Give me an example you have come across.

There would appear to us to be 'transient systems' of interactive 'entities', some of which we call 'living', which operate either individually or as parts of nested wholes. But I would not wish ascribe the word 'existence' to such systems or entities 'except for 'human purposes'. For example, 'the heart' may count as either an individual system, or part of 'the body'. (Individuality of 'an entity' implies the possibility of functional replacement).

On the contrary, I have asserted we SHOULD reject 'existence' not mediated by human understanding because 'existence' is a human concept like any other. That is the perhaps the point where courage is needed to shed the bouyancy aid !

Hands up who has been in a situation where the idea of 'a heap of sand' has been an issue !

Surprise...surprise !...I don't see any hands !...Maybe that's because the social dynamics we call context always renders such 'paradoxes' superficial.

As far as I am concerned, ' where concepts originate from' is just another vacuous endeavor played by ' aspiring 'realists' desperate for 'axioms'. Biological understanding of languaging as 'behaviour' needs no such 'axioms' (Maturana).
But with our 'philosophy hats on' we can play such word games ad infinitum. I have called it 'seminaritis' .For me, this one amounts to 'naive realists' squirming on the uncomfortable hook arising from Kant's point about the inaccessibility of noumena and the subsequent ditching of 'noumena' by later phenomenologists.
Obviously, an 'objective world' is useful picture for everyday transactions involving contextual attempts to 'predict and control', (maybe like a 'geocentric world' is useful for farmers). But it perhaps requires a bit of intellectual courage to realize that such 'pictures' are always human constructs, expressed in socially acquired language, and subject to delimitation or revision.

I'm taking a Pragmatist (Nietzschean) perspective that there is no way of seperating 'description' from 'actuality'. All we can ever have are 'descriptions' which vary in functionality according to context.

This so_called 'paradox' is similar to that of 'the Ship of Theseus,' in that they both illustrate the inability of classical logic to deal with the dynamics of shifting set membership as a function of transient perceptual states. See 'fuzzy logic' for possible alternative formalisms.
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Your query about 'numbers' is perhaps handled by the Lakoff & Nunez idea that all 'mathematics' can be be related to 'bodily metaphors'. This is a side issue of the 'embodied cognition' movement at Berkeley, which was one reaction to the failure of computer modelling of cognition.

In the beginning was the INTERACTION.
'Agents' doing 'deeds' are concepts privileging one side of the interaction.
(Note the biblical backcloth which sets up an absolutist axiom)

Foolso4

Fine if we discount the fact that 'before' and 'after' are also parochial human constructs.
We were born into a world of concepts which WERE of our own making. Start from there if you want to see 'productivity'.

LOL. I know you didn't...but I did !
Naive realists think that what we humans call 'the physical world' has nothing to do with the active perceptual needs of us as a species. They don't understand that a picture of 'a world devoid of humans' is a current human construction useful for current purposes. As those purposes evolve, our perceptual states evolve, and with them the picture of what we call 'the world' (or 'universe').

Are you prepared to stick your neck out and say that potential solutions to current enigmas, like 'dark matter', will not not radically change are current concept of 'physicality' ? Or do you deny that current research in quantum gravity implies that 'things' are merely 'repetitive events' ?

Remember that what we call 'science' has only been going for a few hundred years...the blink of eye in the history of humanity.

Because there was a physical world a billion years ago.

You presumably mean that in your current human mind's eye with your current language and current psychological construct of 'time', your sentence 'makes sense' to 'like minded' humans ?
Correct !... for those humans a philosopher might call 'naive realists'.

As for 'creationism', I don't even know what that means except in terms of the imagined actions of a hypothetical anthropomorphic entity.

I suggest '5' is merely the ubiquitous cultural expectancy involved of a verbal utterance associated with a human activity we call 'counting' used for other human activities like 'sharing'. In apocryphal 'less sophisticated cultures' whose counting system is '1, 2, many' our notion of '5' would be meaningless, Further more, 'counting' is already predicated on ' naming a thing' , a linguistic activity (the nominal level of measurement) so 'thinghood' is an ontological issue which precedes that of 'the physical world'.

A pragmatist might ask why 'the physical world' is not also 'a language object'. Why is 'physicality' not merely 'a set of experiential expectancies' associated with those aspects of human physiology we call 'the senses'?

'Rationality' is merely a mental exercise with a particular 'coherence' claim, 'logic' being merely one such exercise. And you appear to be using 'truth' in an absolutist sense which for me begs the question of dubious status of any 'absolute' including 'God'.

IMO, debates about 'existence of God' are futile. As an atheist, the 'God concept' has no utility for me, whereas for believers it does. As a pragmatist any concept stands or falls on the basis of its utility. Hence I'm quite happy with 'God's existence' for believers provided that belief doesn't impinge on my well being. Atheists who engage in debate on the basis of 'evidence' or 'logic' are wasting their time since 'evidence' lies in the eye of the beholder, and 'logic' has limited applicability even in physics.

The best refutatation is these...my socially acquired words which you are reading now!
(apologies if this has been covered in the comments from others above !)

Why do believers need 'proof' ?
On the basis that 'proof', 'existence', 'thinghood', 'limit' and 'God' are all concepts with contextual utility, I suggest the main reason believers have for these (incestuous) word games is a 'belief reinforcement exercise' to shore up weaknesses in their 'utility insurance policy'.

It is my 'real life' experience of a monthly philosophy discussion group, that not a single one of us has significantly changed their core positions over the last 10 years. Yes, we have introduced each other to different readings but whether that made us 'wiser' rather than 'entertain us' is itself a matter of debate.

But a more general point with respect to the OP is that 'confusion' is contextually dealt with involving negotiations of limitation of 'applicability'... not by attempting the futile task of trying to use words to define words.

What do you mean by 'a productive conversation' ?
Suppose we take the cynical view that 'philosophy is merely mental recreation for those of us fortunate to have time on our hands', how would you measure 'productive'...'killing time' ?
My point is that 'conversation' (whether internal or social) can only be deemed 'useful' with respect to deciding subsequent action, or giving 'reassurance', in specific contexts

The OP puts 'language' and 'consciousness' in the same context. From the pov of the strong form of the Sapir-Whorf hypothesis (language determines thought) and from the pov that 'all reported experience involves verbalization' so it easy to see why 'theories' using one term or the other are considered to be interrelated irrespective of other concepts like 'awareness'. But given that 'theorizing' is essentially a linguistic activity transcendent of 'perception' per se we have either the problem of 'non anchored verbiage' (words about words) or we look for a reductionist approach to language/consciousness which can be evaluated in terms of its functionality, like other theories. Such an approach (Maturana) tends to deflate, all three concepts (language, consciousness, awareness) as anthropocentric culs-de-sac with respect the more general concept of 'cognition' (which Maturana equates to that interractive system we call 'the general life process').

I don't see the phrase 'human context' being used in any of the above. (apologies if I missed it). Without that context, the behaviour we call 'using language' is meaningless,

IMO There two sorts of atheist. The first, and most usual type are those that simply consider 'God' to be a useless concept for them. The second, sometimes called 'militant' are those that consider religion in general, and some monotheism in particular as 'socially pernicious'. And some theists can move between those positions according to current events.

No. Agnosticism is the one which 'defies reason' because agnostics are merely sitting on a fence of whether a 'God concept' is useful to them or not. A secondary argument... that 'a God' is the source of human morality... is one fall back position that 'intelligent' theists have adopted in the wake of the scientific dismissal of biblical accounts for the origins of 'the universe'. However, this is opposed by evolutionary accounts of 'morality' as advantageous.

Theories are not 'provable'. They are paradigms which are offered 1. to fulfil explanatory criteria and 2. to yield new applications. In terms of the first, Occam's Razor would seem to mitigate against placing 'language' in a behavioral category of its own, and in terms of the second, both 'systems theory' and the anchoring of language in 'context' ( both physiological and social) have been fruitful.

Surely, on the basis that 'language' is a necessary aspect of 'consciousness', the central problem is that 'language' is trying to 'explain itself'.
If (as at least one writer has suggested) that 'languaging' is merely a form of complex behaviour which serves to organise other behaviours, and to coordinate joint actions, then 'the problem' is deflated.
But of course, this pov would also tend to deflate 'philosophy' to the level of social dancing !

Correct !
"Things" require thingers to thing them !
The apparent persistence and independence of 'things' is promoted by the abstract persistence and independence of the words we use to conceptualise aspects of what we call 'the world'.

Language is not moving information from one head to another. It's doing things with words.

That is more or less Maturana's position on 'languaging', which rejects the concept 'information' as a requirement for 'cognition'.
http://www.enolagaia.com/M78BoL.html

Understood. However I still see the issue as one of 'applicability' rather than one of 'metaphysical assumption'. Nietzsche's dismissal of the distinction between 'description' and 'reality' seems to be be relevant to our case.
And in terms of 'applicability' we might remember Niels Bohr's adage: ''No, no...you are not thinking...you are just being logical ! ''

(Edit problems)
I can't see that the law of identity makes any ontological claim at all other than that 'objects' might have static fixed identity rather than dynamic continued functionality. But that is the essence of the OP and the basis of the pseudo-problem of the Ship of Theseus. If that is what you are driving at then I agree.

I don't think I did. I gave the pragmatists reaction to those who do/

The 'mathematical modelling' you suggest may already operate under names like 'nested systems theory' or 'state transition theory'. But the 'intuitive rationality' involved tends to take us away from a naive view of independent 'objects' towards constructivism and the role of language in promoting ideas of 'persistence'.

There is no account of 'truth'. Its an ineffable abstraction....a word contextually used where agreement is being saught about 'certainty of what is the case'. But a shift of focus to is-ness just takes you further round a language loop...a point recognized by the philosophical,'Eprime' movement, which attempted to eliminate the verb 'to be'.

I didn't actually say that. With my pragmatist's hat on I might say 'truth' is 'what works for you'...'objective truth; is a claim about 'what works for everybody'.

Once again, I am surprised. This time that some posters on this forum do not understand the difference between a formal coherent model, like classical logic, and potential problems in its application to what we call 'the world'. Kornelius os correct as far as logic based on 'set theory' irrespective of whether an 'object' or ' member of a set' can be said to 'exist in the world'. Indeed 'existence' is a whole other ball game transcendent of the one we usually call 'formal logic'

The law of identity is therefore a subset of reality; something that happens when either the time or the speed of change is zero, and the other term is not infinite. In a larger picture, things both change and remain the same. This is something of course that many people understand intuitively; but it takes reasoning and mathematics to understand it at a rational level.

The problem with this quote taken from the OP is that phrases like 'a subset of reality' are already kowtowing to the 'logic' they are seeking to transcend. The only way out of this would seem to be to resort to neologisms (as for example in Heidegger), or to compare and contrast different 'logics' (as in 'fuzzy sets')

I'm surprised that nobody has considered 'identity of A' as 'continued contextual functionality as A'.

Yes.. 'it matters'...because playing with the word 'truth' can involve contexts such as religion where 'revealed truth' is contrasted with 'objective truth'.

My (pragmatic) answer to the question 'do we need objective truth ?' is ' yes', because the concept is useful in particular human contexts. But when an attempt is made to play with the individual words in that proposition (...play =philosophize...) ...words like 'we' or 'truth', or 'objective' ...the question becomes meaningless.

How about Gurdjieff's view that we are being farmed like sheep to 'transform psychic energy from coarse to fine for higher beings' ! :wink:

You appear to be familiar with the resource texts for The School of Practical Philosophy (aka Scool of Economic Science). If so, I am sure you would also be aware of its 'cult status' as described by some of its escapees.