Part II. I

On Logic and Mathematics

I. LOGICAL INFERENCE

1. Is it because we understand the propositions that we know that q entails p?

Does a sense give rise to the entailment?

q does not entail p

entailment is not a property of propositions

no proposition ‘follows from’ another

entailment is as action performed on propositions –

entailment is a way of relating q and p –

it is a propositional construction –

if you like – a propositional game – a logical game

the point of such a construction is to present p as a product of q –

as to understanding –

the form q entails p – is a construction on propositions –

it is a language-game

you can appreciate the form – the language-game – whether or not – or to what extent – you understand the propositions –

and of course – understanding – is always up for grabs –

open to question – open to doubt – uncertain

‘does a sense give rise to the entailment?’

or is it that the construction – the language-game that is entailment – gives rise to the sense?

either / or – I would suggest

the question really is how do we explain sense?

my point here is simple –

whatever account we give of sense – whatever ‘explanation’ – is advanced –

the logical reality is – any proposal will be open to question – open to doubt – will be uncertain

whatever explanation you find useful – in whatever context you are operating in – will be the account you run with

as to the point of entailment – it is a model for action –

it presents process as ordered – and action as derivative and productive

the ‘ground’ of entailment –

and for that matter of any language-game –

is utility – is usefulness

and language-games – propositional models – if they are useful – can become entrenched in propositional practise

however any language game – any propositional use – entrenched or otherwise – is contingent –

is open to question – open to doubt –

is uncertain

2. If it follows from q, then thinking that q must involve thinking that p.

yes – if that is the game we are playing

the ‘must’ here – is the rule of the game –

and the rule is ‘if q then p’

if you play the entailment game – you play in accordance with this rule –

and ‘thinking’ here is just a description of the action –

a description that would fit certain contexts –

but not all

where the entailment game is played in or by a machine – do we say the machine thinks q then thinks p?

no

3. The case of infinitely many propositions following from a single one.

a proposition – a proposal – is open to question – open to doubt – is uncertain

there is no logical end to interpretation of a proposition –

to the generation of propositions

no proposition follows from another proposition as such

action can be performed on a proposition

the result of which is another proposition –

and this proposing in relation to proposals –

can go as long as propositional action is performed

if we are talking about an infinity of human actions –

we have moved from empirical reality –

to imaginative fiction

4. Can experience show that one propositions follows from another?

experience is propositional –

experience is what we propose

so the question becomes –

‘can a proposal show that one proposal follows from another?

a proposal can link proposals –

is this a ‘showing’? – yes –

but what it shows is that a propositional action has been performed on propositions

there is no mysterious ‘follow on’ from one proposition to another

there is only propositional action

and further there is no ‘necessity’ in propositional action

propositional action is contingent –

with all the uncertainties that go with that

yes we create propositional models –

but proposing a propositional form –

is no different – logically speaking –

to putting forward a proposal –

any proposition – any propositional construction –

is open to question – open to doubt – is uncertain