Multiverse set theory and absolutely undecidable propositions

Väänánen, Jouko

doi:10.1017/cbo9780511756306.013

Cited by 18 publications

(8 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…For this purpose we also consider a special atomic formula NE the only role of which is to say that the team is nonempty. This so-called non-emptiness NE was introduced in [32] and in [29]. We give examples which suggest that NE is not completely alien to common usage of language although it seems hopelessly abstract.…”

Section: Introductionmentioning

confidence: 98%

Propositional team logics

Yang

Väänánen

2017

Annals of Pure and Applied Logic

Self Cite

View full text Add to dashboard Cite

We consider team semantics for propositional logic, continuing [34]. In team semantics the truth of a propositional formula is considered in a set of valuations, called a team, rather than in an individual valuation. This offers the possibility to give meaning to concepts such as dependence, independence and inclusion. We associate with every formula φ based on finitely many propositional variables the set φ of teams that satisfy φ. We define a full propositional team logic in which every set of teams is definable as φ for suitable φ. This requires going beyond the logical operations of classical propositional logic. We exhibit a hierarchy of logics between the smallest, viz. classical propositional logic, and the full propositional team logic. We characterize these different logics in several ways: first syntactically by their logical operations, and then semantically by the kind of sets of teams they are capable of defining. In several important cases we are able to find complete axiomatizations for these logics.

show abstract

Section: Introductionmentioning

confidence: 98%

Propositional team logics

Yang

Väänánen

2017

Annals of Pure and Applied Logic

Self Cite

View full text Add to dashboard Cite

show abstract

“…Rather, he is not disposed to dominate his peers by pushing his views on the pluralism debate upon them. His aim in (Väänänen 2014) is to bring a mathematical discourse that is currently had by philosophical means into the realm of mathematically traceable formalisms. There is a sense in which intellectual humility is a driving force for the writing of the paper.…”

Section: Discussionmentioning

confidence: 99%

Intellectual humility in mathematics

Rittberg

2021

Synthese

View full text Add to dashboard Cite

In this paper I explore how intellectual humility manifests in mathematical practices. To do this I employ accounts of this virtue as developed by virtue epistemologists in three case studies of mathematical activity. As a contribution to a Topical Collection on virtue theory of mathematical practices this paper explores in how far existing virtue-theoretic frameworks can be applied to a philosophical analysis of mathematical practices. I argue that the individual accounts of intellectual humility are successful at tracking some manifestations of this virtue in mathematical practices and fail to track others. There are two upshots to this. First, the accounts of the intellectual virtues provided by virtue epistemologists are insightful for the development of a virtue theory of mathematical practices but require adjustments in some cases. Second, the case studies reveal dimensions of intellectual humility virtue epistemologists have thus far overlooked in their theoretical reflections.

show abstract

“…In this sense, an absolutist interpretation of set theory is proposed. Nevertheless, there is an obvious connection with multiverse views such as that of [Hamkins 2012], [Steel 2014], [Väänänen 2014]. We have seen how every state that B can be in determines a boolean-valued set theoretic universe V (B) .…”

Section: Kaleidoscopic Absolutismmentioning

confidence: 99%