I would be interested in knowing more about Ayer's rejection of memory as a means of distinguishing between past and future. Could you elaborate, or cite a reference?

It seems to me that experience (which happens in the present) is more than capable of distinguishing between before and after (e.g., cause and effect), and designating the measurable change: time (per Aristotle). — Galuchat

I'm not particularly knowledgeable about Ayer's particular ontological views regarding the relationship between memory, phenomena and time, and I am certain that Ayer, like all of us, had no problem acknowledging the practical role that memory serves as (unreliable) testimony to the truth of past-contingent propositions- i'm only referring to his general acknowledgement that the doctrines of logical positivism and verificationism failed -see for instance his interview with Bryan Magee. We still do not possess a theory spelling out what we mean by meaning, evidence and truth, especially in relation to past-contingent propositions for which there cannot exist direct observation or immediate testimony:


Is it logically consistent to be an empiricist who accepts a hard ontological distinction between past and future?

Is the semantic distinction between the past and future somehow reducible to appearances or to relations between appearances, or to potential appearances as a function of potential experiments?

How should physics and computer science categorize "future-directed" behavior in humans and other agents?

How can this be reconciled with the causal theory of reference which identifies the meaning of an utterance with it's causes?

the philosophically enlightening thing about the craft of software engineering is it's cut-throat pragmatism that makes explicit what mathematics and logic are really about, such that the disease of philosophical speculation cannot take hold. There aren't any software engineers debating whether an infinite loop really runs forever, unlike a significant proportion of set-theorists, who as a result of refusing to get their hands dirty in practical application, end up associating mathematical infinity with the religious idea of eternity.

It is certainly true, that from a pure meaning-as-use perspective the distinction between the past and the future is much harder to distinguish than it is from an axiomatic meaning-as-reference perspective (which effectively insists upon an a-priori and axiomatic past-future distinction).

We also anticipate both the future (e.g is this oasis I see a mirage?), as well as the past (e.g. will my current archaeological dig verify the massacre that allegedly took place here in 1942?). Of course in hindsight, yesteryear's predictions that supposedly refer to today are now seen retrospectively as mere instances of retro-futurism that in actuality only ever referred to what occurred when yesteryears so-called "prediction" was made ( how can yesterday's predictions even be wrong?)

We cannot definition-ally distinguish past-contingent propositions from future-contingent propositions on the basis of experiential content, unless we are prepared to bite the bullet and call a certain appearance "the past", such as the contents of a memory or photograph. But once we reject this as a mistake, as did Ayer, we realize we are then unable to provide an experiential distinction between past and future, even while we continue to insist on it.

There is of course, a big difference between an eaten Hamburger and a Hamburger sitting in front of us; if an object is called 'destroyed', then there does not exist a direct and local reference to the object that we can point at. There is instead a potentially infinite and interlinked fabric of facts called "the evidence of the destroyed object" together with our investigatory sense of anticipation. Hence an empiricist might be able to equate the past with our current sense of inferential expectation together with today's appearances taken holistically as an inseparably entangled whole. But this of course is too vague to constitute an empirical "theory" of any description.

Nevertheless, at least we can still speak of our expectations as being fulfilled, as for instance when walking up a hill to inspect the view, or when digging in the earth for relics. We can also partially order our historical knowledge in such a way as to minimize the statistical dependence of the occurrence of so-called "earlier" events on the occurrence of so-called "later" events. Perhaps it is possible to go neo-Kantian and argue that today's perceptual judgments necessitate an axiomatic past-future distinction in order to speak of "types" of objects and events. I don't know about this though.

In my view, a metaphysical assertion is meta-cognitive speech-act whose intention is to influence perception, behavior and values, via a wholesale change of view. A Metaphysical debate is the result of differing views or values being simultaneously incompatible, typically with one party being unable to grasp the sense or value of the other party's viewpoint.

I see metaphysical assertions as value-apt, but not truth-apt in a representational sense. After all, to a certain extent what is at stake is the method of representation, which in turn is decided according to what it is considered to be worth representing.

In my opinion, neither type-theory nor category theory are satisfactory in addressing the ambiguity of standard logic regarding infinitary notions.

Take as an example "My local postbox contains some letters". This proposition isn't a full specification of a set, and hence is not representable as a specific algorithm and hence cannot be constructed, and therefore it must be stated axiomatically as a particular set which exists but without having any internal details. Some people might already interpret set theory, type theory or category theory in this way but this isn't thanks to those theories themselves.

- The Axiom of Choice is wrongheaded in two respects:

i) It isn't a logical rule permitting the universal existence of non-constructable sets. Rather, it is used as a non-logical proposition to refer to a specific set in a domain of inquiry whose number of elements is potentially infinite, that is to say, isn't specified in logical description.

ii) The axiom has nothing to do with choice. On the contrary, it is usually used as a reference to sets for which a choice-function isn't specified.

Whereas classical logicians often mistake AOC for a logical rule, Constructive logicians often mistake the Axiom of Choice for a tautology; for they conflate the existence of a choice-function with the existence of a set; yes it is true that 'constructed set', 'computable set' and 'choice function' are synonyms - but this misses the point as to how the axiom of choice is used, namely in order to represent 'externally provided sets' that provide elements on demand, but whose mechanism and quantity of contents are unspecified.

To nevertheless insist that every physical set must be constituted by a computationally describable mechanism, should be regarded as a physical thesis, rather than being a logical theorem. For logic is a purely descriptive language without physical implications. Physicists might use set theory as a means to document their epistemological certainty and uncertainty regarding the internal operation of physically important sets, but this epistemological interpretation of set-theory isn't part of set theory per-se.

The correct semantics of logic and mathematics is game semantics describing the interaction of entities created and controlled by the logician on the one hand, and the entities of his external environment that he is aware of, but for which he has only partial control or specification of. This semantics serves to reinforce the notion that logic and mathematics are languages of empirical description that documents the interactions of the logician with his external world.

In my opinion,

Metaphysics refers to the conventions of language-games that seem to lack a definite or well-understood collective purpose, or when used disparagingly, to a convention that is believed to be unhelpful with respect to some assumed purpose of the language game.

In my view, I think we first have to distinguish two possible interpretations of the assertion 'induction is habit', namely an empirical interpretation versus a grammatical interpretation.

The empirical interpretation is to view the idea of induction as being distinct from the idea of repetition, whereby 'induction is habit' is viewed as an a posteriori empirically contingent assertion correlating two distinct ideas, say, the internal mental state of expectation and its association to external observations of repetition. As you point out, this interpretation appears to be self-undermining, since according to Hume no empirically contingent proposition can have universal justification, which in this case can lead to semantic skepticism concerning the very meaning of induction.

The grammatical interpretation is that induction is defined directly in terms of observed repetition. In which case, 'induction is habit' is a deflationist assertion, i.e an analytic a priori definition of induction without empirical implications, as opposed to being an empirically contingent assertion. In which case semantic skepticism regarding the meaning of induction might be considered to have been circumvented, assuming one is happy to accept the notion of repetition as being an empirical notion that can ground the rational idea of induction without presuming it's existence. Alternatively, if one rejects the idea that repetition is an empirical notion, one might instead be willing to accept the converse, namely that idea that induction is a directly observable mental state (at least in terms of an inward experience of anticipation) and that it is this 'experience of induction' that serves to ground the idea of repetition within the faculty of reason .

Yet however complicated the phenomenology of induction is, presumably we can at least draw the conclusion that induction doesn't have a purely empirical justification nor a purely rational justification.

Unfortunately neither the empirical nor the grammatical interpretation fits with either our counterfactual intuitions concerning induction; For if a cause of type 'A' is understood to entail an effect of type 'B' when situated within a background context 'C', then an absence of 'A' implies the absence of 'B' whenever 'C' remains the same as in the former case. And whilst there are many cases in which we directly observe frequencies of conjoined absence, we mostly appeal to counterfactual reasoning rather than to observation to infer the consequences of absent causes (e.g. what doesn't happen when a nuclear bomb fails to detonate).

At the very least, we cannot argue for causation without appealing to circularity or to counterfactual situations embedded within vague background contexts, for which we cannot explicitly provide a constructive argument, and in which our observations and logic are inseparably interwoven.

Therefore it is coherent to accept mathematical induction as a principle of construction, and yet reject it's interpretation as a soothsayer of theoremhood. — sime

Sorry, that's confusing and misleading, by theoremhood i was referring to truth in the respective model of the axioms.

What i mean is that mathematical induction 'proves' a universally quantified formula in a completely vacuous sense in that the 'conclusion' of the induction, namely the universally quantified formula (x) P(x), is merely an abbreviation of the very axioms i and ii.

On the other hand, for universally quantified formulas over infinite domains that do not possess a proof by mathematical induction, there is no reason to support their informal interpretation as enumerating the truth or construction of the predicates they quantify over, by the very fact that they do not correspond to a rule of substitution.

For in what sense can a formal system speak of universal quantification over all of the natural numbers?
— sime

The standard way is assuming the principle of induction: if a proposition is true for n=0 and from the fact that is true for n you can prove that is true even for n+1, then you assume that is true for all natural numbers. (https://www.encyclopediaofmath.org/index.php/Induction_axiom)
It cannot be verified in a finite number of steps, so it's assumed as an axiom.
But assuming it to be false is not contradictory: you can assume the existence of numbers (inaccessible cardinals) that can never be reached by adding +1 an indefinite number of times (https://en.wikipedia.org/wiki/Inaccessible_cardinal). — Mephist

So then question is, in what sense does the principle of induction speak of universal quantification over all of the natural numbers?

Take any predicate P with a single argument, then take as axioms

i. P(0)
ii. (x) ( P(x) => P(x+1)) ,

where ii. denotes universal quantification over x, where x is a bound variable.

Then we say, "By informal convention, this predicate is now said to be 'true' for 'all' x."

But what exactly has our demonstration achieved in this extremely small number of steps?

Do we really want to insist that our use of these axioms is equivalent to a literal step-by-step substitution of every permissible number into P?

Do we even want to say that we are assuming the existence of this inexhaustible substitution?

All that i and ii define in a literal sense is a rule that permits the substitution of any number for x.

Nowhere does this definition imply that induction is a test for the truth of every substitution.

Therefore it is coherent to accept mathematical induction as a principle of construction, and yet reject it's interpretation as a soothsayer of theoremhood.

The main teething problem of data-science is the current absence of integrated causal modeling (let alone stakeholder legible causal modelling) which is a situation changing rapidly due to the ongoing invention of problem-domain-specific software simulations, along side the development of probabilistic programming libraries for quantifying simulation accuracy.

In this regard I expect that outside of computer-vision and speech recognition, where deep-learning as a strong inductive bias, the black-box neural network approaches in other problems domains will begin to take a back seat as transparent models of network logic come to the forefront. For you cannot easily inject human-readable logic clauses into a distributed neural network with positive and negative activations.

But our use of real numbers (at least for the most part) is in integrals and derivatives, right?
So the "dx" infinitesimals in integrals and derivatives should be the morally correct model? This is how real numbers are intuitively used since the XVII century. — Mephist

First of all, does our imprecise use of real numbers warrant a precise account?

What does it even mean to say that a real number denotes a precise quantity?

For in what sense can a formal system speak of universal quantification over all of the natural numbers?

Recall that in a computer program, an infinite loop is merely intended to be an imprecise specification of the number of actual iterations the program will later perform; it is only the a priori specified number of iterations that isn't upper-bounded in the logic of a program, that is to say before the program is executed.

Therefore if the syntax and semantics of a formal system were to mimic a programmer's use of infinity, it wouldn't conflate the 'set' of natural numbers with an a priori precise set, but would instead refer to this 'set' as an a priori and imprecise specification of an a posteriori finite construct whose future construction is generally unpredictable and isn't guaranteed to exist for a given number of iterations.

A universal quantifier over N would not longer be interpreted as representing a literally infinite loop over elements of N, but as representing a termininating loop over an arbitrary and unspecified finite number of elements, where the loop's eventual termination is guaranteed, even if only through external intervention that is outside of the constructive definition of the program or formal system.

By interpreting 'infinite' quantification as referring to an arbitrary finite number of elements, the law of double negation is then naturally rejected; for an arbitrarily terminated loop cannot conclusively prove anything in general.

This interpretation also has the philosophical advantage that semi-decidable functions are no longer informally misinterpreted as talking about their 'inability to halt', and likewise for formal systems supposedly 'talking about' their inability to prove certain statements.

So in short, an imprecise and pragmatic model of the real numbers is what is important, corresponding to how numerical programmers implement them in practice, with particular attention paid to numerical underflow.

Arguments for or against anti-natalism depend upon one's ontological beliefs, particularly with respect to personal identity, personal continuity and other-minds. Different positions on these topics will lead to radically different conclusions regarding anti-natalism.

the morally correct model of real numbers is the model most resembling our use of real numbers, i.e. the model that treats the real numbers as being subcountable, wherein the absence of a bijection between the natural numbers and the real numbers is interpreted to imply the following profundity:

There is an absence of a bijection between the natural numbers and the real numbers.

How is it possible for these dream characters that populate a dream world to have, seemingly, an intent of their own? Why would they? I mean, given that a dream world is practically tantamount to living in a solipsistic world, you would assume that you are the only person with a 'mind' within a dream. Yet, even in dreams where I am aware that I am dreaming (lucid dreams), I still find it hard to shake off the preprogrammed belief that the friend I meet, the father or mother I talk with, or the siblings I interact with in a dream have a mind of their own... — Wallows

In my lucid dreaming experiences, a dream character tends to lose their autonomy as soon as I demand them to act autonomously. For example, if I ask them a question in the hope of receiving a novel and autonomous answer they turn into a puppet and say nothing. This effect is presumably related to artist's block.

So if we replaced your brain with sawdust, you'd still be conscious? — Marchesk

For a phenomenologically minded empiricist, the very meaning of a scientific hypothesis is the sense in which experience is said to corroborate or refute the said hypothesis and this sense cannot be transcendent of experience. Therefore this empiricist is likely to reject your question as meaningless and inapplicable in the first-person.

Nevertheless, neuro-phenomenology can potentially have sense in the first-person, in terms of an association between sensory experiences and brain-probing-experiences, as for example in an experiment in which the subject records his experiences when probing his own brain.

You know Chaitin's Omega? Very cool number, because it's actually a specific example of a noncomputable real number, or rather any one of a specific class of noncomputable reals. We can define it because it's a definable real even though it's not computable. It's not computable because if it were, it would solve the Halting problem, which Turing showed we can't do. — fishfry

I think in that in an ideal mathematical language, Chaitin's Omega wouldn't be stateable. To say 'Omega is definable but non-computable' is surely not a statement about a number, but a statement about the syntactical inadequacy of our mathematical language for permitting the expression of Omega.

For if a sentence is understood to express logical impossibility, then it cannot be an empirically meaningful proposition. It can only serve as a rule of grammar for forbidding the syntactical construction of certain sentences in order to preserve the semantic consistency of the respective language.

It isn't empirically clear when two things are identical or different, even when comparing two 'identical' photographs.

Therefore, to my mind A=A should be rewritten A <--> A' to denote a rule of inter-substitution between two entities that are treated as being the same.

I don't quite think this is right. How would you explain the clinical symptom of anhedonia? — Wallows

While there are undoubtedly neurological correlates of depression, i think that in many cases they are likely to be the product of the brain's normally functioning neuro-plasticity, where the brain has responded in an expected and predictable fashion to long-term repeated stressors in a hostile or unrewarding environment. This will be the case if a person's anhedonia is sufficiently improved by having his actual psychological needs fulfilled.

Unfortunately, psychiatrists and GPs don't normally have the resources to test this hypothesis, whilst society is eager to blame the biology of depressives in order to let itself of the hook, thereby preventing wealth redistribution.

So, you are equating the two here? If so, then what does that mean? — Wallows

I'm saying 'will-power' should be considered as referring to the expression of motivation, but not the cause of motivation. For behaviour is goal-driven, and the causes of motivation are incentives.

Unfortunately, society has a habit of referring to motivated people as being 'self motivated', which is illogical and leads to the social stigmatization and neglect of depressed people, who often depend on society to provide them with meaningful incentives.

You seem to implicitly assume an objective reality that can be somehow accessed, referring to 'causes' as something objective that everyone would agree on, to personal dialects as being objectively translatable into one another. How could we agree on causes of what we experience if we don't agree on what we experience? How could we agree on an objective translation if in the first place we don't have access to what other people experience?

We use language as a rough way to try to see what others experience, if we had direct access to what others experience then your idea would be practical, but we don't, and that's the problem. Seeing the problem as a mere limitation of our current language is masking the deeper issue, it isn't a limit of our language, it is a limit of our ability to know what others experience. Words do not convey what others experience, they convey what we believe they experience, from our first-person point of view, making our language more precise wouldn't change that.

If there are experiences some people have that other people don't, why would the people who don't have these experiences agree that these experiences exist? For all they know those who claim having such experiences could be lying, or they could interpret these experiences falsely in terms of other experiences they've had. And that's not a limitation of our current language, that's a fundamental limitation of us not being omniscient. It seems to me that if we have different experiences, then we can't find something that everyone agrees on, or maybe everyone could agree on something temporarily but later on some would realize that they didn't have the same thing in mind when they were agreeing.

Maybe you will come to agree with me on this, but if you don't then that would only serve to support the idea that truth is personal. Until we find an example of truth that everyone agrees on, the concept of truth that applies to everyone is merely an idea that some people have. — leo

l was actually arguing for your position. I'm saying that truth is personal, as evidenced by the fact a super-flexible linguistic convention could be publicly adopted relative to which the public notion of truth is trivially and vacuously true. But that wouldn't abolish what each of us individually means by 'truth', but merely serve to highlight that truth is a non-representational, personal and practical notion.

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.