I think the third-person perspective gives rise to a lot of confusion though, because it gives the impression that what we say applies to everyone and everything, instead of simply to the people who share a given truth. And then people fight each other to prove that their truth is right and others are wrong, to make their truth prevail. If we stopped having that third-person perspective, I think there are a lot of things we could solve, a lot of problems that would disappear. We would listen more, and impose less. — leo

This problem, of course, is due to the conflation of truth and meaning. The 'official' semantics of our shared language is too coarse and inflexible to accommodate the idiosyncrasies of every person's bespoke use and interpretation of their national language. One can imagine a futuristic society in which each person's private dialect of their national language is publicly translatable into every other person's private dialect. If in addition the causes of every person's utterances were also understood, then every utterance in the language could be publicly interpreted as being necessarily correct.

All boils down to a matter of willpower, which I have analyzed endlessly. People demand that the world change them, and in this sentiment, weakness is born. Quite Nietzscian. — Wallows

As a sentiment perhaps. But willpower isn't a scientifically admissible cause of human action. Rather, willpower is the force one exerts in the pursuit of an incentive. Depressives most often lack the latter, rather than the former.

Do you then agree with the idea that truth is individual-dependent and not something that has independent existence? — leo

Yes, as far as truth is concerned, perspectivism is unavoidable. But that isn't to say that I necessarily believe in the possibility of first-person centered epistemology. A far as epistemology is concerned, the 'third-person' subject seems unavoidable, in so far as knowledge is communicable representation.

Cambridge dictionary defines truth as "the real facts about a situation, event, or person". Who gets to determine what the real facts are? If I say what the real facts are and others disagree, who is right? The same dictionary defines objective as "based on real facts". If we say that the real facts are determined through social consensus, then truth is a social consensus. — leo

The individual might use the social consensus as an estimator for what is true, but ultimately it is environmental feedback, experience and reason that determines an individual's concept of truth and not social consensus per-se.

However, social consensus certainly decides how a person's private use of language is to be publicly interpreted, and therein lies the root of many philosophical confusions. For another person's beliefs could be interpreted as being necessarily and always true, regardless of whatever the person says or does, with any apparent error on that person's behalf being an illusion caused by the public misinterpreting the person's words, actions and intentions. Conversely, another person's beliefs could be interpreted as being necessarily and always false.

You first need to distinguish truth from objectivity; the difference being that the latter is dependent upon linguistic convention.

Oughts and expectations are close cousins, due to the inferential semantics of propositions. For example, the meaning of the sentence "this apple is red", if it is to express anything inter-personal, is for it to express how it ought to appear to different observers under different circumstances. Yet this causal sort of 'ought' , has as Hume points out, no purely rational justification. Therefore causal oughts must express emotional sentiment, and hence causal justifications cannot be cleansed of moral sentiment.

If Suicide is tempting, then presumably the solution might be to contemplate the mysterious state of suicide, such that with any luck one 'virtualises' the expected benefits of suicide, and thereupon no longer feels the urge to go through with it.

For example, imagine in as much detail as possible the experience of falling off a tall building and hitting the bottom, either through accident or willful suicide, and contemplate the resulting loss of perception, thoughts and memories. Any realistic contemplation of death should reject the association of any particular thought or experience with it. Hence this contemplation, which works with suicidal thoughts rather than fighting them, could potentially constitute a therapeutic process of "letting go" of everything, including introspection and suicidal thoughts.

In my opinion, the sleeping beauty problem and the doomsday argument aren't meaningful epistemological problems, and merely serve as reductio ad absurdums against the conceptual atrocities of Bayesian epistemology and it's accomplice Set Theory, which together confuscate the empirical foundation of reason.

Say what? You're defining "objective" as "whatever one is willing to accept"? — Terrapin Station

Yes, I am tempted to think that such notions are non-cognitive expressions of one's epistemic disposition ,-although the more general world "truth" sounds more fitting for what i had in mind, rather than objectivity. The difference being that objectivity stresses a perspective-invariant truth.

For example, if one were to say "Tinned tomatoes taste horrible", a person might accuse one of being subjective in failing to recognize their personal predilection. But if one were merely to say " tinned tomatoes taste horrible for me", there wouldn't normally be any objection.

So let's suppose that all sentences of the form "X has property Y", are formally understood to be an abbreviation for " X has property Y, for me". With respect to this new interpretation of language, is there still a notion of objectivity that is distinct from the notion of truth? And isn't truth now understood to be the mere expression of epistemic acceptance?

What would be an "objective justification" in general? — Terrapin Station

I think Quine's web of belief provides a reasonable picture of the broad notion objectivity in terms of epistemic acceptability; the objectivity of a proposition being it's degree of coherence with respect to the rest of one's existing belief system.

The definition of objectivity in terms of a particular witness of a fact is a mistake. Simply put, a proposition is called 'objective' if one is willing to accept it.

That's simply another way of effectively saying, "We're going to consider argumentum ad populums 'objective.'" — Terrapin Station

Not necessarily; Only that the objective-subjective distinction has no objective justification on pain of infinite regress. I am still nevertheless prepared to accuse the public of subjectivity.

Objectivity refers to a public balance upon which impressions are weighed. Yet I only possess impressions of a public balance.

But in fact the question is: Is the green ball more likely to be the green ball in the second case than in the first case?



I think we are asking something like: Is there a smaller chance of you being you when there are more people in existence. — Mind Dough

You first need to define what makes each ball unique. What makes one green ball different from another green ball? Do the green balls each possess essential and intrinsically individuating properties, or is their individuation a holistic property of the set they belong to?

If you have children who are identical twins, they will always at least possess geographical uniqueness. But if you yourself are part of an identical twin, any conceptual notion of uniqueness here is unrelated to the former notion.

Suppose you were one half of a pair of Siamese twins and you experience pain. Does it necessarily make sense to attribute your pain sensation to only one of the bodies? It is conceivable that your opinion might be irreconcilable with those of onlookers, in virtue of irreconcilable notions of sameness.

"my consciousness is an illusion" can only mean that my stimulus-responses aren't publicly understood.

If society concludes that my judgement of an object's color is wrong, it only means that my behavioral reaction towards the object isn't inferentially useful for society.

Supposing Dennett tricks you in a change blindness experiment, whereby you are provoked to gasp
"I could swear that I was talking to the same person!". Your statement at this point says nothing about your original experience. Rather, you are merely reinterpreting your original expression of your experience as being inconsistent with your present inclinations.

None of the opinions I have tomorrow about today, can refute my current opinions about today. Because tomorrow isn't today. And it is only through a post-hoc reinterpretation of yesterdays judgments, that we can say yesterdays judgments about today are wrong. For today didn't exist yesterday.

The philosophical problem here, is that there is no definite meaning of 'living at a particular date', and we get very different answers to our question depending on whether we are referring to phenomenal aspects of time comprehension, mathematical descriptions of time, or public denotations of time as a network of synchronized clocks and calendars. These relations are very complex, and our theoretical definitions are under-determined.

If we think of time in the traditional realist way, we think of nature as the real calendar of events that we culturally represent and approximate using our calendars; we naturally end up interpreting existential probabilities across time in terms of a linear scatter-plot of calendar-ordered frequencies. Consequently we end up with a philosophically dissatisfying answer to our philosophical question as to the probability of living at a particular time, for all we end up here is with a circular framing of the problem that answers in terms of frequencies, when we were implicitly questioning the relationship between calendar use, physical time, and personal experience.

On the other hand, when trying to understand time directly in terms of personal experience, we run into the problem that the content of personal experience is vague and repeatable without an absolute ordering; I cannot, for instance, distinguish the current appearance of my living room wall from its appearance last Wednesday. So my living room wall does not serve as a calendar.

I am only able to refer to the appearances of my living room wall at different dates by taking it's appearance in conjunction with something else serving as a calendar - for example, other memories I have that are different from one another and that I associate individually with the respective dates. Or if my memory is failing, photographs. But then a similar problem of repeatability resurfaces with respect to the conjunctions of experiences; we can therefore only speak of calendar-like relations as existing between phenomena when they are suitably interpreted, but we cannot phenomenally speak of the existence of absolute calendars - in direct contradiction to realist intuitions.

Phenomenal time therefore isn't linearly ordered and non-repeating as suggested by calendars; and the psychological past isn't immutable and separable from the psychological future, rather they are both mutable and inseparable aspects of present experience. Therefore any empirical attempt to conceptually reduce physical time to a phenomenal foundation must abandon the linear-ordered-time orthodoxy; Cartesian notions of time are merely practically convenient, without a phenomenally legible basis.

On the surface, the law of entropy sound appealing as a justification for absolute temporal ordering. However, entropy cannot serve as a justification for an absolute temporal order; for the notion of increasing disorder is relative to the labeling conventions we use for describing a system, and in science our labeling conventions are deliberately chosen so as to maximise the information we get from an experiment. Entropy is therefore an epistemological notion as opposed to a physical or metaphysical notion. From an omniscient perspective, there is no absolute 'law' of entropy.

The assumption of time symmetric microscopic laws is a big give-away that entropy isn't real; for any microscopically time-symmetric system that is observed to decrease in order, there exists an alternative labeling of it's micro-states in which it is described as increasing in order; to see this, simply imagine a simulation of a deck of cards being shuffled. At the end of the simulation, identify the top three cards on the shuffled stack and give them an identical label. Then replay exactly the same simulation from the beginning, remembering the cards we previously labelled. When re-interpreted with respect to this new labeling convention, the card shuffle increases in order. Therefore entropy isn't a phenomenal intuition and neither is it a physical concept. Entropy refers purely to epistemological uncertainty; to state it mathematically: Given a random assignment of labels to micro-states, the average entropy change of a time-symmetric system is zero.

Well, for Presentism and neo-Kantianism, the probability of living now is one :)

From the standard realist perspective, averaging over all possible futures that are consistent with current cosmological information makes the probability of living at this moment of time vanishingly small, i.e. undetermined but convergent towards zero.

At the risk of antagonizing most of the contributors above, I would say any 'bunch of words we care to utter or write', including this one, has one function only...to attempt to facilitate the choice of future action, including the next 'bunch of words'. From that pov, dichotomies like 'subjective-objective', 'truth-belief' have import only in their promoting 'what, if at all, happens next'. The only context that matters is this one, and unless these discussions impinge on our praxis of living, we are indulging in little more than a type of social dancing with a bit of jockeying about 'who leads'. — fresco

I agree that there is much to be gained by considering philosophical disputes to be cultural conflicts, in which the role of the philosopher is that of a propagandist or social influencer. But personally I don't see this position as being necessarily negative or critical about the role or status of philosophy.

The problem is, the truth conditions and semantics of our physical ontology, i.e. our enumeration of 'what things exist', is defined in terms of publicly observable criteria that are definable in terms of third-person subject predicates, where the "third person" is generally the response of a measuring instrument; for example a physicist might say "The presence of an electron here is confirmed by the presence of this white streak in the bubble chamber". As a consequence, our physical ontology has no direct experiential interpretation, that is to say physics is epistemically irreducible to first-person experience - contrary to the hope of phenomenalism.

Unfortunately, to many this suggests that physics must also be metaphysically irreducible to experience - which is nonsensical given that first-person experience is the tribunal upon which all claims of existence are judged.

Suppose somebody sends you a circle in the post. You then proceed to verify that the circle isn't perfect. Does "perfect" here refer to an internal property of the circle or to our inspection of it?

Here is what I think. Whenever we construct a set ourselves, we must choose the next element to include in the set, either explicitly, or by implicitly by defining a rule of selection. But in order to do so, it must be first be assumed that our elements are individuated a priori for a process of construction to make sense. Yet if we are given a set, say a parcel through the post, it's elements aren't individuated until we inspect the set. If the parcel we are given is called "infinite", all this means is that we shouldn't expect the termination of our parcel inspection to be decided by a property internal to the parcel.

Mathematics tends to call parcels with non-individuated elements "equivalence classes" of elements. Like in the above example, this allows mathematics to either construct sets in a 'bottom up' fashion from elements, or to construct elements in a 'top down' fashion from parcels.

Probability should be considered as part of set theory, rather than classical set theory being considered to be a foundation for probability theory. For the semantics of probability is the semantics of empiricism and directly concerns both "volatile", uncertain and undetermined empirical sets as well as logically constructed sets, yet unfortunately these two meanings of probability are obscured if probability theory is reduced to classical set theory.

For instance, consider a sigma algebra (i.e. a sample space) denoting the set of possible outcomes for an infinite sequence of coin tosses t(1),t(2),... i.e. a coin toss process whose length is undefined a priori. Coin tosses aren't a mathematical concept but an empirical affair, and conversely mathematics isn't an empirical theory. Therefore it makes no sense to insist that the sigma algebra of infinite coin tosses must be constructive. For it might well be the case that a sequence of coin-tosses is truly random in the sense that cannot be represented by any computable function. This is the case if it is believed that for any computable binary function f there exists a subsequence of observations t(1)..t(n) that isn't equal to f(1)...f(n). Unfortunately, set theory fails to distinguish externally observed processes from internally constructed processes, hence the reason why finitists and infinitists continue to argue past one another.

I don't know what is a volatile and unbounded set. Can you provide some examples so I can understand what you're saying? — fishfry

Yes, any programmer's use of an infinite FOR loop. We all know in practice that infinite loops are, in a pragmatic sense, merely finite loops whose termination condition isn't specified by the program. In other words, the termination of the algorithm isn't internally constructive from the point of view of the program itself.

Volatile is not a term of art in math at all. And its use in C programming is very specific as I think we agree. It just tells the compiler not to optimize the variable. — fishfry

Right, i'm am not so much referring to compiler mechanics, as to the logic of volatile types. Programmers use a richer notion of logic than is used by traditional set theory that equivocates internally constructed sets with externally supplied sets. The consequence of this is mistake is the kludge known as the Axiom of choice that allows the specification of arbitrary unbounded sets, but only for unbounded sets, effectively conflating arbitrariness with unboundedness [/quote]

The integers are unbounded because you can't draw a finite circle around them all. The unit interval is bounded since all its elements are within 1 unit of each other. Yet the unit interval has far larger cardinality than the integers. So I am not sure what you're trying to get at. — fishfry

Whenever we refer to an integer, we are either referring to a integer which we ourselves have or will construct using an algorithm in our possession, or we are referring to an arbitrary integer that is to be delivered to us by some external source. Constructivists make the mistake of conflating existential quantification with construction. It is a mistake, because, say, we cannot run society on software that uses only predictably terminating bounded for loops. Platonists on the other hand, while rightly insisting that non-constructed sets are indispensable in practice, wrongly locate the source of that indispensibility to a priori notions of existence.

In C programming, the equivalent symbol to infinity is the volatile keyword.
— sime

Jeez that's not true. A volatile variable is one that is, for example, mapped to an external data source. Declaring a variable volatile tells the compiler that it can't depend on nearby code statements in order to optimize the variable. — fishfry

sorry, I should have said infinity is equivalent to volatile and unbounded. I am saying volatile and unbounded is equivalent to the specification of an infinite set, considered as extension, in cases where the infinite set is not directly defined in terms of a constructive algorithm.

This simply has nothing at all to do with transfinite ordinals and cardinals as understood in math. It's apples and spark plugs.

it also fails to discriminate sets which are volatile and bounded from sets which are volatile and unbounded.
— sime

This has no referent in math. I am not sure where you are getting these notions. — fishfry

Likewise, Transfinite ordinals divide into those which are specified constructively as tree-growing algorithms and those which denote unspecified trees to be supplied by the environment, whether bounded or unbounded.

Finitism overlooks the fact that the practical use of 'infinity' is merely to denote an unspecified unbounded number. Consequently, If infinity wasn't part of mathematics, then mathematics could not be used by science to describe current physical laws, rather it would only document previously verified event occurrences.

In C programming, the equivalent symbol to infinity is the volatile keyword. When a C program declares a volatile object, say "volatile int myInteger" , the program is declaring that the value of "myInteger" isn't specified by either the programmer or the program itself, but that the value will be supplied later at an unspecified time by the environment. The specification of an 'infinite' number of iterations in a computer program, say while(true) {..}, is therefore equivalent to writing while(volatile int myInteger){....}.

Unfortunately, set theory and logic do not possess an equivalent concept. The closest axioms they possess is the Axiom of Choice, but this axiom is flawed because it is considered to be either accepted or rejected universally across all sets, and it also fails to discriminate sets which are volatile and bounded from sets which are volatile and unbounded. Consequently the status of the axiom of choice remains confusing and controversial.

In my opinion, the historical cause of debates over the existence of infinity is the result of logicians failing to recognise that the semantics of logic and maths isn't fully a priori.

In my opinion, Wittgenstein wanted to use the word "grammar" to refer to the pre-theoretical, intuitive, ineffable and phenomenological aspects of meaning - but found himself unable to do so, due to

i) the common usage of the word "grammar" to refer to the conventions of linguistic protocol.

ii) The paradox that some form of linguistic protocol must be used if grammatical sentiment is to be communicated - which leads to verbal contradictions in cases where we say that a particular word or set of words has meaning but cannot be given a verbal definition.

Am i right in suspecting that Speculative realism is continental-philosophy's muddled attempt at analytic philosophy?

Turn the question around: Is it right for humans to allow other animals to commit cannibalism?

Suppose that we can synthetically mass-produce artificial meat. Then in order to minimize earthly suffering, then ideally, shouldn't we enforce ALL carnivores within the animal kingdom to eat synthetic meat only and prevent them from killing for food?

What is the justification for not extending human ethics into the rest of the animal kingdom? Is it merely a matter of pragmatism?

The idea of the Turing test involves interaction between two open systems. This implies that the dispute over the significance of the Turing test is independent of the dispute as to whether humans or machines are automata.

For whether or not a human or machine is considered to be an automaton depends upon one's definition of their conceptual boundaries across space an time. Is a machine that suffers an internal fault the same machine running the same program? Are sensory inputs considered to be part of the machine's operation? etc. etc.

There are two ways to interpret the Turing test, namely the realist/cartesian interpretation and the anti-realist/non-cartesian interpretation.

The public usually understands the Turing test epistemically according to the realist interpretation, since they normally by cultural default understand consciousness in a cartesian fashion as referring to intrinsic functional semantics of the brain. They consequently view the Turing test as a fallible appearance test of a machine's internal functional properties, properties that exist independently of appearances to the contrary, say if the Turing test gave a false-negative.

The less popular alternative view, that appeared to be the view of Wittgenstein, is the anti-realist, non-cartesian interpretation of the Turing Test, whereby it is understood that if a machine passes our consciousness test, then the machine is conscious by definition. In other words, a Turing test isn't so much a test for Turing-test independent consciousness, rather the Turing test articulates the visible circumstances in which we say that a thing is conscious or not conscious.

The critical ontological difference of this latter view, is that the functional semantics of a brain or machine are understood holistically as being irreducible to the brain or machine in and of themselves. As Wittgenstein hinted in PI, A game of chess is only recognized as a game of chess when embedded within a relevant culture. Therefore Wittgenstein would likely have sided with Searle and rejected Dennett's "China Brain"; for while the population of china might be able to use semaphore to simulate the brain's internal organisation, the surrounding context isn't present to attribute intentionality.


As for the question you actually asked, i believe the notion of free-will is to a large extent orthogonal to understandings of the Turing test.

The following is a link to some similar ideas to mine, although not entirely similar, but close.

https://www.academia.edu/7298912/Hinge_Propositions_and_the_Logical_Exclusion_of_Doubt — Sam26

That is pretty close to what i thought you were saying. I wasn't questioning your views, just pointing to directions of further discussion.

My conclusion based on these ideas is that many bedrock beliefs or hinge-propositions are causally formed, that is, there is a causal connection between the reality around us, our sensory experiences, and our mind. This, it seems to me, is what triggers the belief. — Sam26

Supposing a speaker, perhaps a schizophrenic, behaved in a certain fashion while talking in a contradictory manner about his actions (much like a politician). Whereabouts is the contradiction between his actions and his words? Is it in the speaker's mind? or does the contradiction purely concern linguistic convention, with any confusion being solely in the mind of the listener as a result of misinterpreting the speaker?

Supposing a speaker incorrectly guesses the lottery numbers. What is the difference between saying "the speaker's guess about the lottery outcome was wrong" versus saying "the speaker's 'guess' was correct, for he didn't really intend to win the lottery, for his report was in fact a causal response to his environment and we mistook his words for a prediction" ?

The problem is, there aren't any conceivable means for distinguishing the content of a bedrock belief from the content of a verbal belief apart from appeals to linguistic convention. And if beliefs, whether bedrock or verbal, are causal responses, then they cannot be objectively falsified, since behavioral goals are also interpretable in terms of causal responses to immanent environmental conditions.

In constructive logic, the logical rule for introducing existential quantification replaces a proposition that directly refers to a particular, say "My cat is named 'Zeus' ", with a similar proposition that is non-referring, e.g "There exists a cat named Zeus'". Conversely, constructive logic guarantees that an existential quantifier can always be replaced by a reference to a particular bearing the relevant properties.

By constructive logic, "X exists" doesn't refer to a spiritual essence of a particular to which one is presently acquainted,i.e. uniqueness, but merely expresses the ability to locate or to create at least one object possessing the observational properties described by the predicate 'X'.

So the meaning of "Elvis Presley does not exist", "Unicorns don't exist", and so on, without further assumptions, merely expresses the inability to create or to find objects described by the respective predicates.

The difficulty here, is to reconcile the fact that we can talk about unicorns whilst at the same time claiming that we cannot exhibit them. This can be reconciled by first giving unicorns a constructive definition within a hypothetical universe of discourse in which unicorns can be said to exist according to our definitions, and then afterwards asserting that such a constructive definition is inapplicable within our actual universe.

In other words, the non-existence of an object is understood to refer to a constructed object within one universe, that has no equivalently constructed partner within another universe, thereby making non-existence a relation between two universes.

Check out the Rorty clip above. The relativity of 'existence' thesis renders 'things in their own right' meaningless i.e. Kant's 'inaccessihle noumena' was abondoned by later phenomenologists as a useless concept. — fresco

Given that Existence was one of Kant's modal categories of understanding, perhaps Kant was arguing for your very position, namely that existence isn't 'noumenal' i.e. it is an expression of human judgement rather than an assertion of an absolute property.

In that case, it sounds like you are more interested in the policy optimization of Decision processes. Such problems can be implicitly solved via adaptive sampling, i.e. reinforcement learning, of action policies, state transitions and rewards, assuming they caneach be respectively sampled. If the utility function as a function of state, is known explicitly, it might even possible to analytically derive an agent's optimal policy, assuming linearity, Markovian dynamics, observability of states and actions, etc.

And this. Why must logic and maths be either discovered, or invented. Why not both? — Banno

The problem is, set theory fails to explicitly distinguish 'constructed sets' that correspond to an algorithm known to the logician, from 'discovered sets' encountered externally in the real world, but whose construction is unspecified.

If Set Theory were to insist that all sets can be constructed by an algorithm, then Set theory would also insist that nature is describable by an algorithm, i.e. that a Theory of Everything exists. Yet it cannot ever be known if such a Theory of Everything exists:

Take the example of a vending machine that dispenses a set of items. Should it be the job of set theory to insist that every vending machine has a mechanical implementation, whether or not we know of it's inner workings? Should Set theory automatically assume that every can of coke within the vending machine has a distinct identity before it is dispensed?

Standard non-constructive set theory has a means of specifying an "unspecified set", such as that produced by a mysterious vending machine, namely the Axiom of Choice. But ironically the name of the axiom is a misnomer, because the Axiom of Choice is only useful in mysterious situations where we cannot specify a choice procedure.

I think you're referring to modal logic, i.e. to possibility.

Syntactically, modal logic looks like the inverse of deduction, due to the fact that deduction allows different premises to lead to the same conclusion.

yes, we appeal to external witnesses, such as the operations of computers, or to the opinions of others, in order to conform whether or not our reasoning is tautologous. But this external checking not only confirms whether or not our reasoning is in accordance with our logical definitions, but it also constitutes part of the very meaning of our logical definitions. For the meaning of "ideal" logic must ultimately be witnessed by practical state of affairs, if it is to have public meaning.

So in my opinion, logical necessity is empirically contingent, although not contingent upon the testimony of any particular external witness.

"Logic doesn't require facts" - Only when our process of deduction isn't in question.

Remember, we usually need to verify our proofs via appealing to external facts, e.g. a calculator.

Presumably you mean formal logic (since the question is logical in its very nature). Formal logic is in an identity crisis imo, due it's failure to explicitly distinguish "necessary" objects that are constructed according to convention and are hence fully specified, from objects encountered in nature that are vague and unspecified.

For example, I can construct a sequence of cakes from a bunch of ingredients by iterating a recipe in my possession. But I can also obtain an identical sequence of cakes by repeatedly pressing a button on a vending machine. Neither logic nor set theory take care to distinguish these two sets, because the process of construction is viewed as being either irrelevant to, or identical to, the meaning of "existence".

Consequently a hideous "bugfix" called "the axiom of choice" was invented in order to accommodate "non-specified" entities, causing mass confusion and yielding ridiculous implications in failing to treat sets and their construction on a case by case basis.

Yes, as I understand it, verbal knowledge - the sort of knowledge discussed by epistemologists, is trivial and irrelevant to Gettier problems, for verbal knowledge must, at least under a naturalistic understanding of the mind, be reducible to linguistic convention.

For example, suppose Bob insists "The Earth is flat" and Alice is convinced that the opposite is true.
Then Bob and Alice aren't referring to the same thing. For if they were both referring to the same thing, then they wouldn't be in disagreement.

Rather, Bob and Alice are separately expressing to one another their own observations, goals and behavioral dispositions in a jointly incompatible way with respect to their shared language. Their conversational disagreement is only the result of each of them attempting to enforce their semantics on one another - and not just verbal semantics but behavioral as well; For example, perhaps Bob, in order to maintain his assertion that the earth is flat, refuses to circumnavigate the earth. His personal refusal to circumnavigate the earth would be part of his meaning of "the earth is flat".

On the other hand, the non-verbal practical knowledge of a solitary person, comprising of his actions in his personal pursuit of a goal, is where the Gettier problem has relevance. For here, linguistic convention matters not, while it is generally important to an individual that he can trust his watch, which necessitates a concept of practical-knowledge justification.

In PI Wittgenstein examines "Moore's Paradox", namely the sentence "It is raining, but I believe that it is not raining" and as I recall he concludes, in contrast to moore, that the sentence does indeed have sense when spoken about oneself in the present, namely as a situation in which one comes to realize that one's verbally expressed beliefs are in contradiction with one's actual behavior.

So the sentence "It is raining, but I know that it is not raining" also makes sense, when one is verbally certain about one's beliefs but comes to question one's behavioural "bedrock". So philosophers shouldn't equate behaviorally implied beliefs with verbally expressed beliefs.

Ironically, lucid dreamers use the presence of their dream hands within a dream as a cue to detect that they are dreaming. Said in this dream situation, is the sentence "I know I have hands" a hinge proposition or an epistemological claim? If a dreamer insisted the former they would fail the reality check and remain non-lucid.