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Ideas of George Boolos, by Text
[American, 1940  1996, Professor of Philosophy at MIT.]
1971

The iterative conception of Set


p.59

18192

Do the Replacement Axioms exceed the iterative conception of sets? [Maddy]

1975

On SecondOrder Logic


p.152

14249

Boolos reinterprets secondorder logic as plural logic [Oliver/Smiley]


p.245

13841

Why should compactness be definitive of logic? [Hacking]

p.44

p.516

10829

A sentence can't be a truth of logic if it asserts the existence of certain sets

p.45

p.518

10830

Secondorder logic metatheory is settheoretic, and secondorder validity has settheoretic problems

p.46

p.519

10832

'∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed

p.48

p.521

10833

Many concepts can only be expressed by secondorder logic

p.52

p.525

10834

Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences

1984

To be is to be the value of a variable..


p.

7785

The use of plurals doesn't commit us to sets; there do not exist individuals and collections


p.105

10225

Monadic secondorder logic might be understood in terms of plural quantifiers [Shapiro]


p.201

13671

Secondorder quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Shapiro]


p.234

10267

We should understand secondorder existential quantifiers as plural quantifiers [Shapiro]


p.359

7806

Boolos invented plural quantification [Benardete,JA]

Intro

p.71

10736

Boolos showed how plural quantifiers can interpret monadic secondorder logic [Linnebo]

§1

p.74

10780

Any sentence of monadic secondorder logic can be translated into plural firstorder logic [Linnebo]

p.54

p.54

10697

Identity is clearly a logical concept, and greatly enhances predicate calculus

p.66

p.66

10698

Plural forms have no more ontological commitment than to firstorder objects

p.72

p.72

10699

Does a bowl of Cheerios contain all its sets and subsets?

p.72

p.72

10700

First and secondorder quantifiers are two ways of referring to the same things


p.227

13547

Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects) [Potter]

1997

Must We Believe in Set Theory?

p.121

p.121

10482

The logic of ZF is classical firstorder predicate logic with identity

p.122

p.122

10483

Mathematics and science do not require very high orders of infinity

p.126

p.126

10484

The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first

p.127

p.127

10485

Naïve sets are inconsistent: there is no set for things that do not belong to themselves

p.128

p.128

10488

It is lunacy to think we only see inkmarks, and not wordtypes

p.128

p.128

10487

I am a fan of abstract objects, and confident of their existence

p.129

p.129

10489

We deal with abstract objects all the time: software, poems, mistakes, triangles..

p.129

p.129

10490

Mathematics isn't surprising, given that we experience many objects as abstract

p.129

p.129

10491

Infinite natural numbers is as obvious as infinite sentences in English

p.130

p.130

10492

A few axioms of set theory 'force themselves on us', but most of them don't

1997

Is Hume's Principle analytic?


p.75

8693

An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect
