[spsp-members] Call for Paper: The contingency of mathematical proofs and results? [Philosophia Scientiae 31/1, February 2027
Lena Soler
lena.soler at univ-lorraine.fr
Mon Mar 10 10:31:38 UTC 2025
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: 1^st August 2025
Notification date: 1^st January 2026
Revision deadline: 1^st March 2026
Final version: 1^st June 2026
Submission addresses: lena.soler at univ-lorraine.fr
<mailto:lena.soler at univ-lorraine.fr?subject=Submission%20Philosophia%20Scientiae%2031/1>,
andrew.arana at univ-lorraine.fr
<mailto:andrew.arana at univ-lorraine.fr?subject=Submission%20Philosophia%20Scientiae%2031/1>,
S.D.Zwart at tudelft.nl
<mailto:S.D.Zwart at tudelft.nl?subject=Submission%20Philosophia%20Scientiae%2031/1>,
bart.van.kerkhove at vub.be
<mailto:bart.van.kerkhove at vub.be?subject=Submission%20Philosophia%20Scientiae%2031/1>
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 results /than 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
<http://dx.doi.org/10.1007/978-1-349-17273-3>
Bloor, David. 1991. /Knowledge and Social Imagery/, 2^nd 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
<http://dx.doi.org/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 <http://dx.doi.org/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 <http://dx.doi.org/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 <http://dx.doi.org/10.1086/392809>
Hacking, Ian. 2014. /Why is There Philosophy of Mathematics at All ?/New
York : Cambridge University Press.
DOI : 10.1017/CBO9781107279346 <http://dx.doi.org/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
<http://dx.doi.org/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
<http://dx.doi.org/10.1017/S1755020309990128>
Martin, Joseph D. 2013. Is the Contingentist/Inevitabilist Debate a
Matter of Degrees ? /Philosophy of Scienc/e, 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 <http://dx.doi.org/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
<http://dx.doi.org/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
<http://dx.doi.org/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
<http://dx.doi.org/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 monde. In /Les multiples dimensions
de l’Homme et de la connaissance, Questions 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 and Philosophy of Science/, 39, 220-264.
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.
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
<http://dx.doi.org/10.21825/philosophica.82219>
------------------------------------------------------------------------
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
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studies in the history of German and French philosophy of science.
It is published by Kimé Editions
<http://perso.orange.fr/kime/index.htm>(Paris).
/Potential authors and topical issue editors are invited to discuss
their projects with our Managing Editors. Manuscripts should be
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review. Abstracts in French and English of 10-20 lines in length should
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