Part II. 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

the point of such a construction is to show that p is as it were 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

at the same time this model can be regarded as – a description of  – or an explanation of ordered derivative productive action

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.”

q then p –

is here interpreted – or explained – in terms of thinking –

thinking here is if you like a passenger on the proposition –

q then p – goes forward with or without the passenger

loading the proposition up with thinking – is really extra baggage –

extra – unnecessary baggage

and one suspects that thinking here – really has nothing to do with the proposition

q then p

that it is introduced in order to prosecute some other agenda –

be that as it may – we have a proposition – q then p –

and an interpretation of it in terms of thinking

now just what thinking amounts to – is not a settled matter –

and as with any interpretation – open to question – open to doubt – uncertain

I think it is fair enough to interpret – as you wish – for your purposes

having said that though – it seems to me that  putting thinking – whatever it is supposed to mean – into the equation here –  just loads up a simple and elegant proposition – with unnecessary hubbub

3. The case of infinity 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

© greg t. charlton. 2015.