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Ideas of Stephen Read, by Text
[British, fl. 2001, Professor at St Andrew's University.]
1994

Formal and Material Consequence

'Logic'

p.245

14187

If logic is topicneutral that means it delves into all subjects, rather than having a pure subject matter

'Logic'

p.245

14188

Not all arguments are valid because of form; validity is just true premises and false conclusion being impossible

'Reduct'

p.240

14182

If the logic of 'taller of' rests just on meaning, then logic may be the study of merely formal consequence

'Repres'

p.243

14184

In modus ponens the 'ifthen' premise contributes nothing if the conclusion follows anyway

'Repres'

p.244

14186

Logical connectives contain no information, but just record combination relations between facts

'Repres'

p.244

14185

Conditionals are just a shorthand for some proof, leaving out the details

'Suppress'

p.242

14183

Maybe arguments are only valid when suppressed premises are all stated  but why?

1995

Thinking About Logic

Ch.1

p.9

10966

A proposition objectifies what a sentence says, as indicative, with secure references

Ch.2

p.35

10970

A theory of logical consequence is a conceptual analysis, and a set of validity techniques

Ch.2

p.39

10971

A logical truth is the conclusion of a valid inference with no premisses

Ch.2

p.41

10972

The nonemptiness of the domain is characteristic of classical logic

Ch.2

p.43

10973

A theory is logically closed, which means infinite premisses

Ch.2

p.43

10975

Compactness does not deny that an inference can have infinitely many premisses

Ch.2

p.43

10974

Compactness is when any consequence of infinite propositions is the consequence of a finite subset

Ch.2

p.44

10976

Compactness makes consequence manageable, but restricts expressive power

Ch.2

p.44

10977

Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite)

Ch.2

p.47

10978

In secondorder logic the higherorder variables range over all the properties of the objects

Ch.2

p.47

10979

Although secondorder arithmetic is incomplete, it can fully model normal arithmetic

Ch.2

p.49

10980

Secondorder arithmetic covers all properties, ensuring categoricity

Ch.2

p.51

10982

How can modal Platonists know the truth of a modal proposition?

Ch.2

p.51

10981

A possible world is a determination of the truthvalues of all propositions of a domain

Ch.2

p.52

10983

Knowledge of possible worlds is not causal, but is an ontology entailed by semantics

Ch.2

p.53

10984

Logical consequence isn't just a matter of form; it depends on connections like roundsquare

Ch.2

p.54

10986

Not all validity is captured in firstorder logic

Ch.2

p.54

10985

We should exclude secondorder logic, precisely because it captures arithmetic

Ch.2

p.59

10987

Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism'

Ch.2

p.62

10988

Any firstorder theory of sets is inadequate

Ch.3

p.66

10989

The standard view of conditionals is that they are truthfunctional

Ch.3

p.72

10992

The point of conditionals is to show that one will accept modus ponens

Ch.4

p.101

10995

A haecceity is a set of individual properties, essential to each thing

Ch.4

p.106

10997

Von Neumann numbers are helpful, but don't correctly describe numbers

Ch.4

p.106

10996

Actualism is reductionist (to parts of actuality), or moderate realist (accepting real abstractions)

Ch.4

p.107

10998

The mind abstracts ways things might be, which are nonetheless real

Ch.4

p.117

11000

If worlds are concrete, objects can't be present in more than one, and can only have counterparts

Ch.4

p.118

11001

Equating necessity with truth in every possible world is the S5 conception of necessity

Ch.4

p.118

11004

Necessity is provability in S4, and true in all worlds in S5

Ch.5

p.123

11005

Negative existentials with compositionality make the whole sentence meaningless

Ch.5

p.125

11007

Quantifiers are secondorder predicates

Ch.5

p.133

11011

Same say there are positive, negative and neuter free logics

Ch.5

p.140

11012

A 'supervaluation' gives a proposition consistent truthvalue for classical assignments

Ch.5

p.142

11013

Identities and the Indiscernibility of Identicals don't work with supervaluations

Ch.6

p.154

11014

Selfreference paradoxes seem to arise only when falsity is involved

Ch.7

p.178

11016

Would a language without vagueness be usable at all?

Ch.7

p.184

11017

Some people even claim that conditionals do not express propositions

Ch.7

p.189

11018

There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers

Ch.7

p.200

11019

Supervaluations say there is a cutoff somewhere, but at no particular place

Ch.8

p.214

11020

Realisms like the full Comprehension Principle, that all good concepts determine sets

Ch.8

p.236

11025

Infinite cuts and successors seems to suggest an actual infinity there waiting for us

Ch.9

p.229

11024

Semantics must precede proof in higherorder logics, since they are incomplete
