KRITERION�Journal of Philosophy.
Pickering, Andrew. 1984.�Constructing Quarks�: A Sociological History of Particle Physics.
Chicago�: University of Chicago Press.
Pickering, Andrew. 1995.�The Mangle of Practice�: Time, Agency, and Science. Chicago�:
University of Chicago Press.
DOI :�10.2307/j.ctv11smg5w
Pickering, Andrew. 2015. Science, Contingency, and Ontology. In Soler�et al.�2015, 117-128.
DOI :�10.1126/science.os-2.56.329
Radick, Gregory. 2005. Other Histories, Other Biologies. In�Philosophy, Biology, and Life,
Anthony O�Hear (ed.), Cambridge�: Cambridge University Press, 21-47.
Radick, Gregory (ed.). 2008. Counterfactuals and the Historian of Science.�Isis, 99, 547-584.
Salanskis, Jean-Michel. 2015. Freedom of Framework. In Soler et al. 2015, 240-261.
Soler, L�na. 2008a. Are the Results of Our Science Contingent or Inevitable�?�Studies in History
and Philosophy of Science Part A, 39(2), 221-229.
DOI :�10.1016/j.shpsa.2008.03.014
Soler, L�na. 2008b. Revealing the Analytical Structure and Some Intrinsic Major Difficulties of
the Contingentist/Inevitabilist Issue.�Studies in History and Philosophy of Science Part�A,
39(2), 230-241.
DOI :�10.1016/j.shpsa.2008.03.015
Soler, L�na. 2015a. The Contingentist / Inevitabilist Debate�: Current State of Play,
Paradigmatic Forms of Problems and Arguments, Connections to More Familiar Philosophical Themes.
In Soler�et al.�2015, 1-44.
Soler, L�na. 2015b. Why Contingentists Should Not Care about the Inevitabilist Demand to
�Put-Up-or-Shut-Up��: A Dialogic reconstruction of the Argumentative Network.�In Soler�et
al.�2015, 45-98.
Soler, L�na. 2018 (manuscrit non publi� de l�Habilitation � Diriger des Recherches, consultable
sur demande).La Science telle qu�elle aurait pu se faire�? Contingence ou in�vitabilit� des
r�sultats de notre science,�1-597.
Soler, L�na. 2024. ��La�� nature de la science�? R�flexions sur les pr�suppos�s monistes et
in�vitabilistes inh�rents aux conceptions et pratiques de la science dans notre monde. In�Les
multiples dimensions de l�Homme et de la connaissance, Questions �pist�mologiques, �ducatives et
culturelles, Laurence Maurines & Jos�-Luis Wolfs (eds.), 57-85.
Soler, L�na & Howard Sankey (eds.). 2008. Are the Results of Our Science Contingent or
Inevitable�? A Symposium Devoted to the Contingency Issue.�Studies in History and Philosophy of
Science, 39, 220-264.
Soler, L�na & Emiliano Trizio, Andrew Pickering (eds.). 2015.�Science as it Could Have Been.
Discussing the Contingency / Inevitability Problem, Pittsburgh�: Pittsburgh University Press.
Van Bendegem, Jean Paul. 2015. Contingency in Mathematics�: Two Case Studies, in Soler�et
al.�2015, 223-239.
Van Kerkhove, Bart, & Hans Comijn (2004). The importance of being externalist about
mathematics���one more turn�?�Philosophica�74,103-122.
DOI :�10.21825/philosophica.82219
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�
General submissions within this range are welcome.
Philosophia Scientiae�is a journal of peer-reviewed research in analytic philosophy,
epistemology, and history and philosophy of science. It is particularly concerned with topics
arising in mathematics, physics, and logic, but is open to contributions from all scientific
fields.�Philosophia Scienti�has a tradition of publishing studies in the history of German and
French philosophy of science.
It is published by�Kim� Editions�(Paris).
�
Potential authors and topical issue editors are invited to discuss their projects with our
Managing Editors. Manuscripts should be submitted in French, English, or German, and prepared
for anonymous peer review. Abstracts in French and English of 10-20 lines in length should be
included. Submissions should be sent by e-mail to:
phscientiae-redac@univ-lorraine.fr.
�
The Journal is available online at:
http://philosophiascientiae.revues.org/
http://www.cairn.info/revue-philosophia-scientiae.htm
�(back issues :�http://www.numdam.org/journals/PHSC�)
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For any further information (for instance, submission guidelines, back issues, abstracts),
please refer to the�website of the
Journal:�http://poincare.univ-lorraine.fr/fr/philosophia-scientiae/accueil
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