To clarify Wittgenstein's "epistemology", background historical context is required with regards to "Wittgenstein's Verification Principle" in 1930 that the Vienna Circle enthusiastically adopted for several years, but that Wittgenstein came to reject shortly after he proposed it. According to the verification principle, the sense of a proposition is its means of verification.

Wittgenstein explained the verification principle to Schlick:

"If I say, for example , 'Up there on the cupboard there is a book', how do i set about verifying it? Is it sufficient if I glance at it, or if I look at it from different sides, or if I take it into my hands, touch it, open it, turn over its leaves, and so forth? There are two conceptions here. One of them says that however I set about it, I shall never be able to verify the proposition completely. A proposition always keeps a back-door open, as it were. Whatever we do, we are never sure that we are not mistaken.
The other conception, the one I want to hold, says, 'No, if I can never verify the sense of a proposition completely, then I cannot have meant anything by the proposition either. Then the proposition signifies nothing whatsoever.'
In order to determine the sense of a proposition, I should have to know a very specific procedure for when to count the proposition as verified. "

But, in line with a common tendency displayed in this forum, the logical positivists mistook his idea of verification for a dogmatic theory of meaning. Indeed Wittgenstein himself was briefly seduced by this principle in 1930 before abandoning it. Wittgenstein told the Moral Science Club in Cambridge:

"I used at one time to say that, in order to get clear how a sentence is used, it was a good idea to ask oneself the question: 'How would one try to verify such an assertion?' But that's just one way among others of getting clear about the use of a word or sentence. For example, another question which it is often very useful to ask oneself is: 'How is this word learned?' 'How would one set about teaching a child to use this word?' But some people have turned this suggestion about asking for the verification into a dogma - as if I'd been advancing a theory about meaning. "

Hopefully everyone here will see that abandoning the identity 'meaning is verification' as well as it's weaker cousin 'meaning is dependent upon some process of verification' implies abandoning every theory of meaning , including meaning is proof or derivation, meaning is convention, meaning is contingent upon social verification, meaning is falsification etc. For each of these cases involves appealing to case-specific criteria of meaning that aren't universally employed across all language-games, and are mostly of relevance to formal language-games in which meaning is directly defined identified with verification. Verification criteria aren't generally present in other use-cases of propositions. For example, many everyday uses of "2+2 = 4" don't involve any checking for equality beyond one's immediate first impression.

His rejection of the principle of verification also demolishes common misconceptions referred to as "Private language arguments" that argue for a rejection of private meaning on the basis of an absence of independent or external verification criteria. Wittgenstein gave an example of private meaning without verification criteria as early as may 1930 in Philosophical Remarks:

"How do I know that the colour of this paper, which I call 'white', is the same as the one I saw here yesterday? By recognizing it again; and recognizing it again is my only source of knowledge here. In that case, 'That it is the same' means that I recognize it again"

As for the status of philosophical skepticism. Wittgenstein did not believe that "hinge-propositions", had prescriptive value. His criticisms of Moore weren't criticisms about the truth of Moore's assertion that he has hands (which depending on one's interpretation of Moore's intended meaning could either be viewed as true, false, both or neither) but were criticisms pointing out the distinction between the use of propositions as auxilliary hypotheses, versus the use of propositions under evaluation.

au contraire, Wittgenstein is saying is that all observations (word usage) are compatible with any conceivable law. — Agent Smith

Not quite. Wittgenstein only criticised logical conceptions of meaning, especially in relation to the view that the meaning of a proposition is static and a priori decidable . He didn't criticise individuals for their idiosyncratic interpretations of rules and language, which generally don't invoke theoretical interpretations of meaning.

There is a world of difference between speculating that an event E must logically follow from the a priori definition of a law L, versus recognising for oneself post-hoc, that E follows from L.

For example, often when you judge for yourself that two colours are the same, (which you usually do without any external guidance), your recognition wasn't contingent upon you invoking a priori definitions of the colours involved and calculating a truth value.

This is the reason why Wittgenstein wasn't a verificationist - meaning doesn't normally involve processes of verification - ergo Wittgenstein wasn't against the idea of private meaning.

Consider the propositions

"The sequence x1, x2, ... is determined by the function f(x)"

"The function f(x) is determined by the sequence x1, x2, ... "

There are two permissible interpretations of the word 'determined' in the above propositions:

A) As an imperative when for instance normatively insisting that " f(x) means the sequence x1,x2,..

B) As a descriptive hypothesis when for instance alleging that a given sequence x1,x2,... obeys f(x)

Classically, the sign 'x1,x2...' is interpreted as an abbreviation for a particular sequence of infinite extension for which there isn't time to write the whole sequence down. Under this identification, interpretations of the form A leads to the identification of f(x) as also denoting a particular domain and image of infinite extension. Thinking of functions extensionally in this way leads to scepticism whenever it is asked if some unbounded sequence S obeys a given f(x), given that only a finite prefix x1,x2,..xn of S can be observed. In conclusion, hypothesis of the sort (B) aren't verifiable when thinking this way.

On the hand, in the Russian school of constructive mathematics, functions aren't directly interpreted as representing entities of infinite extension, but as being finitely describable computable maps whose domain is unbounded. But this can lead to the same impression of such functions as having actually infinite and precise extensions if one thinks of such functions as denoting ideal and physically infallible computation. Thus the same platonistic skepticism about rule-following arises as in the classical interpretation.

The alternative to adopt Brouwer's philosophy of Intuitionism, in which ' x1,x2,... ' is interpreted as referring to partially defined finite sequence of unstated finite length, rather than as referring to an exactly defined sequence of actually infinite length. In other words, x1,x2,... is interpreted as referring to a potentially infinite sequence whose length is unbounded a priori, but whose length is eventually finitely bounded a posteriori at some unknown future date. Likewise, the domains and images of functions are also interpreted as being potentially infinite rather than as being actually infinite. Relative to this philosophy, rule-following scepticism is avoided due to the fact that the meaning of potentially infinite sequences and functions are both understood to be semantically under-determined a priori.

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All of you must be talking nonsense. It's easy to demonstrate that nothing can change in space. How can the same thing exist in two different positions? It's also easy to demonstrate that nothing can change in time. How can the same thing exist in two different points in time? It must be two very similar things, but they are not the same, since they exist at different times. There is no such thing as change. — pfirefry

Nevertheless, one can still create the idea of 'change' by using an indexical such as 'this' to refer to two or more referents, as when recognising that the colour of an object has changed - something that is objectively nonsense for the reasons you point out, and yet subjectively meaningful.

Perhaps one can say that the mind is change, implying that philosophical theories concerning personal identity over time are unnecessary and redundant.

"the primary value of truth and knowledge is for use in decision making to help identify, plan, and implement needed human action." — T Clark

But that is likely to be accepted as true by many non-pragmatists.

Am I right in suspecting that what you are actually protesting about is the artificial distinction between theory and practice that classical philosophy has been prone to insinuating?

Of course, not only philosophers but mathematicians, scientists and engineers are prone to thinking dogmatically in holding certain propositions, models or techniques to be infallible, lending to occasional calamities such as financial crises. One of the modern culprits of dogmatism is statistical and probabilistic modelling and deep learning for making implicit the assumptions of their respective models. The joke called Bayesian epistemology, which can encourage the delusional practice of smuggling assumptions into a model in the name of not making any assumptions, further adds fuel to the fire.

Here is a description of William James' definition of truth from an article I found on his book "Pragmatism.

Beliefs are considered to be true if and only if they are useful and can be practically applied. At one point in his works, James states, “. . . the ultimate test for us of what a truth means is the conduct it dictates or inspires.” — T Clark

Note that James appealed to such arguments when justifying the beliefs and practice of religion, and Richard Rorty has given pragmatic arguments for increasing the cultural prioritisation of the humanities (including Continental philosophy), relative to the natural sciences, by arguing that different communities in different subjects get to decide their own criteria of truth.

Pragmatism can encourage the identification of truth with what is expedient to believe, in line with post-modern cultural relativism, which I'm pretty sure you don't agree with. Something far from being an ally of the enlightenment values embodied by modern engineering.

Change vs Difference:

In terms of McTaggart's B series, every temporal referent, e.g. date, is different - by definition of "referent" . This is used in calendar logic, but also applies to the above colour difference picture in which one instantaneously recognizes more than one colour referent. In both calendar logic and the above picture, what is called "difference" is recognized without any concept of temporal passage coming into play. ( a stimulus-response to an image shouldn't be interpreted as being an inference, because the future is irrelevant as far as the stimulus-response is concerned)

"Change" refers to two referents being associated with the same indexical. For example, if one thinks that "now" becomes "now", then one creates the confusion of temporal passage. But if instead one thinks of the first act of "now" as referring to '09:09 on 26th Jan' and the second act of "now" as referring to '09:10, 26th Jan' then no change can be acknowledged.

I think it's clear from what I've written that I don't agree. — T Clark

I'm not sure that we do disagree. You presumably agree that modelling assumptions , which are ultimately causal or logical, aren't empirically verifiable, and that on the other hand, unless modelling assumptions are made, to speak of learning from data is meaningless.

It isn't clear to me how to philosophically distinguish epistemological pragmatism from a supposed anti-thesis. I am under the impression that epistemological pragmatism is being defined here in terms of the practicality of the problem pursued, rather than in terms of the method of inquiry which at every step hangs upon intuition regarding non-verifiable assumptions of causality.

"Life after life" (anti-anxiety placebo) is nonsense like e.g. north of the North Pole. — 180 Proof

Does tomorrow come after today, or is today always today?

One cannot justify the usefulness of a model of data without first making ontological commitments. The concept of usefulness only comes after committing to some notion of truth, that cannot be pragmatically determined on pain of circularity.

I think out of sheer intellectual curiosity it can be interesting to try to determine what happens after death. Does it really serve any practical purpose? Maybe not. — Paul Michael

On the contrary it very much does, considering the fact that all moral and ethical conclusions are relative to the premise of death that one adopts. In my opinion, society's beliefs regarding death are very much decided according to the behavioural advantages that result from holding those beliefs, which under capitalism tends to favour beliefs that motivate someone to work and spend intensely, as if they only lived once.

On the other hand, if the general public believed in reincarnation, and hence that there is no escape from the physical suffering perpetuated by unfair economic outcomes and environmental destruction, then I cannot see why they would continue to accept the current system of capitalism.

Cultural atheism under capitalism is more a less a sect of Protestant Christianity rather than being it's antithesis. The myth of the afterlife has only slightly changed, with ethereal promises of a heavenly paradise being substituted for an equally ethereal promise of perpetual nothingness - which most boomers are banking on for their post-humus escape from the mess they created on Earth.

The other conclusions beg the question. They assume that an entity or substance exists within the biology but is not the biology, and second, that this entity or substance can somehow persist beyond the biology itself. It seems to me one should be proven before contemplating the other. — NOS4A2

The presentist/idealist alternative doesn't speculatively assume a soul substance, rather it simply treats first-person experience as ontologically fundamental and unchanging. Of course, it's conclusions beg it's own ontology, but this is unavoidable whatever stance one takes.

The question one needs to ask, is given that different ontological assumptions about life lead to radically different conclusions about death that are in large part tautological, why choose a single ontology as being correct? Why not accept all of them and accept their respective conclusions relative to their respective ontology?

Note that the most primordial beetle of all beetles, so to speak, is conscious awareness itself. The question is asked, “Does conscious awareness occur in myself, in humans at large, in other lifeforms?” To which Witt replies, “It would be a beetle in a box, so who knows and who cares? It’s irrelevant.” — javra

The point of the Beetle box analogy was only to dispel the idea that there could be a meaningful inter-subjective notion of sensations in the form of Fregean referents. Yet recall that Witt likened the sense of the word "pain" to a picture of a boiling pot containing real boiling water - in other words, one understands so-called "other people's" pains directly; partly through observing a person's behaviour and partly by drawing upon one's own experiences of pains. Therefore the concept of objective sensation referents is redundant in that it isn't needed for understanding or justifying the existence of so-called 'other minds' (the word 'other' being responsible for most of the grammatical confusion).

Alternatively, to solve this sort of problem using the smallest number of brain cells and the least amount of graphics, restate the given premises formally, using a single variable x of universal type U

i) ∃x:U , A(x) ∧ B(x)
ii) ∀x:U, S(x) ⇒ B(x), which is equivalent to ∀x:U, ¬B(x) ⇒ ¬S(x) which immediately gives D.

Then state the theorems

A) ∃x:U , A(x) ∧ S(x) (which can instantly be seen to not be derivable from i and ii)
B) ∃x:U , A(x) ∧ S(x) (same as A)
C) ∀x:U , S(x) ⇒ ¬A(x) (instantly recognizable as not derivable)

We already know what happens after death, have the cadaver farms to prove it, and it ain’t pretty. — NOS4A2

That 'we know' what happens after death in the sense to which you refer, is a valid, albeit tautological conclusion relative to the biological definition of death. This 'conclusion' however, is not a conclusion in the sense of an empirically inferred contingent proposition, given that it is more or less a restatement of the premise that death means biological extermination in the sense that is ascertainable by third-parties.

Such behavioural definitions of death are therefore not in conflict with the supposedly conflicting conclusions arrived at via other definitions of death in relation to other conceptual frameworks, such as solipsism, phenomenology and presentism which present a different tautological conclusion.

It's amusing how much air-time the BBC has devoted to shaming Boris's breaking of Covid rules, given that five years ago they barely raised an eyebrow over the BMJ's study that linked 120 thousand deaths to needless Tory austerity and benefits custs that even provoked UN condemnation - policies that the BBC were happy to promote in the name of journalistic neutrality, the same BBC that has previously devoted thousands of hours to climate skepticism and the benefits of Brexit.

Yes. Another way of putting it in order to sound less speculative, is to remark that the predicate 'being conscious of' has the grammar of an indexical, like 'this', 'here' , 'now' etc. It doesn't make sense to speak of two 'nows', let alone a succession of them, because 'now' isn't an observable referent. Rather, 'now' is an ostensive means of referring. Likewise, it makes no sense to speak of consciousness as changing, appearing or disappearing, for in all of those cases what is being referred to are various observations that one 'is conscious of' .

Think of time as an umbrella concept for the following notions:

P) Process. (meaning observable change and concurrency).
H) History. (meaning memories, records and archives )
C) Causality (meaning modal logic)

Are these three concepts irreducible, or does one or more reduce to the others?

Consider

C = P + H. This is essentially the Humean notion of causality.

P = C + H. This is equivalent to assuming that laws of physics exist.

H = P + C. This is presentism in which the past is said to not exist.

I see "mind-independence" as theoretical equivocation that results from ignoring praxis, because whilst theories can be presented aperspectivally, the use of a method cannot be.

For instance, traditional theories of causality identify the causal order with the temporal order. And yet methodologically speaking, I usually observe effects before their causes.

From a logical perspective, the beginning of time can be chosen arbitrarily. All one has to do is reorder their knowledge accordingly. One can choose the beginning of time to be right now, by conceptually separating the temporal order from the causal order, and then choosing the temporal order to start now.

think that you are talking about another kind of beliefs, since you involve society. I'm talking simply about "belief" as a concept and referring to individuals: "an acceptance that something exists or is true". It is something very very, but very, simple. — Alkis Piskas

Sure. I am only suggesting to make things even simpler by dispensing altogether the idea that beliefs are properties of individuals, given as you say, that an individual's beliefs are merely what the individual considers to be true.

For logically we get

I believe(x) implies x is true, and
x is true implies I believe(x)

implying that belief predicates of the first-person are redundant in merely asserting what is the case.

Of course, the above analysis appears to be wrong to most people, with beliefs appearing to be indispensable, due to the fact that we say that previously held beliefs can be proven "wrong". But this is just a turn of phase in which we reinterpret the past as referring to the present for the sake of maintaining our linguistic conventions.

Nevertheless, it remains an intuitively useful fiction to externally predicate beliefs and goals on behalf of third-party agents when attempting to predict or control their behaviour, as for example in machine learning when informally analysing a reinforcement learning algorithm in terms of "goals" and "belief states"

I share your point of view, as I see Trivialism as a corollary of truth-conditional semantics, which can be the only scientifically respectable semantics from a causally objective point of view. But i am inclined to express that position by saying that beliefs are concepts defined by, and pertaining to, the social convention of language, as opposed to properties pertaining to the psychological states of individuals.

For example, society is unlikely to attribute false beliefs to Amazon Alexa if she said something or acted in a way that we call "untrue", because in her case society considers itself to have causal understanding of her stimulus-responses.

A proposition is usually taken to be the intentional object of a belief, by definition of both "proposition" and "belief". By this understanding, they are internally related on a conceptual level and neither concept can be understood without the other, as opposed to each concept existing independently and being contingently related through external happenstance.

Part of the confusion might stem from the fact that in logic, propositions are expressed using a formally recognizable linguistic structure in the form of composable predicates, terms and quantifiers, leading to the paradox of the unity of the proposition, which indicates that the meaning of propositions isn't syntactically decomposable into reusable terms and predicates in the way that logical analysis appears to suggest.

The mutually dependent definitions of belief and proposition also invites scepticism regarding the existence or utility of belief concepts. For example, in Wittgenstein's remarks concerning what turns an arrow sign into a pointer, he comments to the effect that the a priori phenomena that we might associate with the propositional attitude of an observer of the arrow (e.g feeling that the arrow is pointy), is only partially relevant, if at all, to the observer's eventual use of the arrow.

Likewise, Bertrand Russell identified the intentional object of a state of hunger to be whatever food is eventually used to satisfy the hunger, as opposed identifying the intentional object with the imagined food that a hungry person thinks about before eating.

Beliefs and other propositional attitudes don't objectively exist.

For example, I notice a person standing at a bus stop. Unless I subjectively empathise with the person who is doing the standing, I cannot form the proposition that the person is waiting for a bus . Objectively speaking, I can at most hypothesize a causal explanation as to their standing behaviour, an explanation that refers only to their past behavioural conditioning and makes no reference to belief-states or to future-contingent phenomena such as whether or not a bus comes and the person gets on it.

I am more than willing to interpret the person as waiting for a bus, via an instinctive act of empathy, but in doing so I am mixing together my own beliefs regarding the person with my concept of their beliefs.

Science is a practical means for relating and translating different perspectives, and isn't descriptive of perspectives per-se, due to the fact that perspectives are a meta-logical concept that are external to the inter-subjective concept called 'scientific investigation'. Science isn't troubled by the fact that our perspectival uses of language come into conflict with our shared linguistic conventions , because science's concerns are only inter-subjective.

You never lose awareness during sleep, for you cannot meaningful assert that you are unconscious in the present. Rather, when awake you have no memories about being previously asleep, which you call "being previously unconscious". And when we say that a subject is 'presently unconscious' "because" he isn't responding, the word "because" isn't being used in the sense of the justification of a hypothesis , but in the sense of defining what is meant by the word "unconscious" from the perspective of external observers.

So to answer your question, sleep is a useful 'private' model of death in that both concepts pertain to the concept of amnesia and nothing else.

To borrow from Berkeley's anti-representationalist ontology, all concepts, including "mind" and "brain" are reducible to ideas, where "ideas" (or in modern parlance, "qualia"), share the grammar of indexicals likethis and that, i.e. "ideas" are the medium of empirical understanding, and in themselves are neither substances nor representations, in spite of the fact they are presented that way during communication. Perhaps we can say that "ideas" are the very conceptual material of what we call "substances", "relations" and "representations".

The problematic part of Berkley's ontology (as I interpret Berkeley) , are "spirits" that refer to subjects with respect to which ideas are relativized, a move which appears to translate the dualism between mind and matter into a dualism between minds and ideas, and Berkeley apparently didn't consider third-party subjects as being reducible to ideas of the mythical first person "subject", and i'm not sure as to why.

You might understand the paradox differently to me, but for me the paradox concerns only the concept of length, and since points are volumeless they cannot contribute to the paradox. Not to mention the fact that the OP's visual demonstration of the paradox only made reference to line lengths and a limiting argument.

From this perspective, the paradox is reproducible by using a point-free topology consisting of the lattice of right-angled triangles with rational-valued endpoints, with an analogous dissolution to what i mentioned above.

This paradox shows that intervals dx are not the same as x. All dx tògether have length 2, because you lay them together mutually orthogonal. Points can't be laid aside mutually orthogonal. The continuum can't be constructed from points x. But it can from dx's. — Raymond

Only finite intervals exist in the standard euclidean space, but this doesn't matter because infinitesimals aren't even quantities, meaning that limits and their approximations never meet in the plane, which resolves the paradox.

Whatever. As I mentioned in another thread, a simple isomorphism between physical reality and mathematical structures provides a way of saying they are the "same" without being identical. But if this is truly what Tegmark had in mind he overdid his arguments - as do some posters on this forum. :cool: — jgill

But if meaning is use - which is essentially a structuralist standpoint - then it isn't clear to me that maths and physics aren't identical, at least partially, in a tautological sense. From the perspective of use, the meaning of Newtons Laws of motion, for instance, includes the mathematical activities which are used in their application. Conversely, the meaning of "2 + 2 = 4" can be understood to include the physical experiments that verify it.

What i was mostly objecting to earlier was Tegmark's aperpsectival take on the conceptual overlap that is a consequence of his scientific and metaphysical realism.

Differentials are funny things. They are not points, but infinitely small pieces of a continuum. The small stairs has the same length as the big one. The smooth diagonal has a different structure as the infinitely small stair. You could put the differentials in a variety of ways together around the diagonal. Mutually orthogonal, like a stairs, or in a general zig-zag pattern, which will lead to a total length bigger than sqrt2. Maybe even an infinite length. Can one project all parallel differentials placed together to form an infinite line, squeeze together on the diagonal? If you rotate all dx on the infinite line 90 degrees, can the be layed side by side on the diagonal? — Raymond

Differentials, i.e. infinitesimals cannot denote regions of Euclidean space, due to the fact the reals are an Archimedean field, which prohibits the definition of infinitely small intervals. Yet infinitesimals are indispensable to analysis, due to the mathematical importance of potential infinity, of which they are the reciprocal concept.

According to Cauchy

"When the successive numerical values of a variable decrease indefinitely so as to be smaller than any number, this variable becomes what is called infinitesimal , or infinitely small quantity... One says that a variable quantity becomes infinitely small when it's value decreases numerically so as to converge to the limit zero"

In other words, an infinitesimal should not be understood as being a quantity, but understood as referring to a variable that refers to a non-infinitesimal value chosen at random from a monotonically decreasing process whose limit is zero. In practice, the use of an "infinitesimal" is analogous to running an algorithm that generates it's respective process, then stopping the algorithm after a finite random amount of time and using the last value obtained as the value of the infinitesimal variable (which is necessarily a non-infinitesimal quantity)

More generally, the (ε, δ)-definition of a limit of a function f(x) at some point b has a similar interpretation, namely as a process denoting a winning strategy in a sequential game played between two players. Player one first fixes a value for L, then in every round of the game player two chooses a positive value for ε and player one then chooses a value for δ in response. If δ is such that |f(x) - L| < ε whenever |x - b| < δ , then player one wins the round. If player one has a strategy for winning every round, then the limit is L. But all meaningfully defined games must eventually terminate, which in this case is when player two decides to quit, making the eventual value of |f(δ) - L| a random positive quantity determined by player one's last move.

So on reflection, the philosophical paradox raised by the OP is resolved purely through careful inspection of the limit concept; for to say that a sequence of finite staircases comes "arbitrarily close" to a diagonal line, is only to assert that a staircase randomly drawn from the respective process comes boundedly close to the diagonal line, where the looseness of the bound is a monotonically decreasing function of the staircase's position in the sequence.

It's all too easy to accidentally commit the fallacy of absolute infinity.

This is the stupidest discussion I have ever seen on the forum... Well, that's not true. Pretty stupid though. Here's my favorite:

In my opinion, the philosophical paradox is only solvable having gained an intuitionistic understanding of the continuum and of point-free topology, due to the fact that intuitionism is better fitted to the phenomenology of mathematical judgement. — T Clark

hehe You're welcome. But stupid or not, the paradox is due to intuitions that aren't compatible with the definition of the classical Euclidean topology. Rather than insist that our intuitions are wrong and that the mathematics is right, we can instead insist that our intuitions are right by switching to an arguably more realistic axiomatization of geometry in which the paradox is dissolved or doesn't arise in the first place, such as computational geometry or intuitionism.



Can you honestly intuit an extensionally infinite staircase that is arbitrarily close to a diagonal line yet remains different in length? The concept of differentiation is similarly philosophically problematic, due to the ghost of departed quantities.

Tegmark's views are in part the logical corollary of swallowing the subjective-objective distinction, according to which perspective isn't real and only "inter-subjective" laws for translating Lockean primary qualities are real.

His views are also funny, not only for abusing Occam's razor in such a crackpot fashion, but that a parameter-less "model" of physics is a contradiction in terms; for it is the parameters of a model that correspond to the model's falsifiable propositions, that are revised via fitting the model to data. An infinitely adaptable model that has no parameters makes no predictions and is functionally similar to the largest possible fishing net.

The general thrux of Tegmark's remarks can be interpreted as a Modus-Tollens argument against scientific realism. i.e. that his argument is valid, but that his conclusion is false, implying that his premise of a mind-independent universe is false - which is already an empirically obvious false premise to those who aren't blinded by a dogmatic understanding of scientific jargon.

Both idealists and realists can agree with the Ontic-Structural Realism of Tegmark. For example, British idealism's doctrine of internal relations is in logical agreement with OSR, without jumping the shark to conclude that only unthinkable and unperceivable mathematical structure exists in a way that is divorced from the Lockean secondary qualities of perception.

In my opinion, the philosophical paradox is only solvable having gained an intuitionistic understanding of the continuum and of point-free topology, due to the fact that intuitionism is better fitted to the phenomenology of mathematical judgement.

Consider for example, that it is impossible to visualise or perceive an extensionally infinite staircase, or a perfectly straight path, or vanishingly small point, or a precise angle. The instability, ambiguity and uncertainty that characterises mental imagery and perception complements the realities of mathematical undecidability and finitistic reasoning that intuitionistic geometry recognises and which classical geometry ignores, while Brouwer's theory of choice sequences parallels how one visualises or recognises "infinity" (i.e. as a finite random truncation of a vaguely sized process).

As the pollution of the supposedly sacred Ganges river demonstrates, the sacred lies in the realm of ideas and relates to the physical realm only to the extent that the recognition of those ideas is physically contingent.

Sime, you're wrong about the arrow example, and about a "look up table." Let's see if I can make this clear. Wittgenstein asks in (PI 454), "How does it come about that this arrow -----------> points?" Any sign, be it a word or an arrow, only has an application, a use, that we together as a people, i.e., in socially given situations, give to it. "This pointing is not a hocus pocus which can be performed only by the soul [the soul, as used here, should be understood as the inner thing, the subjective]. So, it seems to me, and not only me, but many other interpreters, that Wittgenstein is saying the exact opposite of your point. This is clear throughout the PI, starting at the beginning when he talks about language-games. — Sam26

" This pointing is not a hocus pocus which can be performed only by the soul "

Does not support your thesis or yield the conclusion

"Any sign, be it a word or an arrow, only has an application, a use, that we together as a people, i.e., in socially given situations, give to it."

unless by that you mean

"Any sign, be it a word or an arrow, only has an application, a use, that a person gives to it."

Which is logically coherent, and avoids the unintelligible requirement of social consensus with respect to meaning and truth, that you often appear to imply.

Notice the context of the PI 454, in which he barely mentions social consensus. He is merely remarking on the distinction between what is said or thought a priori in relation to a sign (e.g the sign's stipulated definition) in comparison to it's actual a posteriori application. The difference between the definition of a sign and it's eventual application - that is under-determined by the definition, undermines the possibility of any theory of semantics, whether private or public.

​"Infinity" is a striking example of a word whose use necessarily belies any stipulated definition. Our convention defines "infinity" as meaning boundless, endless, or larger than any number..., and yet any particular use of the sign of "infinity", such as in an executed computer program, eventually halts and involves strictly finite reasoning and demonstration, - in apparent contradiction to it's stated definition as being "endless" - until that is, it is remembered that the actual uses of the phrases "boundless energy" , "infinite love" and what have you, are also finitistic...

In other words, "infinity" and "going on forever" can be considered as synonymous, but no two applications of either are the same, for they halt at different times or finite numbers, if at all.. Hence the synonymous definition of infinity is a misleading tautology that says nothing of implicative relevance and isn't the semantic ground of anything. This is the logical content of the so-called "private" language argument, and as demonstrated, applies equally to the shared definitions offered by public languages.

The "private language argument" isn't "no private meaning, therefore only public meaning", but rather "no private theory of meaning, therefore no public theory of meaning either".

The concept of "potential infinity" partially circumvents the above issue by defining "infinity" to be an indexical referring to a fallible promise of a future finite number (as is done in computing), but fallible promises, by definition, lie outside of what is determinable by convention,implying the meaninglessness of a theory of so-called "infinite numbers" except as an empty syntactical construct.

Wittgenstein undoubtedly noticed that what is true regarding the definition of "infinity" is also true of every sign in every language, complementing Quine's attack on the analytic-synthetic distinction. For example, we say "Bachelor" is a synonym for "Unmarried Man", but no two individuals use the expressions synonymously. Synonymy isn't use - except when writing definitions.

And since the sentences of our language are infinite, we cannot even ground the linguistic notion of synonymy in personal or social conventions without appealing to a notion of logical implication, which leads to vicious regress if we think of logical implication as being reducible to convention. This observation of Quine in his attack on "truth by convention" predates the post-humus publication of PI by nearly two decades, and Wittgenstein was likely influenced by it. It rules out every stripe of meaning-theory so that neither phenomenalism, physicalism nor communitarianism can serve as semantic or epistemological "givens".

Your logic is on the right lines, imo. In phenomenological application, "Nothing" is only used to refer to the irrelevancy of an experience with respect to some objective, as opposed to referring to absolute absence of experience. Therefore, with some grammatical distortion one could say "experience is logically necessary" , by virtue of "experiential nothingness" referring to ... nothing.

Another source of conflict and confusion, especially among Bayesian statisticians, concerns the distinction between uncertainty and imprecision.

The typical breed of Bayesian accepts premise A.

Premise A: Tomorrow's weather is physically certain, but epistemically uncertain.

On the other hand, a modern physicist with a distaste for folk-psychology (and hence for conventional epistemology and Bayesian statistics) might reject A in favour of the "direct realist" premise B:

Premise B: From the perspective of today, tomorrow's weather is physically imprecise.

Here, physical imprecision refers to the fact that the physical information constituting "today" does not imply a precise weather-outcome tomorrow and that any accurate model of today's information translates this physical imprecision into an imprecise estimation.

I would disagree. Its raining is an axiomatic statement based on an independent variable. That is, it is independent from belief. If it was a belief, they would pose it as an opinion such as: I think it is raining. Calling water falling from the sky a "good justification" for a belief that it is, in fact raining is a bit of an understatement. — john27

People have a confusing tendency to say "I believe X" when exhibiting doubt or a granting concession that one might be wrong - the very opposite qualities to the supposed meaning of "belief".

Also, a person's spoken beliefs often belie their actions.

The meaning of our words or concepts is established necessarily within a social construct, and it necessarily follows that meaning is not a function of an individual’s privately derived sense of meaning; assuming that a privately derived sense of meaning is even linguistically possible, as Wittgenstein’s private language comments seem to suggest. — Sam26

Any interpretation of a social convention is subjective. Wittgenstein was especially clear about this (e.g how can I know the intended direction of an arrow? how I am supposed to interpret a look-up table? ) . So there is no escape from purely private meaning, at least for Wittgenstein, even if such meaning cannot be linguistically translated.

Of course, he did understand that there is no logical room for an intermediate "private language" mediating between one's percepts and one's use of public language, recalling his attack on the Is/Seems distinction with regards to perceptual judgements.