AGAINST CUMULATIVE TYPE THEORY
AGAINST CUMULATIVE TYPE THEORY
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反对累积型理论
DOI：
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
R. Trueman
中科院分区：
文献类型：
--
作者：
Tim Button;R. Trueman
Abstract Standard Type Theory,
${ extrm {STT}}$
, tells us that
$b^n(a^m)$
is well-formed iff
$n=m+1$
. However, Linnebo and Rayo [23] have advocated the use of Cumulative Type Theory,
$ extrm {CTT}$
, which has more relaxed type-restrictions: according to
$ extrm {CTT}$
,
$b^eta (a^alpha )$
is well-formed iff
$eta>alpha $
. In this paper, we set ourselves against
$ extrm {CTT}$
. We begin our case by arguing against Linnebo and Rayo’s claim that
$ extrm {CTT}$
sheds new philosophical light on set theory. We then argue that, while
$ extrm {CTT}$
’s type-restrictions are unjustifiable, the type-restrictions imposed by
${ extrm {STT}}$
are justified by a Fregean semantics. What is more, this Fregean semantics provides us with a principled way to resist Linnebo and Rayo’s Semantic Argument for
$ extrm {CTT}$
. We end by examining an alternative approach to cumulative types due to Florio and Jones [10]; we argue that their theory is best seen as a misleadingly formulated version of
${ extrm {STT}}$
.
Abstract Standard Type Theory,
${ extrm {STT}}$
, tells us that
$b^n(a^m)$
is well-formed iff
$n=m+1$
. However, Linnebo and Rayo [23] have advocated the use of Cumulative Type Theory,
$ extrm {CTT}$
, which has more relaxed type-restrictions: according to
$ extrm {CTT}$
,
$b^eta (a^alpha )$
is well-formed iff
$eta>alpha $
. In this paper, we set ourselves against
$ extrm {CTT}$
. We begin our case by arguing against Linnebo and Rayo’s claim that
$ extrm {CTT}$
sheds new philosophical light on set theory. We then argue that, while
$ extrm {CTT}$
’s type-restrictions are unjustifiable, the type-restrictions imposed by
${ extrm {STT}}$
are justified by a Fregean semantics. What is more, this Fregean semantics provides us with a principled way to resist Linnebo and Rayo’s Semantic Argument for
$ extrm {CTT}$
. We end by examining an alternative approach to cumulative types due to Florio and Jones [10]; we argue that their theory is best seen as a misleadingly formulated version of
${ extrm {STT}}$
.
影响因子：
1.5
作者：
Florio S
通讯作者：
Florio S
一切，然后是一些
影响因子：
1.8
作者：
Stephan Krämer
通讯作者：
Stephan Krämer