Are There Mathematical Hinges?

2020 ◽  
Vol 10 (3-4) ◽  
pp. 346-366
Author(s):  
Annalisa Coliva
Keyword(s):  
Philosophy Of Mathematics ◽  
On Certainty ◽  
Normative Function ◽  
Hinge Propositions

Abstract In this paper I argue that, contrary to what several prominent scholars of On Certainty have claimed, Wittgenstein did not maintain that simple mathematical propositions like “2 × 2 = 4” or “12 × 12 = 144,” much like G. E. Moore’s truisms, could be examples of hinge propositions. In particular, given his overall conception of mathematics, it was impossible for him to single out these simpler mathematical propositions from the rest of mathematical statements, to reserve only to them a normative function. I then maintain that these mathematical examples were introduced merely as objects of comparison to bring out some peculiar features of the only hinges he countenanced in On Certainty, which were all outside the realm of mathematics. I then close by gesturing at how the distinction between mathematical hinges and non-hinges could be exemplified and by exploring its consequences with respect to (Wittgenstein’s) philosophy of mathematics.

Common Knowledge

2016 ◽  
Vol 6 (2-3) ◽  
pp. 309-325
Author(s):  
John Greco
Keyword(s):  
Recent Literature ◽  
Common Knowledge ◽  
On Certainty ◽  
Transmission Of Knowledge ◽  
Advantages And Disadvantages ◽  
Hinge Propositions ◽  
Distinctive Role

A promising idea in the recent literature is that the concept of knowledge serves to govern the flow of actionable information within a community of information sharers. In this connection, several authors have argued that knowledge is the “norm of assertion,” while others have explored the distinctive role of testimony in the transmission of knowledge. This paper investigates the role of “common knowledge” in such a community, and compares it to Wittgenstein’s notion of “hinge propositions” in On Certainty. Wittgenstein’s thinking is evaluated in this context, and an account of common knowledge along Wittgensteinian lines is considered. I do not here endorse the account of common knowledge that results. Rather, I consider some of the advantages and disadvantages of what looks to be a promising approach.

scholarly journals Dobradiças, Vertigem Epistémica e Moralidade

2019 ◽  
Vol 27 (53) ◽  
pp. 125-140
Author(s):  
Nuno Venturinha ◽  
Keyword(s):  
On Certainty ◽  
The Third ◽  
Inexact Knowledge ◽  
Hinge Epistemology ◽  
Hinge Propositions ◽  
Rational Evaluation

This paper explores central themes of Duncan Pritchard’s epistemology intimately related to the Wittgensteinian idea of a “hinge epistemology”. The first section calls attention to the eminently empirical character of our “hinges”. The second section focuses on Pritchard’s notion of “arational hinge commitments”, more specifically his distinction between the pair “über hinge commitments”/“über hinge propositions” and the pair “personal hinge commitments”/“personal hinge propositions”. The third section brings to the discussion Timothy Williamson’s view of “inexact knowledge” and examines another pair of notions introduced by Pritchard, namely “antiskeptical hinge commitments”/“antiskeptical hinge propositions”. I conclude with a reevaluation of the diagnosis made by Pritchard that, confronted with a sceptical scenario, our “epistemic angst” can be surpassed if we follow Wittgenstein’s teaching in On Certainty about the “structure of rational evaluation”, but that an “epistemic vertigo” can never be ultimately dispelled. My argument is that in a moral scenario there is no room for vertigo.

scholarly journals Wittgenstein on Scepticism. An Interpretation of Wittgenstein's On Certainty

2021 ◽  
Author(s):  
◽  
Agata Orłowicz
Keyword(s):  
On Certainty ◽  
The World ◽  
Hinge Propositions ◽  
New Interpretation

<p>The thesis puts forward a new interpretation of Ludwig Wittgenstein’s On Certainty and contrasts it with the standard reading of the book, also known in literature as the Framework Reading. The Framework Reading sees hinge propositions, that is our most basic and indubitable beliefs, as framing our practice of talking about the world, and, therefore, external to this practice. As such, they are seen as not truth-apt, purely regulative in character and our relation to them as non-epistemic. According to the interpretation put forward in this thesis, we should instead see hinges as uncontroversially correct moves in our practice of talking about the world, and, therefore, we should see them as obviously true and playing both a regulative and a descriptive role.</p>

Sextus and Wittgenstein on the End of Justification

2014 ◽  
Vol 4 (2) ◽  
pp. 81-108 ◽  
Author(s):  
Shaul Tor
Keyword(s):  
Belief System ◽  
On Certainty ◽  
Sextus Empiricus ◽  
Hinge Propositions ◽  
Suspension Of Judgement

Following the lead of Duncan Pritchard’s “Wittgensteinian Pyrrhonism,” this paper takes a further, comparative and contrastive look at the problem of justification in Sextus Empiricus and in Wittgenstein’sOn Certainty. I argue both that Pritchard’s stimulating account is problematic in certain important respects and that his insights contain much interpretive potential still to be pursued. Diverging from Pritchard, I argue that it is a significant and self-conscious aspect of Sextus’ sceptical strategies to call into question large segments of our belief systemen masseby exposing as apparently unjustifiable fundamental propositions which are closely related in their linchpin role to Wittgenstein’s hinge propositions. In the first instance, the result is a more complex account of both a deeper affinity between Wittgenstein’s approach to hinge propositions and Sextus’ approach to what I termarchaipropositions and a divergence between the two. In the second instance, I suggest how the comparison withOn Certaintycan be illuminating for the interpreter of Sextus. In particular, it can help us to see how the Pyrrhonist’s everyday conduct—common assumptions to the contrary notwithstanding—involves rational procedures of justification, in line with a naturalism reminiscent of Wittgenstein. Furthermore, it can help us to reflect on the Pyrrhonist’s attitude to what Wittgenstein would have called her ‘worldview’. Throughout, I suggest that the comparison with Wittgenstein is interesting, although it must be cashed out differently, not only on the interpretation—or, perhaps, strand—of ancient Pyrrhonism which has the sceptic exempt ordinary beliefs from her suspension of judgement, but also on the interpretation (or strand) which has her disavow all beliefs categorically.

scholarly journals Wittgenstein on Scepticism. An Interpretation of Wittgenstein's On Certainty

2021 ◽  
Author(s):  
◽  
Agata Orłowicz
Keyword(s):  
On Certainty ◽  
The World ◽  
Hinge Propositions ◽  
New Interpretation

<p>The thesis puts forward a new interpretation of Ludwig Wittgenstein’s On Certainty and contrasts it with the standard reading of the book, also known in literature as the Framework Reading. The Framework Reading sees hinge propositions, that is our most basic and indubitable beliefs, as framing our practice of talking about the world, and, therefore, external to this practice. As such, they are seen as not truth-apt, purely regulative in character and our relation to them as non-epistemic. According to the interpretation put forward in this thesis, we should instead see hinges as uncontroversially correct moves in our practice of talking about the world, and, therefore, we should see them as obviously true and playing both a regulative and a descriptive role.</p>

Mathematical Knowledge and the Interplay of Practices

2015 ◽  
Author(s):  
José Ferreirós
Keyword(s):  
Mathematical Knowledge ◽  
A Priori ◽  
Philosophy Of Mathematics ◽  
Advanced Mathematics ◽  
New Approach ◽  
Agent Based ◽  
Epistemology Of Mathematics ◽  
Actual Experience ◽  
Elementary Math ◽  
Mathematical Tradition

This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction in the philosophy of mathematics, the book uses the crucial idea of a continuum to provide an account of the development of mathematical knowledge that reflects the actual experience of doing math and makes sense of the perceived objectivity of mathematical results. Describing a historically oriented, agent-based philosophy of mathematics, the book shows how the mathematical tradition evolved from Euclidean geometry to the real numbers and set-theoretic structures. It argues for the need to take into account a whole web of mathematical and other practices that are learned and linked by agents, and whose interplay acts as a constraint. It demonstrates how advanced mathematics, far from being a priori, is based on hypotheses, in contrast to elementary math, which has strong cognitive and practical roots and therefore enjoys certainty. Offering a wealth of philosophical and historical insights, the book challenges us to rethink some of our most basic assumptions about mathematics, its objectivity, and its relationship to culture and science.

Acerca del supuesto fundamentalismo de Wittgenstein en Sobre la certez

2007 ◽  
Vol 13 ◽  
Author(s):  
José M. Ariso Salgado
Keyword(s):  
Ludwig Wittgenstein ◽  
On Certainty ◽  
In Virtue Of ◽  
Basic Beliefs

RESUMENAl analizar si Ludwig Wittgenstein mantiene una posición fundamentalista en Sobre la certeza, suele discutirse si la citada obra se adapta al modelo de fundamentalismo propuesto por Avrum Stroll. Tras exponer las líneas básicas de dicho modelo, en esta nota se mantiene que Sobre la certeza no se adapta al modelo de Stroll debido al importante papel que Wittgenstein concede al contextualismo. Además, se añade que Wittgenstein no puede ser calificado de fundamentalista porque no reconoce ninguna propiedad que, sin tener en cuenta la diversidad de casos particulares, permita justificar de forma conjunta todas nuestras creencias básicas.PALABRAS CLAVEWITTGENSTEIN, FUNDAMENTALISMO, CONTEXTUALISMO, CERTEZAABSTRACTDid Wittgenstein hold a foundationalist position in On Certainty? When this question is tackled, it is often discussed, whether On Certainty fits in the foundationalist model devised by Avrum Stroll. After expounding the main lines of this model, I hold that On Certainty does not fit in Stroll’s model, because of the important role Wittgenstein attaches to contextualism. Furthermore, I add that Wittgenstein cannot be seen as a foundationalist –or a coherentist–, because he does not admit any feature in virtue of which the whole of our basic beliefs are justified without considering circumstances at all.KEYWORDSWITTGENSTEIN, CERTAINTY, FOUNDATIONALISM, CONTEXTUALISM

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