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1

Mereology then and now

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Gruszczyński R., Varzi A. C.

Logic and Logical Philosophy

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2015

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vol. 24

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issue 4 Mereology and Beyond

409-427

EN

This paper offers a critical reconstruction of the motivations that led to the development of mereology as we know it today, along with a brief description of some questions that define current research in the field.

2

Set-theoretic mereology

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Hamkins J. D., Kikuchi M.

Logic and Logical Philosophy

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2016

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vol. 25

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issue 3 Mereology and Beyond (II)

285-308

EN

We consider a set-theoretic version of mereology based on the inclusion relation ⊆ and analyze how well it might serve as a foundation of mathematics. After establishing the non-definability of ∈ from ⊆, we identify the natural axioms for ⊆-based mereology, which constitute a finitely axiomatizable, complete, decidable theory. Ultimately, for these reasons, we conclude that this form of set-theoretic mereology cannot by itself serve as a foundation of mathematics. Meanwhile, augmented forms of set-theoretic mereology, such as that obtained by adding the singleton operator, are foundationally robust.

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Giuseppe Veronesego podstawy matematyki

88%

Dadaczyński J.

Zagadnienia Filozoficzne w Nauce

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2013

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issue 53

53-92

PL

The aim of this paper is to analyze Veronese’s philosophical principles of mathematics. He tried to begin the construction of mathematics (geometry) with the concept of the Thinking Subject and the phenomenon of thinking, which is discussed in detail. It is very likely that this idea had an impact on Hilbert’s concept of the Mathematical Subject. Some similarities between Veronese’s view and the intuitionistic thinkers are also shown.

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2 Logic and Logical Philosophy

1 Zagadnienia Filozoficzne w Nauce

1 Dadaczyński J.

1 Gruszczyński R.

1 Hamkins J. D.

1 Kikuchi M.

1 Varzi A. C.

1 2016

1 2015

1 2013

Mereology then and now

Set-theoretic mereology

Giuseppe Veronesego podstawy matematyki