CALL FOR PAPERS
[online version of the Call for
Papers: https://journals.openedition.org/philosophiascientiae/4524]
Philosophia Scientiæ 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 Scientiæ 31/1 (February 2027)
Guest editors:
Léna 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.so...@univ-lorraine.fr,
andrew.ar...@univ-lorraine.fr, s.d.zw...@tudelft.nl,bar
t.van.kerkh...@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 [Pérez-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.
Pérez-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, Léna. 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, Léna. 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, Léna. 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, Léna. 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, Léna. 2018 (manuscrit non publié de l’Habilitation à Diriger des
Recherches, consultable
sur demande).La Science telle qu’elle aurait pu se faire ? Contingence ou
inévitabilité des
résultats de notre science, 1-597.
Soler, Léna. 2024. « La » nature de la science ? Réflexions sur les présupposés
monistes et
inévitabilistes inhérents aux conceptions et pratiques de la science dans notre
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épistémologiques, éducatives et
culturelles, Laurence Maurines & José-Luis Wolfs (eds.), 57-85.
Soler, Léna & Howard Sankey (eds.). 2008. Are the Results of Our Science
Contingent or
Inevitable ? A Symposium Devoted to the Contingency Issue. Studies in History
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Soler, Léna & 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.
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about
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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
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