Sean Morris. Quine, New Foundations, and the Philosophy of Set Theory. Cambridge: Cambridge University Press, 2018. Pp. x+209. $105.00 (cloth). ISBN 978-1-107-15250-2.

2020 ◽  
Vol 10 (1) ◽  
pp. 340-343
Author(s):  
Sander Verhaegh
Keyword(s):  
Set Theory ◽  
Cambridge University ◽  
New Foundations ◽  
Philosophy Of Set Theory

Quine, New Foundations, and the Philosophy of Set Theory

2018 ◽  
Author(s):  
Sean Morris
Keyword(s):  
Set Theory ◽  
New Foundations ◽  
Philosophy Of Set Theory

Intuitive and Regressive Justifications†

2020 ◽  
Vol 28 (3) ◽  
pp. 385-394
Author(s):  
Michael Potter
Keyword(s):  
Set Theory ◽  
Recent Book ◽  
New Foundations ◽  
Philosophy Of Set Theory

Abstract In his recent book, Quine, New Foundations, and the Philosophy of Set Theory (2018), Sean Morris attempts to rehabilitate Quine’s NF as a possible foundation for mathematics. I explain why he does not succeed.

Quine, New Foundations, and the Philosophy of Set Theory by Sean Morris

2021 ◽  
Vol 59 (2) ◽  
pp. 342-343
Author(s):  
Gregory Lavers
Keyword(s):  
Set Theory ◽  
New Foundations ◽  
Philosophy Of Set Theory

scholarly journals MORRIS, Sean: Quine, New Foundations, and the Philosophy of Set Theory

Filozofia ◽  
2019 ◽  
Vol 74 (6) ◽  
Author(s):  
Ádám Tamas Tuboly
Keyword(s):  
Set Theory ◽  
New Foundations ◽  
Philosophy Of Set Theory

Categoricity and the sets

2018 ◽  
Author(s):  
Tim Button ◽  
Sean Walsh
Keyword(s):  
Set Theory ◽  
Second Order ◽  
Order Logic ◽  
First Order ◽  
The Status ◽  
Second Order Logic ◽  
Philosophy Of Set Theory ◽  
Order Set

In this chapter, the focus shifts from numbers to sets. Again, no first-order set theory can hope to get anywhere near categoricity, but Zermelo famously proved the quasi-categoricity of second-order set theory. As in the previous chapter, we must ask who is entitled to invoke full second-order logic. That question is as subtle as before, and raises the same problem for moderate modelists. However, the quasi-categorical nature of Zermelo's Theorem gives rise to some specific questions concerning the aims of axiomatic set theories. Given the status of Zermelo's Theorem in the philosophy of set theory, we include a stand-alone proof of this theorem. We also prove a similar quasi-categoricity for Scott-Potter set theory, a theory which axiomatises the idea of an arbitrary stage of the iterative hierarchy.

scholarly journals On Forms of Justification in Set Theory

2020 ◽  
Vol 17 (4) ◽  
pp. 158
Author(s):  
Neil Barton ◽  
Claudio Ternullo ◽  
Giorgio Venturi
Keyword(s):  
Set Theory ◽  
Contemporary Philosophy ◽  
Philosophy Of Set Theory

In the contemporary philosophy of set theory, discussion of new axioms that purport to resolve independence necessitates an explanation of how they come to be justified. Ordinarily, justification is divided into two broad kinds: intrinsic justification relates to how ‘intuitively plausible’ an axiom is, whereas extrinsic justification supports an axiom by identifying certain ‘desirable’ consequences. This paper puts pressure on how this distinction is formulated and construed. In particular, we argue that the distinction as often presented is neither well-demarcated nor sufficiently precise. Instead, we suggest that the process of justification in set theory should not be thought of as neatly divisible in this way, but should rather be understood as a conceptually indivisible notion linked to the goal of explanation.

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