News to me. You claim that being a Platonist ixs equivalent to believing in the axiom of choice? I'd take those two things to be totally independent of one another. You could be a Platonist or not, and pro-choice or not. I don't see the connection. — fishfry

The connection is the fact that the axiom of choice is equivalent to the law of excluded middle, which for infinite objects dissociates truth from derivation. This in itself wouldn't imply platonism if it wasn't for the fact that most proponents of classical logic and ZFC make no attempt to justify the formalisms pragmatically with respect to real world application.

Yes, I'm already aware of all of that, and was only speaking approximately on set theory. My point was only attacking the idea that quantity is reducible to ordering.

Demanding that the notion of quantity is synonymous with the notion of order is misguided, for a set is normally specified as a collection of things which satisfy a given predicate, and the "quantity" of such things usually makes no reference to a constructive ordering of the elements concerned but merely to the existence of other sets for which there exists a proveable bijection to the present set, a bijection that can merely involve a bi-directional translation of any given element of a set into another.

Ironically, it is the the platonists who insist that every set must be "well-ordered" which is an assumption equivalent to the axiom of choice. But for those who deny the axiom of choice, it is nevertheless meaningful to compare the "sizes" of different sets even if the determined sizes are not synonymous to counting elements.

Then there is the little matter of potential infinity. Mathematically, it might well be the case that the number of grains of sand in a heap is neither finite nor actually infinite, but indefinitely large. To argue differently is to argue the religion of physics rather than maths.

Suppose that a heap of sand is indefinitely large, in that every time a grain of sand is extracted from the heap it might be possible to remove from the heap yet another grain of sand. Even though the heap of sand is indefinitely large, it is nevertheless meaningful to speak of the original heap of sand as being larger than the heap with a grain of sand removed, and yet in this case it is only possible to count the grains removed from the heap.

Well, yes; if you have historical information then by that very fact you have a distinction between past and present... not at all sure what "ontological" is doing there, since the sentence works better without it. — Banno

Are the tenses of past, present and future reflective of distinct physical relations or substances, as the block universe advocates suggest?

According to the block universe in which the past, present and future are ontologically distinct, how is historical information even possible? For this view seems to imply that appearances in a given frame of reference at time t can speak only of what exists at time t. In which case, how can such appearances, whether taken individually or collectively, obtain historical significance?

How can the study of physics, which begs the ability to observe history, whether directly or indirectly, be even justified in relation to this block universe understanding, which seems to tacitly insist that all "historical evidence" can speak only of it's moment of existence?

Perhaps one could appeal to the existence of some form of information preserving causality, by which the present always "contains" the past, but that would imply physics to be mere religion, given that any supposed experimental confirmation of such a theory would be question begging. Plus it flies in the face of the second law of thermodynamics, which permits different potential histories of the universe to arrive at the same state in the future.

In the block universe there remains a distinction between how things are at one time and how things are at another. — Banno

Yes, but the same could be said of a diary. The fundamental question is, does the existence of historical information necessitate an ontological distinction between past and future? or do we merely record information in a linear fashion for convenience?

Consider your hard-disk. If you wipe your hard disk, then as far as your hard-drive is concerned the information that you had previously stored on your hard-disk not only does not exist, but it never existed.

The meaning of "the information that was on your hard-drive" only makes sense as a reference to information that continues to persist in another medium. But if the universe is a closed and bounded system, then the history of the universe doesn't have an external back-up. In which case, the block universe is objectively false and is merely a diary. For any change to the present state of the universe necessarily entails the deletion of historical information, meaning that history isn't static, time isn't a line from past to future and causality doesn't have a direction.

Another way of putting it is in terms of Lockean primary versus secondary qualities; Traditionally, the discipline of Physics charts only the primary qualities of objects, events and processes i.e. their mathematical interrelations, where the relationship of their primary qualities to their secondary qualities (i.e. qualia) is ignored and undetermined. The reason why the secondary qualities are classically ignored by physics is as a consequence of traditional physics treating it's subject matter to be independent of any particular observer, which is itself due partly to convenience and simplification, and due partly as a consequence of the objective of physics to model the causal relationships that hold between action and consequence irrespective of the contextual nuances and discrepancies of any given observer.

Strictly speaking, the propositions of physics are senseless, like an unexecuted computer program, until as and when the propositions are used by an agent and thereby become grounded in the agent's perceptual apparatus in a bespoke fashion, at which point Locke's secondary qualities become temporarily welded to the physical concepts.

Classical physical concepts are therefore by design irreducible to mental concepts; something has been a central feature of physics rather than a bug, at least up until the discovery of special relativity and quantum mechanics, both of which show that even the Lockean primary qualities of objects are relative to perspective.

Physicalism is the idea that the meaning of language is grounded in third person testimony and the results of unperformed experiments, i.e. counterfactuals. For if the meaning of language was considered to be grounded in first-person observations and the results of actually performed experiments, then the words "mass", "electromagnetic force", "neuron" and so on would reduce in a literal sense to the lived experience of the first-person, making physicalism ontologically reducible to mentalism.

In contrast to Darwinian life, transhuman life will seem self-evidently wonderful by its very nature.[/quote]

Is it rational to seek to eliminate death in the absence of any proof that life is better than death?
— Foghorn
But the problem, to quote Wittgenstein, is that "Death is not an event in life". Even if we share a Benatarian pessimism about the human predicament, we should have compassion for aging humans tormented by increasing decrepitude and their own mortality – and the loss of loved ones. Defeating the biology of aging is morally imperative.
In contrast to Darwinian life, transhuman life will seem self-evidently wonderful by its very nature. — David Pearce

"6.4311 Death is not an event in life: we do not live to experience death. If we take eternity to mean not infinite temporal duration but timelessness, then eternal life belongs to those who live in the present. Our life has no end in just the way in which our visual field has no limits."

Wittgenstein's quote indicates the logical inexpressibility of death as 'eternal oblivion' from the perspective of Tractatarian phenomenalism, which as a maximally empiricist theory of meaning is unavoidably both solipsistic and presentist. For such doctrines, all propositions about change, including so-called 'temporal passage', reduce to observational change relative to a present that only exists in the sense of a logical construct. The quote therefore doesn't appear relevant to arguments for defeating biological ageing, and if anything appears to undermine it.

As the quote indicates, presentists have no motivation to biologically preserve their own life for the purpose of avoiding eternal oblivion, given that they understand eternal oblivion to be nonsense. For the presentist, the present already is their immortality, implying that there isn't a moral imperative to prevent ageing. At most transhumanism offers the presentist a potential happiness-gradient following strategy for seeking a 'local optima' of happiness relative to their current circumstances. A presentist with an appetite for risk however, could rationally decide to abandon happiness gradient following and instead resort to nature's evolutionary search strategy, by committing suicide and hoping for a favourable rebirth, depending on his beliefs in karma.

The most charitably I can put it is this: the afterlifer is after something so radically different from life that it would simply have nothing to do with what we understand as life. It would be something wholly different that one could not even call it an afterlife. But what, exactly, would that be? Once the afterlife becomes unmoored from anything recognizable as life, then what conceptual bearings do we have to even talk of it? And here, the concept needs to be defined, long, long, long before any search for 'evidence' would even be remotely contemplated. — StreetlightX

But nobody agrees, or even can agree in principle, as to what life "means", since everyone's use of a proper name contradicts with each other. Society's use of proper names is physically and psychologically indescribable in terms of closed type-token relations, for each and every person uses the same proper name differently and in an off-the-cuff bespoke fashion that does not conform to any a priori definition of "personhood". The concept of "another mind" is essentially a perspectival, dynamic and open relation, whereby to imagine, to remember or even to recognise a physically present person is in some sense to construct that very person.

Consider a funeral gathering. It is remarkable how the mourners focus almost exclusively upon the sense of the person remembered, and how they pay so little attention to the physical referent of their mourning that lies in the coffin. And yet according to any public truth criteria of type-token physicalism that insists upon making a hard subject-object distinction, the mourners have nothing to be upset about, for only the physical referent of a proper-name objectively matters; the proper-name the mourners associate with their grief is either meaningless due to it referring to nothing, or it refers to what is in the coffin. Either way, the mourners feelings and personal memories are irrelevant to the ontological status of living or dead persons, and their personal experiences never come into contact with other minds.

I mean it though - the notion of an afterlife simply has no conceptual coherence. After-life = life beyond death. This is no different to a square circle. The woo peddlers reckon they get get around this by cleaving life into two such that there is bodily life on the one hand and then - depending on who you ask because there is no precision here at all - mental, spiritual, conscious or soul-life. But no one has any idea what this last kind of 'life' is, or exactly how 'life' and any of these categories are meant to be conceptually articulated. Or how the 'life' that qualifies any of these latter things has anything in common with the 'life' of the body. It's complete wordplay. A grammar mistake that, because it is so obviously incoherent to anyone with a basic grasp of english ("dead life that is alive"), must cover it up by making internal distinctions that have no purport at all, and fall apart at the slightest prodding because held together by nothing than pseudo-grammatical glue.

One doesn't need to 'argue' that square-circles don't exist: anyone who thinks they do disqualifies themselves as a speaker of english. So too peddlers of 'the afterlife'. — StreetlightX

That's true but it somewhat misses the point, given the flexibility of one's choice of grammar.

Chemists has no problem with the statement "Gold was destroyed on Earth, but later discovered in Alpha Centauri" - in spite of absence of information transfer.

Why are natural kinds such as gold and operating systems entitled to "after lives" , but not persons?

Consider the fact that a person isn't rigidly defineable as a type of object, due to an absence of essential criteria.

Why must Elvis Presley be treated as a rigidly designating proper name as opposed to a universal?

Isn't it purely down to the qualities of his impersonators singing and the legal politics of his estate?

o. But 'failure of imagination' is not itself an argument against even ludicrous, evidence-free ideas like "after lives" or "past lives". — 180 Proof

Supposing that one is an atomist to the point of being a mereological nihlist. Then isn't even the idea of a "living person" also evidence-free?

None. The question is metaphysical and therefore doesn't really concern evidence, for any answer to the scientific question "is there an after-life" whether "yes", "no", "maybe" or "mu" (meaning the question is nonsense) is tautologically decided.

For the scientific question to make sense, the concepts of "Persons", "lives" and "After-lives" must first be given definitions in terms of physically contingent types and/or natural kinds. At which point scientific evidence becomes relevant in so far as deciding whether a given "person" is now in the "after-life" state relative to the assumed ontology, which begs the entire metaphysical question.

I'll plead ignorance about this point, I don't know enough physics to comment on that.

But I guess my point is that the notion of “cause” may not be applicable to the total, as Russell pointed out in his famous debate with Copleston.

If we see the universe as a “set” or “collection/bundle of events”, then there may be no sense in asking what its cause is, just as there is no sense in asking what the cause of “the set of all ideas” is, in the same sense as we would ask what the cause of a rock, or of lightning, is.

But then again, Russell did also say that matter could also be seen as a way of grouping events into bundles, so maybe there is a sense in asking for the cause of sets after all. — Amalac

Right. As you point out, a notion of causality cannot play a role with respect to any data-set that is regarded as complete and self-contained. This creates a conflict within realism, for realists tend to simultaneously assert i) the transcendental reality of causality, ii) the transcendental existence of a completed universe whether finite or actually infinite, and iii) that counterfactual propositions have a definite truth value independent of actual measurements and observations.

By contrast, if the reality of an inter-subjectively complete universe is denied, then causality can not only retain it's useful meaning as referring to the potential outcomes of an intervention relative to an agent's perspective, but also it's ontological status to a limited extent, albeit not necessarily as a linear ordering of events from "past" to "future". Bayesian networks come to mind here.

By asymmetric causality, I am referring to either the belief or definition of causality such that causes come before their effects. This is a physically problematic assumption due to the fact that the microphysical laws are temporally symmetric.

mean, the past is either finite or it's infinite, right? What is meant by “potentially infinite” then? — Amalac

The realist interpretation of potential infinity is that it is epistemic ignorance of the value of a bounded variable. For the realist an unobserved variable has a definite value irrespective of it's measurement or observation . Hence for the realist, the value of a variable is either actually infinite or it is finite, with no third alternative.

Likewise, the constructive interpretation of potential infinity also refers to a bounded variable whose value if measured, is necessarily finite. The difference is, it doesn't assert the existence of any value until as and when the value is constructed. In computer programming terms, a potentially infinite natural number in this sense refers to a natural number variable that is lazily evaluated . Only upon evaluation, does the variable possess a definite (and finite) value.

The logic of a potentially infinite past in this constructive sense is superficially demonstrated in the video games genre known as "roguelikes", where a player assumes the role of an adventurer who explores a randomly generated dungeon that is generated on the fly in response to the player's actions.

The existence of the games are effectively a demonstration of the coherence of retro-causation that is conditioned upon the players present choices. Of course, a realist will be quick to point out that the implementation of such games demonstrates nothing of the sort, being as it is an ordered sequence of instructions with a beginning and end. The deficiency of the realist interpretation of the game must therefore be argued by other means, such as by the Quantum Mechanical refutation of local causation + counterfactual definiteness + no conspiracy.

In the current context regarding the truth of past-contingent propositions , a constructive interpretation of history is that a past cause of an event does not exist over and above the construction of presently existing historical information. For example, if the present state of the universe is compatible with Jack the Ripper having any number of historical identities, then according to historical constructivism Jack the Ripper did not exist and does not exist until as and when his/her identity is constructable from historical information. And because historical evidence is rarely conclusive, the constructivist is forced to reject the assignment of a definite truth value to most, if not all, past-contingent propositions.

The idea of an actually infinite past in the extensional sense of actual infinity is incompatible with the beloved premise of asymmetric causality running from past to future. In order to accept the premise of an actually infinite past, one must both theoretically reverse the direction of causality and somehow square that against physics and intuition, and in addition posit a finite future - a situation that is at least as problematic as the original picture. Or else one must entirely reject the notion of causality altogether - with the presumable consequence that having abandoned the doctrine of causality one must accept that one can no longer construct a theoretical or experimental argument for or against one's position.

In physics , the notion of actual temporal infinity is metaphysical in the literal sense of meta-physics, i.e it is a proposition that cannot be falsified, verified or even weakly evaluated through experiments.

However, there cannot be any empirical evidence on the basis of the observable universe to posit a past of any particular length. Therefore, the idea of a potentially infinite past is both perfectly consistent and the least assuming position to adopt. This position is adopted by presentists, who view the past and future as logical constructs that are reducible to sense-data. It's also compatible with quantum mechanics, due to the fact that QM has perpsectivalist retrocausal interpretations.

According to Oxfam in 2020, the world’s 2,153 billionaires have more wealth than 4.6 billion people, i.e. 60 percent of the world's population.

According to Statista, the wealth of US billionnaires grew by a trillion dollars since the start of the pandemic.

According to inequality.org, "US Billionaire wealth is twice the amount of wealth held by the bottom 50 percent of US households combined, roughly 160 million people."

According to americansfortaxfairness.org, "From 2010 to March 2020, more U.S. billionaires derived their wealth from finance and investments than any other industry. The financial sector boasted 104 billionaires in 2010 -- ten years later the number had grown to 160."

UBI amounts to a forced redistribution of capital from this tiny minority to everyone else. Correct me if i'm wrong, but I suspect that there aren't any billionnaires participating in this forum thread, so I am somewhat confused by the personal anxieties in this thread concerning the idea of UBI.

As a global redistribution of capital from the haves to the have-nots, UBI is also a form of collective bargaining that reduces the incentive for people to work in the non-desirable jobs, thereby putting upward pressure on the wages of those jobs. It should also encourage the elimination of bullshit jobs that don't need to exist in the first place, as well as hastening the robot revolution in order to completely eliminate the undesirable jobs whose cost of labour is increasing.

hmm, would you reject the cosmological argument for the existence of God? As the main principles use causality as a means to prove His existence — Charlotte Thomas-Rowe

For me, a causal proposition is merely a synthetic proposition used to describe an intervention, that has the form "If an action A is performed upon a system in state S then the system possibly produces state R" .

Since my view of causality is anti-realist , game-theoretic and possibilistic, I suppose that my view is closest to the Occasionalists, at least as I understand them when squinting in an attempt to see past their surface-level dualism.

Do false beliefs really exist?

For example:

If the Earth is in fact round, then the assertion "The Earth is Flat" cannot be referring to the non-existent fact that the Earth is flat. And so at most "The Earth is Flat" refers to the possibility that the Earth is flat. But how can beliefs refer to possibilities?

If it is possible that the Earth is flat, then presumably the Flat Earther is referring to this possibility, in which case his assertion cannot be judged as false. On the other hand, if it isn't even possible that the Earth is Flat, then the Flat Earther can only be referring to other facts of his life, such as his present mental-state. In which case his assertion still isn't false when understood.

That is, must consciousness always only occur, or exist, in a first person, present tense mode? — charles ferraro

That position has the advantage of deflating away the "hard problem", for consciousness becomes merely a synonym for present and actual objects.

I think the central question concerns the elasticity of the rope. For liberally minded persons who only believe in "death by definition", the rope is infinitely elastic. For conservatively minded persons however, the rope is very taut.

You, not we. There's nothing in the list of things that constitute the self that continues past death — Banno

What is the ontological justification for us treating an individual as being the same person throughout the course of single lifespan?

we treat it as a single rope, despite no single thread running through the whole. — Banno

presumably in that case we can treat any consecutive processes as being a single rope, in which case we have arrived at the Buddhist position of rebirth

The "I" is memory, body, intent, narrative...

None of which survive death. — Banno

But are these things even persistent during the course of a single lifespan?

I cannot for instance remember my childhood before the age of 5. So does this childhood belong to somebody other than I?

Category theory is a popular mathematical area. An offshoot of algebra, it can be used as an alternative to establish the foundations of math. It searches for so-called universal properties in various categories. Personally, I find it alien and entirely non-productive in the nitty gritty stuff I study in complex variables.

The Wikipedia page for Category theory gets 575 views/day, a respectable number. The page you linked gets 5 views/day and is classified as low priority (like my math page). So it may not help. But good try. — jgill

I'm unsurprised that you dislike CT. Abandoning elements feels a bit like abandoning nouns in ordinary language. It isn't a coincidence that the Turing Machine has been the predominant model of computing over the Lambda calculus - the modular conceptualisation of systems in terms of reusable and independently existing entities or elements is cognitively and practically expedient relative to the holistic structuralism of type theory/CT, albeit at the mere cost of potential philosophical confusion.

Although in the case of comp-sci, the practical expedience has recently moved towards CT due the shift to multi-core parallel programming, where control flows can be containerized, layered and equalized in a logically concise fashion using Monads. I also suspect that some generalisation of CT will become important to AI and machine learning over the next few years, due to it's notational emphasis on processes and interaction.

If nothing else, CT serves as an elitist language for getting ahead in the programming jobs market.

You point is obscure. The caterpillar becomes a butterfly. — Banno

So by analogy, is personal identity over time an illusion? How should persons being counted?

I baulk at having a different sort of truth for science than for religion. Truth is truth. The you that awakes forma coma has the very same body as the you that entered the coma. There is a publicly available way to asses the meaning of "I" in "But was I really unconscious previously". It's missing from reincarnation. — Banno

Are caterpillars identical to butterflies?

"Theology as grammar" - Wittgenstein.

This question concerns the grammar of intervention; What do we mean when we say that an agent "intervenes" upon a system to bring about a particular state of affairs?

For example, one might say that the Earth considered as an isolated system has "no choice" but to assume a particular orbit when subjected to gravitational forces exerted upon it by the rest of the solar system. Hence in this situation we have a notion of causality that relates a system taken independently and in isolation, namely the Earth, to the rest of the solar system considered as an external system. Here "no choice" means that the earth is expected to move differently given a different arrangement of the surrounding solar system, but it should also be noticed that the meaning of "different arrangement of the solar system" is itself partly determined by how the Earth itself moves. Hence even in this materialistic and atomistic example of an isolated system subject to external forces, the meaning of having no-choice is somewhat fuzzy and tautological in character.

But what about when considering the orbit of the Earth jointly with the motions of the rest of the solar system taken as a single, collective holistic system? When considering the solar system jointly, all that physics needs and has is an equation that describes the simultaneous motion of all the planets. As Bertrand Russell observed, the notion of causality that we had in the previous instance disappears when considering everything jointly, and in this latter context it would be meaningless to say that the earth's trajectory was determined by the solar system that it is simultaneously modelled with.

In a nutshell, causality is a meta-theoretic relation that relates a system considered as "foreground" to a context considered as "background". This implies that the question of free-will versus determinism is meaningless in the absolute sense in which everything is (hypothetically) considered simultaneously.

The category theoretic description of the natural numbers does away with the pesky elements of the natural number "set" and externalises the notion of 'element' onto the objects counted.



https://en.wikipedia.org/wiki/Natural_numbers_object

And so the notion of elements isn't needed for the pure purpose of constructing abstract numbers.

Does that help?

..and no basis for calling it true. Reincarnation becomes a form of life that does not make contact with truth or falsehood. It's use - meaning - can only be in its social function. — Banno

Scientifically speaking, I agree, but of course, your argument also applies to the "you only live once" position, so it's a moot point.

But i don't agree that scientific truth and metaphysical truth are synonymous, due to the fact the latter directly concerns the logic of first-person experience, whereas the former is precluded from coming into contact with first-person experience due to the public semantics of scientific discourse , where identity relations are decided by public agreement with respect to propositions stateable in the third-person. Hence it is possible, imo, to accept the public meaningless of the scientific question, whilst accepting the private question to be metaphysically meaningful, and even potentially answerable in some philosophically critical sense.

To give a related example, if i awaken from a coma then I am said to have been "previously unconscious" by definition of the circumstances i am presently in, which includes such things as medical opinions i hear from loved ones around me, a brain-scan i am presented with showing an absence of critical neurological activity, and my self-observed tendency to abstain from memory recalling behavior (amnesia). As with the question of reincarnation, it is logical for me to ask "But was I really unconscious previously", or only in the tautological sense decided by public convention, where my "previous unconsciousness" is ironically decided by present observations that make no actual reference to a non-existence of first-person experience per-se?

Personal identity isn't a topic that science is able to investigate, because identity relations are part of logic and ontology rather than empirically deducible matters of fact, and science is compatible with any set of identity relations, provided they are consistent.

Given any assumed set of identity relations, science only has the power to decide whether or not a given observable process conforms to those relations. For example, if a caterpillar is defined as being identical to the resulting butterfly, then scientific experiments have the potential to confirm whether or not a given caterpillar is identical to a given butterfly. But the result can neither confirm nor deny the reality of the assumed identity relation.

There a multiple cultural and practical factors as to why western culture has converged onto an assumed set of identity relations that makes rebirth not merely physically impossible but logically impossible. I think part of the reason is that scientific theories are initially easier to understand relative to an atomic ontology, such as periodic tables and subatomic particles, than holistic process ontologies. This is also reflected in logic and mathematics, where most students find set theory with elements easier to understand than category theory without elements.

Given that intuitionists who reject the existence of actual infinity also reject the law of excluded middle, they are likely to disagree with the assumption that the universe must either be finite or infinite.

For the intuitionist, truth is synonymous with verification of some sort, meaning that according to this stance there are no unknowable true propositions. This implies that if it is unknowable in principle as to whether the universe is finite or infinite, then there is no transcendental matter-of-fact as to which is the case.

Also, it should be mentioned that the commonest use-case of potential infinity involves an agent querying nature for the value of an unbounded variable and accepting the received response (if any). Therefore it is false to claim that denial of actual infinity entails denial of external reality.

Personally, I am sympathetic with regards to beliefs in rebirth, due to logical reasons connected to the temporal philosophy of presentism that ontologically prioritises the present to the extent of rejecting the literal existence of the past. The implication is that memories aren't so much the recordings of bygone and static states of existence, but are part of the very meaning of what the past presently is.

Essentially by this view, the first-person subject is static and exists only "in a manner of speaking", with the concept of change applying only to presently observed things.

I personally have no problem with someone calling a single grain of sand a heap, even if that isn't my cup of tea. What harm could it do, and who am I to decree otherwise?

There is no a priori linguistic definition of "heap" in terms of any specific number of grains of sand,
— sime

Yes, that is the problem. — bongo fury

Why is linguistic imprecision a problem? "Heap" trades referential precision for flexibility, whilst retaining the necessary semantics for useful, albeit less precise communication.

The only theory of meaning Wittgenstein ever published was in the Tractatus, which was a solipsistic, subjectivist or idealistic doctrine of meaning that constituted conclusions he drew via methodological solipsism , that is to say by phenomenological investigation strictly in the first-person, that discounted the applicability and relevance of third-personal scientific rationalisization.

And the later Wittgenstein, whose solipsistic methodology remained the same as the earlier Wittgenstein and who now directly asserted that philosophy was purely therapeutic and descriptive and wasn't in the business of proposing theories, didn't immediately contradict himself by proposing the frankly ridiculous theory attributed to him that meaning is grounded in inter-subjective agreement or in some publicly obeyed rule-set sent decreed from above by the guardians of meaning in Platonia.

The confusion here, seem to partly stem from the public's lack of understanding of the positivistic epistemological ideas of his time that he was attacking, as well as a general lack of awareness regarding Wittgenstein's so-called "middle period", in which he wrote about his phenomenological inquiries and negative conclusions that there was no hope of obtaining a phenomenological theory of meaning of the sort proposed his earlier self proposed.

But that doesn't mean Witt then concluded "in that case, by appealing to the law of excluded middle realism is true. I propose a new epistemological foundation in which there is only one sort of meaning that is decided by the public, platonia or scientific naturalism in a mind-independent reality". All he concluded is that due to the overwhelming complexity and uncertainty of phenomenological analysis, it is impossible for himself to give an exhaustive and unconditional phenomenal theory accounting for his own use of words.

It is therefore understandable, as to why Wittgenstein was sympathetic towards Heidegger and could personally relate to Being and Time on the one hand, while at the same time insinuating that Being and Time was nonsensical when viewed as a collection of propositions with an inter-subjectively determinable truth-value.

Nonsense doesn't mean "false", it merely refers to an inability to determine the sense of a word when it used in a context from which it did not originate. Wittgenstein's sympathies towards Heidegger demonstrate that he did not believe the most important types of meaning to be inter-subjectively decided. Only inter-subjective meaning is inter-subjectively decided.

We can all agree that we can relate to Being in Time, without pretending to ourselves that we understand each-other's understanding of this work when viewing our agreement from the perspective of a different language-game.

Any finite number of grains of sand does not have this property.
— sime

So... isn't a heap? — bongo fury

There is no a priori linguistic definition of "heap" in terms of any specific number of grains of sand, which is why "heap" must be logically represented as referring to a potentially infinite number of grains of sand.

The role of potential infinity in a logical specification is to act as a placeholder for a number that is to be later decided by external actors or the environment, rather than the logician or programmer.

Agreed. But what is the smallest number of grains that would need considering by speakers as a particular case? Is it 1? — bongo fury

It is you and only you who gets to decide the answer to that question whenever you are next confronted by a growing or diminishing collection of sand grains.

I would be surprised if there isn't a population study that has attempted to quantify the mean number of grains of sand at which speaker of English judge a collection of sand to be a heap. A few hundred grains?? A few thousand?

like imagining a heap of sand that never changes after a grain is removed or added.
— sime

... leading to the conclusion (incompatible with a premise, or there's no puzzle) that a single grain is a heap. Does that happen also with your "infinite" element, so that it can evaluate to 1? — bongo fury

No, that isn't the case. To summarise, a heap of sand can be defined as the list:

Heap := [ Heap, grain]

The list remains constant, regardless of how many grains are added to it or subtracted from it. Any finite number of grains of sand does not have this property. That is precisely what it means to say that a heap of sand has no inductive definition.

Where i differ with the OP, is his belief that it is an approach unconnected to ideas of fuzziness or ambiguity. This isn't the case, because the practical usage of infinity, such as the use of infinite loops in computer programs, is to defer the termination of the program to the environment. Or in the case of heaps of sand, the semantics which concern the precise moment when an actual heap of sand is considered to be mere grains of sand, isn't linguistically specified a priori but is decided by speakers on a case specific basis.

Your proposed solution sounds to be in a logical sense the same as mine, which is to consider the heap to be a co-inductive type.

First consider the recursive definition for the set of inductively constructed lists.

Inductive List := { [ ] AND x : Inductive List }

Evaluating this equation by substituting the left-hand side into the right-hand side is analogous to building every possible collection of sand-grains by starting from nothing and adding a grain at a time. Yet we don't call a collection of sand-grains constructed by this process a heap, because "heaps" aren't defined by induction.

In contrast, the set of co-inductively constructed lists is defined by switching the AND for an OR:

Co-inductive List := { [ ] OR x : Co-inductive List }

The set of co-inductive lists contains the inductive set of lists, but because it isn't obligated to build lists by starting from empty, it also includes an additional list of "infinite" length. By "infinite" we are merely referring to the fact this set contains the definition of list that might never terminate upon iterated evaluation.

The former type of list corresponds to the natural numbers, whereas the latter type corresponds to the conatural numbers, otherwise known as the extended natural numbers that includes a numeral for infinity, which in computing can be used to denote programs will never halt to produce an output.

I think that the grammar corresponding to "a heap of sand" is analogous to the "infinite" element of a coinductive list, which as you say is like imagining a heap of sand that never changes after a grain is removed or added.

What's a "theorem prover"? Computer program? A tutor? — jgill

More generally, it is a dependently typed logical programming language, with clause resolution and other rules of logical inference, together with SAT solvers, methods of analytic tableaux and heuristics for automated or interactive theorem proving.

Lean with Mathlib, to my understanding is a state of the art approach to logic and mathematics programming that embodies the above principles , an approach which together with advances in deep learning theorem proving will undoubtedly revolutionise mathematics education , automation and research. Remarkably, the mathematics library of lean now codes the proofs of a lot of undergrad level mathematics.

https://leanprover.github.io/live/latest/

I don’t regard professional mathematicians as being trustworthy or helpful with regards to the literal truth of their subject, for several reasons.

1. They can be expected to exhibit a political bias towards inflating ontological claims in mathematics , in the same way that professional chess players can be expected to inflate the importance of chess and exhibit bias against other games. Traditionally this is bias is evident in the continued prevalence of classical logic in the justification of mathematical claims and the high percentage of mathematicians who are platonists, a position that is troubling to any engineer or computer scientist who unlike pure mathematicians have actual responsibilities regarding the physical actualization and interpretation of mathematical results.

2. The subject of ontological claims and commitments is the domain of logic rather than of mathematics, and the classical mathematician isn’t logic savvy, unlike today’s generation of mathematics undergraduates who are studying mathematics using theorem provers from the outset.