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Ideas of Ian Rumfitt, by Text
[British, fl. 2014, Pupil of Dummett. At University College, Oxford. Then at Birkbeck, then Birmingham, then All Souls Oxford]

p.784

11210

Standardly 'and' and 'but' are held to have the same sense by having the same truth table

II

p.787

11211

If a sound conclusion comes from two errors that cancel out, the path of the argument must matter

III

p.787

11212

The sense of a connective comes from primitively obvious rules of inference

IV

p.797

11214

We learn 'not' along with affirmation, by learning to either affirm or deny a sentence

2002

Concepts and Counting

I

p.43

17461

Some 'how many?' answers are not predications of a concept, like 'how many gallons?'

III

p.56

17462

A single object must not be counted twice, which needs knowledge of distinctness (negative identity)

2007

The Logic of Boundaryless Concepts

p.13

p.

9390

Logic guides thinking, but it isn't a substitute for it

p.5

p.

9389

Vague membership of sets is possible if the set is defined by its concept, not its members


p.10

14532

A distinctive type of necessity is found in logical consequence [Hale/Hoffmann,A]

Intro

p.35

12193

Logical necessity is when 'necessarily A' implies 'notA is contradictory'

Intro

p.36

12194

Contradictions include 'This is red and not coloured', as well as the formal 'B and notB'

Intro

p.36

12195

Soundness in argument varies with context, and may be achieved very informally indeed

§1

p.41

12198

Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths)

§2

p.44

12199

There is a modal element in consequence, in assessing reasoning from suppositions

§2

p.44

12200

A logically necessary statement need not be a priori, as it could be unknowable

§2

p.46

12202

Narrow nonmodal logical necessity may be metaphysical, but real logical necessity is not

§2

p.46

12201

We reject deductions by bad consequence, so logical consequence can't be deduction

§4

p.60

12203

If a world is a fully determinate way things could have been, can anyone consider such a thing?

§5

p.61

12204

The logic of metaphysical necessity is S5

2015

The Boundary Stones of Thought

1.1

p.2

18798

It is the secondorder part of intuitionistic logic which actually negates some classical theorems

1.1

p.3

18799

Intuitionists can accept Double Negation Elimination for decidable propositions

1.1

p.4

18800

Introduction rules give deduction conditions, and Elimination says what can be deduced

1.1

p.9

18802

In specifying a logical constant, use of that constant is quite unavoidable

1.1

p.10

18803

Semantics for propositions: 1) validity preserves truth 2) noncontradition 3) bivalence 4) truth tables

1.1

p.13

18804

The case for classical logic rests on its rules, much more than on the Principle of Bivalence

1.1

p.13

18805

Classical logic rules cannot be proved, but various lines of attack can be repelled

2.3

p.43

18808

Normal deduction presupposes the Cut Law

2.3

p.43

18807

Monotonicity means there is a guarantee, rather than mere inductive support

2.5

p.56

18809

Logical truths are just the assumptionfree byproducts of logical rules

3.3

p.74

18813

Logical consequence is a relation that can extended into further statements

3.3

p.76

18814

'Absolute necessity' would have to rest on S5

3.3

p.78

18815

Logic is higherorder laws which can expand the range of any sort of deduction

3.4

p.83

18816

Metaphysical modalities respect the actual identities of things

4.2

p.99

18817

We understand conditionals, but disagree over their truthconditions

5.1

p.127

18819

The idea that there are unrecognised truths is basic to our concept of truth

5.2

p.133

18820

In English 'evidence' is a mass term, qualified by 'little' and 'more'

6

p.153

18821

Possibilities are like possible worlds, but not fully determinate or complete

6.4

p.166

18824

Since possibilities are properties of the world, calling 'red' the determination of a determinable seems right

6.4 n16

p.166

18825

S5 is the logic of logical necessity

6.6

p.181

18826

'True at a possibility' means necessarily true if what is said had obtained

7

p.184

18827

If truthtables specify the connectives, classical logic must rely on Bivalence

7.1

p.185

18829

The truth grounds for 'not A' are the possibilities incompatible with truth grounds for A

7.1

p.185

18828

If two possibilities can't share a determiner, they are incompatible

7.2

p.196

18831

Medieval logicians said understanding A also involved understanding notA

7.2

p.196

18830

Most set theorists doubt bivalence for the Continuum Hypothesis, but still use classical logic

7.4

p.215

18834

Infinitesimals do not stand in a determinate order relation to zero

7.5

p.219

18835

Logic doesn't have a metaphysical basis, but nor can logic give rise to the metaphysics

8.4

p.240

18836

A set may well not consist of its members; the empty set, for example, is a problem

8.4

p.241

18837

A set can be determinate, because of its concept, and still have vague membership

8.5

p.47

18839

An object that is not clearly red or orange can still be redororange, which sweeps up problem cases

8.5

p.245

18838

The extension of a colour is decided by a concept's place in a network of contraries

8.7

p.261

18840

When faced with vague statements, Bivalence is not a compelling principle

9.2

p.275

18842

Maybe an ordinal is a property of isomorphic wellordered sets, and not itself a set

9.3

p.277

18843

The iterated conception of set requires continual increase in axiom strength

9.6

p.292

18845

If the totality of sets is not welldefined, there must be doubt about the Power Set Axiom

9.6

p.298

18846

Cantor and Dedekind aimed to give analysis a foundation in set theory (rather than geometry)
