England's still - relatively speaking - an abode to free thought, movement and expression.
As far as the entirety of the world is concerned, we're in an unstoppable regress.

If you inflate a balloon, the objects you draw on it inflate too. In reality, objects in space stay the same size. — Gary Enfield

That's impertinent to the analogy; and the latter assertion may not be verified (I'm not accredited to comment on it).

Why not try and acknowledge the results of the faster than light experiment by Gisin - which said that communications at least could be 10,000 times the speed of light even in the circumstances that we occupy? — Gary Enfield

If Gisin's experiment is at all associated with Quantum Entanglement (I'm not certain if it is), then there do exist several rationalizations of QE that remain adherent to SR.

If you want to break the real fundamentals of science, in preference for speculative doctrine, then you need real evidence.... which you don't have. — Gary Enfield

Certainly. I'm the one flailing unprincipled ideas, as opposed to eliciting standardized laws, explanations, articles and analogies.

I hope you don't mind if I refrain from replying to this thread anymore; we're at an irreconcilable discord.

I think I can just about guess what this jargon means - but you seem to be suggesting that I am jumping around between theories, when I am not. I am simply saying that the evidence of distance divided by time - when applied to absolute and agreed values, trumps vague notions based on doctrine over real substance. — Gary Enfield

$Ds/Dt$ can parameterize unchanged spatial distances, on a Minkowski metric - not on a varying one.

As I said before. I acknowledge that your preferred theory may one day be given substance, but it hasn't yet - and the historical fact remains - it was dreamt up to preserve a fixed C — Gary Enfield

I'm not contending that fixing C was one of SR's postulates; all I'm stating is that there exists a valid and demonstrable interpretation of cosmological inflation, that is consistent with that postulate.

For what it's worth, this isn't merely a preferred theory; it's what the majority of Physicists will attest to (not an appeal to authority, but a testament to its perceived credence).

The inflation of space was a notion dreamt up purely to preserve the notion of a fixed value for the speed of light as currently measured. It has no evidence to support it and only exists to preserve doctrine over substance. — Gary Enfield

What you're asserting then, is that the near entirety of Inflationary Cosmology, as physicists apprehend it today, is a facade.

Indeed, in this respect, relativity is open to too many variables to provide a comment on this - when by its nature, any 'absolute factor' must take precedence over relative readings. The width of the universe is such an absolute - and a figure that wasn't available to Einstein. — Gary Enfield

Relativity, despite what its name suggests, is not a triumph of 'relative' readings over 'absolute' ones; despite that you haven't elaborated on what they even entail for you. Einstein geometrically interpreted the universe with a four-dimensional Lorentzian Manifold, whose metric tensor varies with time (again, the tensor equivalent of cosmological inflation). You can't straddle between two, antithetical narratives. Either abnegate General Relativity, and be a proponent of nonstandard ideas - or accept it, with all its known implications (inclusive of an expanding universe - wherein observed, absolute distances on a fabric can exhibit velocity differentials superior to c, without the material on that fabric ever defying SR in localized regions).

Do you acknowledge a semantic difference between the expansion of a spacetime fabric, and the celestial bodies ensconced on that fabric? — Aryamoy Mitra

Okay. I can elucidate, but there's a far more effective analogy.

I'm quoting, verbatim, this article from the Scientific American. Apprise me if you concur with its conclusions (or otherwise, if you don't).

'According to Einstein's general relativity equations, the spacetime containing matter cannot remain stationary and must either expand or contract. Galaxies and other sources, then, are not strictly expanding away from each other but rather are attached to the fixed grid on the expanding fabric of spacetime. Thus, the galaxies give us the impression of moving away from each other. Imagine the surface of a balloon, on which you put dots. Then start inflating the balloon. The distances between the dots will increase, so if you live in one of these dots, you will interpret this as the dots--which represent galaxies in this example--moving away from each other. In reality, of course, they remain in the same positions, with respect to latitudes and longitudes on the balloon, and it is the fabric of the balloon that is actually expanding.'

I have no idea what your words are supposed to mean.

You need to clarify. — Gary Enfield

Can you quote me, on what I've stated that is unclear?

Observing how bodies traverse 'relative' to the fabric on which they're immersed, is the only cosmological dynamic of significance; they're invoked in rationalizations of absolute measurements.

You are again resorting to relative measures, which can be subject to many unknown influences - including your supposition that your measurements of distance between these objects is accurate - which you cannot know. — Gary Enfield

By that token, nobody can ever discern anything at all - and we're forever and inescapably entrapped in the recesses of fallibilism. Inflationary Cosmology formalizes approximations, that are phenomenologically derived - prior to being ascribed a credence, on empirical fronts.

Answer for once, solely this question:

Do you acknowledge a semantic difference between the expansion of a spacetime fabric, and the celestial bodies ensconced on that fabric?

If you don't concede to the existence of that distinction to commence with, you'll be unamenable to any evidence that underpins it.

I didn't think your comments had any pertinence to the theme underlying this thread.

I'm clarifying a (possible) misapprehension of one of your statements, and apprise me if you disagree.

Can rules of law be immoral?
Yes.
Therefore rules of law are not moral laws. — Bartricks

What I believe you mean to say (again, correct me if I'm mistaken - I'm only inferring from your arguments), is:

Rules of law can be 'moral' laws; but they are not laws of morality.

If your statement is instead conveying that rules of law are not 'moral' laws, then I don't believe it bears a semantic consistency with its antecedent.

When professing an immorality across a particular legality (or Jurisprudence), one simultaneously professes a morality across others (that are converses of that legality);
one can't impart a moral generality across all rules of law - from the moral stature instituted by a sole proportion of them.

Find a technology that will counteract the effects of the mechanism. — T Clark

That's interesting.

I know, right? At times, his grandiloquence renders his statements indecipherable, with sentences that are paragraphs long (at least in translated variants). If he was perhaps more direct, he'd not have been misappropriated on as many an occassion.

Nietzsche insists that there are no rules for human life, no absolute values, no certainties on which to rely. If truth can be achieved at all, it can come only from an individual who purposefully disregards everything that is traditionally taken to be "important."
The snake which cannot shed its skin, must die. That's according to the German philosopher, Friedrich Nietzsche. Writing in 1881, Nietzsche wasn't concerned with snakes, but he was making a point about the ability to change. Or rather that those who refuse to adapt are resisting the inevitability of change. — Huh

First and foremost, stating that any philosopher insists upon the truth of a particular stance, without eliciting any caveats or underlying evidence, is a perilous exercise. Nietzsche imparted thousands of aphorisms, each of which was interpretative in nature - and taken to mean a million, oftentimes contrasting realities (a quintessential example - the Kraft vs Macht dichotomy).

Nevertheless, insofar as his renunciation of canonical (and moralistic) 'rules' (especially in Christian, and other monotheistic contexts) is pertained to, I concur.

His (Nietzsche's) book, Beyond Good and Evil , really aims at changing the reader's opinion as to what is good and what is evil
— Bertrand Russell — Huh

Bertrand Russell, so far as most trustworthy documentation suggests, was a detractor of Nietzsche's - and Beyond Good and Evil, in its title, is likely an oversimplification of what the book entails.

Nietzsche
Says create your own
It's just a coincidence we have the same philosophy
Nobody has a monopoly on philosophy — Huh

Nietzsche's teachings are by no means as unequivocal; if he's declaiming to others that they create their own philosophies, is he not simultaneously (and by extension) declaiming to them an abnegation of his own? Under this token, he reaffirms an unshackling of one's ideals, and a consequent usurpation of their cultural constraints - such that one may re-envision their life; but that, in and of itself, is an overarching philosophy.

I'll affix an example; here's a tenet (from Beyond Good and Evil) - the likes of which are often cited, in light of Nietzsche's name being flailed around:

95. To be ashamed of one’s immorality is a step on the ladder at the end of which one is ashamed also of one’s morality

Whilst there will exist an appreciable discordance upon its perception, most individuals will convene that it implies that morality and immorality, in their synthesis and reception, are inextricably bound to one another (that is to say, their fates are not independent, and the lines separating them only blur).

Conversely, here's a far more profound section of Beyond Good and Evil, that illuminates Nietzsche's beliefs on Moral Tyranny:

188. In contrast to laisser-aller, every system of morals is a sort of tyranny against ‘nature’ and also against ‘reason’, that is, however, no objection, unless one should again decree by some system of morals, that all kinds of tyranny and unreasonableness are unlawful. What is essential and
invaluable in every system of morals, is that it is a long constraint. In order to understand Stoicism, or Port Royal, or Puritanism, one should remember the constraint under which every language has attained to strength and freedom—the metrical constraint, the tyranny of rhyme and rhythm. How much trouble have the poets and orators of every nation given themselves!—not excepting some of the prose writers of today, in whose ear dwells an inexorable conscientiousness— ‘for the sake of a folly,’ as utilitarian bunglers say, and thereby deem themselves wise—‘from submission to arbitrary laws,’ as the anarchists say, and thereby fancy themselves ‘free,’ even free-spirited. The singular fact remains, however, that everything of the nature of freedom, elegance, boldness, dance, and masterly certainty, which exists or has existed, whether it be in thought itself, or in administration, or in speaking and persuading, in art just as in conduct, has only developed by means of the tyranny of such arbitrary law, and in all seriousness, it is not at all improbable that precisely this is ‘nature’ and ‘natural’—and not laisser-aller!

Despite lambasting moralistic systems (for being tyrannical and seemingly 'arbitrary'), he actually concedes to the prospect of them being entirely naturalistic; acknowledging herein their creative outcomes under artistic domains, and their underpinnings in Thought itself - before apprehending against Anarchist proclivities. This isn't an aberration of his otherwise fortified stance, either.

His writings need to be discussed in exact contexts (admittedly, a failure of this comment); generalities can succeed, but they shouldn't predominate a philosophical assessment.

I think Nietzsche himself wouldn't like to see that he has dogmatic followers if he rose from his grave, but rather would like to see people who think with their own head. — Amalac

Precisely. I'm no scholar on his life, but I'm certain that he'd be deplored by the notion of thousands of individuals subordinating themselves to the perpetuation of his ideals, as opposed to enacting them and reconstituting their value structures (perhaps, eventually, at the expense of a few of the ideals themselves).

A quote from Nietzsche and 50¢ won't get you a cup of coffee. — Bitter Crank

Underrated, to be honest.

Variant Reinterpretations of Interstellar's Gargantua





It's unfathomable how curved geodesics, metric tensors and differential geometry can render an artistic truth as serene, and visually incalculable.

I can certainly rationalize the majority of your assertions (albeit under specific presuppositions).

I'm inquisitive, nonetheless, with regards to three specific uncertainties:

A) Firstly, do your stances stem from the formalized edifices of Hedonic Morality?

B) Placing a constraint (if not an outright preclusion) on individuals seeking to forge new life, is likely to encroach onto their fundamental liberties. Are you solely promulgating a moralistic perspective, or would you be willing to enact your beliefs in the real world (if accorded the opportunity)?

C) Lastly (and this is solely cursory), what are your views on Schopenhauer's Will to Live (since I imagine you'll bear a tremendous degree of expertise, on him)? I understand that it (presumably) manifests in the aftermath of one's birth; could procreation, however, fall under the purview of the Will to Live (that is to say, instinctively electing to 'live on', by bequeathing one's genetic character)?

My current thought is that the most useful skill is the ability to adapt to change. Change is a most fundamental nature of this world. When we suiffer, it's usually in some part because of a failure adapt to change. We got to where we are as humans because we adapted. — Yohan

Change, when preceded by an acknowledgement of self-inadequacy, is invaluable.

Marx just wasn't thinking deep enough. He was against some exploitation when it came to classes, but not as being born into the human condition as a whole. Why is the assumption that being born at all to produce anything considered "good" for that person? Who is the one that gets to decide that? Why is another person getting to decide that on behalf of someone else? — schopenhauer1

I concur, with regards to the generality. Most Existentialist doctrines, as far as I've witnessed, readily concede to the tragic ramifications of being immersed into the human condition; you can't usurp hierarchies that are intractable, for example. Independent agency, insofar as working conditions/and or welfare are concerned, is a scarce gem of liberty. Exploitative elements are profoundly ingrained into the underlying fabrics of human society; whether remediating those vices is best undertaken with milder variants of Capitalism, Economic Anarchism or Marxism - is a far more contentious bridge to traverse (naturally).

If you agree with Marx on classes, why not on this? If you just want to do the bad argument that we must have people so that we KNOW the conditions of exploitation.. then why does that matter? No person. No exploitation. Period. Any answer otherwise, is just trying to force the hand of what YOU want to see from society, and consequently, what people must do to maintain that society. Why is this the default? — schopenhauer1

Does this not lend itself, to an anti-natalist stance? Not all individuals zealously opposed to exploitation, will prefer a cessation of all births, over being exploited in a constrained fashion. Ascribing a greater significance to life may be the overarching default, since its intrinsic value (to Judeo-Christian ideals and/or other codified monotheisms) overshadows any societal sacrifices that it might introduce (indeed, at the cost of individual liberty, and one's freedom from suffering). Is it ideal? No - almost certainly not.
It does, however, bear a meaningful rationalization to it (in reiteration - synchronous with JC ideals, as opposed to my own beliefs).

Life, with all its unrelenting exploitation, is a catastrophe; even a catastrophe, however - when ameliorated, is preferable to inexistence. Kierkegaard instituted several analogous ideas, if I'm not mistaken.

Personally, I'm apathetic on the matter - on this front, nonetheless, your perspective is characterized by a hedonic appeal (an absence of suffering) - that can't be discerned in its counterarguments.

Would you say those that "lack hatred" for Hitler are "bad"? What is the purpose of "hating" Hitler? — Cobra

Resentment is a sentiment, in consequence of having observed a detestable motive or act; in and of itself, it doesn't accord any degree of moral virtue. Resentment does, however, constitute a directive to wherein one's moralistic edifices stem from (since they engender the specifics of what one finds reprehensible, and what one doesn't) - and what they imply in practical terms.

For instance, if individual Z doesn't particularly 'hate' Hitler, a spectator (namely Y) would likely have to posit 3 additive questions, before forging a stance on Z's moral constitution:

a) How Z rationalizes a non-contempt, of an individual canonically regarded as a genocidal dictator;
b) Whether Z's presuppositions (in relation to Hitler) are commensurate with Y's (and whether both their preconceptions are corroborated with historical documentations of his life);
c) Whether not resenting an individual is tantamount to either venerating him/her, or remaining passive to his/her transgressions.

I think that hatred, in strong aversion or wishing harm to those with specific attributes is connected to psychological projective processes. Take your example of hatred of the fat person, it may be that specific undesirability of fatness as an aesthetic quality is projected onto the individuals who are perceived as fat. The example of hatred of fat people also raises the connection between hatred of others and hatred of self. I have worked with people who have eating disorders and it does seem that they often have internalised self hatred. — Jack Cummins

Exactly. What often happens (perhaps), is that individuals conflate the aesthetic qualities that they're disinclined to, with the total identity of the individual they're berating (preceding a projection) - which shouldn't be surprising, since it's both inductive, and quintessential of being a cognitive miser (an inadequacy most of us are characterized by, to an appreciable extent).

So I say again....

...if you wish to contradict the fundamental definition of 'Distance divided by Time = Speed' then the emphasis is not on me to uphold the basic truth of the definition - but on you and others to prove that the 'inflation of space' is real... in order to simply preserve a fixed C. — Gary Enfield

This isn't an elementary introduction to Classical Mechanics; this is Inflationary Cosmology, with an emphasis on Hubble's law. I'm not contradicting your presuppositions; I'm stating that they're incomplete.

Here's a reminder of why I believe your arguments to be fallacious, in a fashion commensurate with Hubble's law. If this doesn't suffice, I'm afraid we are at an irreconcilable discordance. You can continually arrogate to yourself all 'evidence' on this front; I've only shared a canonical physical law, a demonstrable analogy and a standardized interpretation of cosmological inflation - hardly substantive, I'd imagine.

Imagine that we were tracing two, celestial bodies - A and B, situated at a vast distance from one another (in excess of billions of light-years) - by observing how the absolute distance between them, expanded.

With simplicity in mind, let's visualize a discerned expansion equivalent to $3ct$, in a time interval demarcated by $t$.

If one were to undertake a cursory aftermath of that observation, they might partake in:

$v = \frac{ds}{dt} = \frac{3ct}{t} = 3c;$

When the expansion's symmetric:

$v_{A} = v_{B} = \frac{3c}{2} = 1.5c$.

Is this, by any chance, what your 'speed-of-light violation' construct is accorded sustenance by?

If so, here's an exposition discrediting it - and if not, we can continue quarreling incessantly.

$v = \frac{ds}{dt}$ doesn't suffice herein - since it doesn't attain the velocity of a body on the fabric it's ensconced in, if the fabric migrates too.

Anyone can analogize this idea; if you're seated in a car - and the car's careening at a 100 miles per hour - are you characterized by the same velocity, from within the car? Einstein's constraint is tantamount to asserting that with the car as one's stationary reference frame, one can't exceed c. — Aryamoy Mitra

If there was Big Bang from a singularity at a point in space, and the Universe is now at least 98bn light years across after a period of 13.7 billion years from the big bang, then distance divided by time gives speed - and that says matter/energy in the universe travelled faster than the standard speed of light to get there. — Gary Enfield

I'll no longer be partaking in this conversation; it's as though Einstein was never born. I concede to certain nonstandard narratives in history having usurped standard ones, but you're declaiming yours on a multiplicity of fallacious presuppositions - whose untruths I've elaborated on in previous comments, only to be thoroughly discounted.

Well, kindly show us the way then. How can we marry philosophy with math? — TheMadFool

First and foremost, I'd like to concede that there already exists a concrete, formalized Philosophy of Mathematics, that illuminates how philosophical concerns underpin set-theoretic, axiomatic and abstract Mathematics (quintessential of the hypothetical interrelations you've been suggesting).

For an unequivocal integration, nevertheless (do apprise me if you disagree), a Mathematics of Philosophy should be discovered (that is to say, the redirection of mathematical constructs to philosophical matters, as opposed to the converse). I don't bear any expertise on this dichotomy, but if there were any straddling edifices - they're likely be characterized by:

1) Non-Quantitative Approaches (with the exception of 2) - wherein abstract entities - inclusive of the natural numbers, can be mediated and extended, but without a quantitative rigor (certain sub-fields of Mathematics may accord this liberty);
2) Propositional Quantification (already a hallmark of first-order logic - wherein sentential arrangements (eg: syllogisms) can be thoroughly evaluated with a (sparingly selected) group of quantitative paradigms, and their ramifications made amenable to philosophical explication.

I'm certain that there are other, mathematical objects that can be intertwined with philosophical thought - but they remain elusive.

Once more, it's not that I believe Mathematics and Philosophy are fated to be distant - it's only that they don't (at first glance) share an interlap, with the majority of their territories.

Well, if it doesn't make sense to you then it doesn't. I, on the other hand, see opportunity where you see incompatibility. I see a very profitable synthesis where you see irreconcilable conflict. — TheMadFool

Of course - some of my misgivings may stem from overly fixating on their idiosyncrasies, and ceasing to gauge the landscapes they really are. It's likely that remaining embroiled in them for a longer time, will loosen those perceptions.

All that aside, I must impress upon you that from what I can glean from your posts, you're a very knowledgeable 17 year old. By my standards, those are 17 years well spent. Ergo, given your insightful reservations on my proposal of a union between philosophy and math, I suppose that makes you the right person for the job of doing exactly that. — TheMadFool

Thank you. I'm still learning of course; only the primitive foothill in a portrait whose horizon remains unseen.

In my humble opinion, a man who wants war knows exactly what peace is, right? — TheMadFool

Exactly; and wonderfully reminiscent of Orwell too.

Aryamoy Mitra Quote from a 1960s USA TV show. You'll have to find the rest yourself . . . :nerd: — EricH

I did - and whilst it's a novelty relating to a statement first imparted more than 4 decades prior to my arrival, it's unsurprising that this particular reference hasn't entirely obsolesced (thematically).

In order to cease our reliance on experts, we'd have to get into some fairly kinky experimentation on ourselves and others, and, in my experience, that is not always appreciated. — Baden

Exactly. I'd far rather cease to a defiance of a medical practitioner's oath (with the foreknowledge of its possibility), than succumb to my own partially accurate, and rudimentary understanding of medicine (say, perhaps, by ingesting a fatal tablet). Maximalism, in this regard, is unfeasible; it's a quagmire of two discomforts - one of which is livable, and the other perilous.

People have been brainwashed to believe that they are incapable of doing these things but it is not true. I have had patients that have been incredibly well-educated in their particular issues. Medicine is not that difficult to get a reasonable handle on. It is imperative that everybody do this because if you're depending on your corporate/government people to do this for you, you're SOL. — synthesis

Your cynicism can be commiserated with, and your maxims too; your reductionist assertions, however, not.

You realize that you have just outed yourself as being of a certain age . . . :razz: — EricH

Is that an archaic movie quote, or something of antiquity?

Yes you are but I'm not sure whether you're doing it knowingly or unwittingly. Every time I try to build a bridge between philosophy and mathematics as I've tried my best to do in my previous posts, you immediately start pointing out how either this or that is flawed in my work. Of course I value your criticism and my impression of you is that you're more than qualified to critique matters such as this but, in my humble opinion, many great, productive interactions between disciplines involve a good deal of compromise and that usually involves relaxing the rules, ignoring differences that may even involve sweeping frank contradictions under the rug, and embarking on a cooperative venture that requires, in this case, math to meet philosophy halfway. Does this not seem reasonable? — TheMadFool

I'm a naive 17-year old, who couldn't fathom attending an hour-long undergraduate Mathematics lecture, sans being utterly stupefied and overwhelmed. Terming me 'qualified' (in any respect), is almost certainly unwarranted. In all honesty, you're of a far greater credence than I am (especially in Philosophy); if I didn't feel so fervently with regards to this (perceived) incongruence, however, I wouldn't have remarked on it.

Yes, one can (and perhaps should) neglect their intrinsic differences momentarily; but can we acknowledge how that might unravel (from a practical perspective)? Even if one is willing to compromise on either end, where does one seek a middle-ground between the two? Your motive is fully reasonable; it's solely the pathway to that motive, to which I seek a more profound rumination.

Mathematics bears a specific utility: undertaking abstractions of quantitative (spatial and variable) constructs, and thoroughly evaluating them. Contrarily, Philosophy witnesses its own sustenance in evaluating qualitative ideas. I'd love to be apprised of an ignorance on this subject, but it's hard to envision how the two might be methodically amenable to one another - as they manifest themselves today. I'm not casting aspersions on a 'rule-breaking' paradigm; I'm stating that the underlying fabrics on which their rules are woven, are incomparable.

If an immersion was necessary, one might elect to redefine their fabrics in a manner that wasn't impermanent. For instance, part of why Hilbert was as aberrant a mind as he was (whilst still overshadowing his adversaries on canonical fronts), was that he was willing to transcend the historical (and then demonstrably incomplete) axiomatization of mathematical fields, by instituting a self-referential Metamathematics. Aside from Gödel, very few others were as introspective as he was; and even then, he's likely to have been philosophical in reassessing Mathematics, as opposed to have architected a philosophical edifice within Mathematics.

In reiteration, I'm not eminently setting ablaze a (hypothetical) wedding between Philosophy and Mathematics; I'm merely inquiring (in a critical fashion) whether one might be pragmatic, and foreseeable in their current forms.

You are misinformed. The designation "professional" means they earn money with it. It is their profession, or occupation, and they earn money with it. — god must be atheist

That's what I was dwelling over, too; educational accreditation shouldn't be conflated with being a 'professional', albeit the overwhelming majority of (successful) academic professionals, are educationally accredited.

Furthermore (and this is solely an additive interpretation, with no suggestive insinuation of any kind), being professional doesn't necessitate that you be of an exemplary standard in a stated discipline; countless individuals are duplicitous enough to garner an exorbitant living, whilst desecrating the substance of a discipline, and/or disseminating misinformation to their audiences.

Again you're doing what's unthinkable to the ordinary man - willingly, voluntarily, slipping into the straitjacket of logic and math; the men in white coats don't even have to lift a finger for this one. — TheMadFool

It's not as though I'm exalting mathematicians to an unassailable pedestal, and insulating them from the haphazard thoughts of the 'ordinary man'. I'm solely positing this singular, epistemic question:

How does one interweave two, dichotomous frameworks, without first fixating over their rarefied drudgeries (by perhaps, slipping into their 'straitjackets')?

If I still can't perceive the heart of your rationale, do contemplate re-formulating the argument.

Of course your view of me is exactly the opposite - I'm taking subjects like logic and math which many luminaries have gone to great lengths to perfect as precise, well-organized, crystal clear mental constructs that seem almost muraculously suited for making sense of and describing the world and violating or intending to violate every possible meticulously formulated rule in them. — TheMadFool

That's not necessarily my stance (insofar as it's not a caricature); I only feel that your endeavors to unify (or integrate) Philosophy and Mathematics, can be slightly more adherent to the circumstantial strictures of the latter. If refraining from rule-breaking is a covenant, or prerequisite to that end (not a theme, that I can righteously impart assertions on) - then an insistence on that front, might be wise.

I did see the italics but I did not see a link to the source. So I couldn't tell if you were quoting someone else or quoting yourself from some other publication or forum, or just separating out your ideas into quoted form. — fishfry

Pardon me, for not properly citing the source; here's the mystical entity, from which this passage stems.

I believe what they mean is this. For definiteness let's take Peano arithmetic (PA). By Gödel's second incompleteness theorem, PA can not prove its own consistency. That means PA can not prove that it can't prove that 2 + 2 = 5. Agreed so far? Then if PA can prove that it can't prove that 2 + 2 = 5, then PA must have proved its own consistency, which it can only do if it's inconsistent; and if it's inconsistent, then it can prove that 2 + 2 = 5. — fishfry

For everyone else's following (and that of my own), let me distill this with arrows:

A) Gödel incompleteness (2)$\longrightarrow$PA can't demonstrate its own consistency$\longrightarrow$PA can't prove, that it can't prove that 2+2=5;

B) Now, if PA can prove, that it can't prove that 2+2=5 $\longrightarrow$PA shall be consistent;

C) And, if PA can prove, that it can't prove that 2+2=5 $\longrightarrow$PA needs to be inconsistent$\longrightarrow$PA should be able to prove, that 2+2=5.

The point is that proof and consistency are relative to given axiom systems. It's true that PA can't prove its own consistency; but we CAN prove the consistency of PA by other means.

So, to sum this all up: Using ZF (which at least I understand, as opposed to Gentzen's proof, which I don't) I can indeed prove that PA is consistent, and that PA can't prove that 2 + 2 = 5, and that PA can prove that it can't prove that 2 + 2 = 5.

I can always do this as long as I'm willing to go outside PA. And this is true in general. Just because some given system can't prove its own consistency doesn't mean we can't prove its consistency. — fishfry

Thank you, for expanding. PA can't show its own consistency, but PA can be proved consistent outside itself (with other axioms) - and that's a generality that may hold for other arithmetic systems; is that the crux of the argument?

Have I significantly misapprehended the argument,
— Aryamoy Mitra

At (5) and (6), yes. — bongo fury

Can you pinpoint how I've faltered? I ask, since (5) was at the heart of Gödel incompleteness.

'By the way, in case you'd like to know: yes, it can be proved that if it can be
proved that it can't be proved that two plus two is five, then it can be proved
that two plus two is five.'
— Aryamoy Mitra

No — fishfry

As a clarity, are you refuting the original exposition? This passage, for instance, was word-for-word sourced from another, non-technical resource.

Nope, certain mental states ARE neuronal states. It’s not that there exists “mental states” as separate from neuronal states, and the formal is caused by the latter no, they are literally the same thing. It’s not dualistic. — khaled

What does 'are' mean? Superficially, it's not easy to unravel; if one is downtrodden, then is being downtrodden interchangeable with demonstrating a specific neurochemistry? Is the relation semantic, or metaphorical?

Is there an afterthought, that underlies the statement? Without one, this seems an absurd equivalence.

First and foremost, there'll always remain an indeterminacy at the heart of the mind-body problem
— Aryamoy Mitra

There is no mind body problem in identity theory. How does your emotion of “anger” interact with your body? Confused question. Your emotion of “anger” IS a body state. It’s not something external that “interacts with” your body.

as opposed to creating a satisfactory and infallible scheme, for deriving answers to unforeseen questions
— Aryamoy Mitra

Why not?

Personally, I adhere to Epiphenomenalism in this regard
— Aryamoy Mitra

I think epiphenomenalism is the only way out for a dualist who wants to respect the science. — khaled

Since the two, preliminary statements were apparently inconsistent with Identity Theory, none of these conclusions (the ones you've questioned) bear any significance anymore.

Topological ideas don't necessarily have a quantitative context. The concept of what continuous means in continuous transformations has been discussed at length in this forum. — jgill

I'm not familiar with topological spaces, but they are a counterexample to the (otherwise) quantitative norm that several mathematicians witness.

For instance, Functions pertain to continuous variables across domains,
— Aryamoy Mitra

Not necessarily. A basic definition lies in set theory and may be discrete. — jgill

I'm certain that you're of the expertise, to contend that. I wasn't rigorously defining Functions; I was merely referring to what they pertain to, in other areas of Mathematics (in my understanding). Aren't domains of continuous variables and images the two, conceptual schemes at the forefront of most individual's minds - when apprised of a 'function'? Once again, I might be mistaken.

Of course. Political concerns are often what encourage atheists to be evasive of religious ideals, in combination with their irreligious personalities - they're an additive element, as opposed to a characteristic one.

I gave my understanding with several examples which did include evidence and rationale.
You may not like them, but unless you can show they are not correct, they remain a valid interpretation in their own right. I don't need to cite anyone else. — Gary Enfield

They remain an aberrant interpretation; whether they are valid, or not - is determined almost exclusively by how you rationalize standardized and reconfirmed beliefs through them.

A fixed C was always a presumption, and now that the evidence exists to question that assumption, various people have tried to distort the basic facts in the hope that it might preserve their treasured belief in an insurmountable C instead of accepting another, more simple possibility - that it is possible in certain circumstances to go faster than light. — Gary Enfield

C's constancy was one of SR's foundational postulates - nobody's vehemently contending that.
In any event, it was pivotal in resolving the incommensurate nature of Maxwell's Electromagnetism and Newton's Classical Mechanics; insofar as it wasn't a whimsical afterthought of Einstein's eccentricities.

If several individuals are fixated on its truth, it's likely since the idea's entrenched in the foundation of other canonical edifices (that are empirically grounded), and is nearly incontrovertible - as opposed to them being intransigent.

Even if you truly believe that space does expand, something must be causing it to expand, and the combined effect of thrust and expansion would be what makes things travel faster than light in absolute terms compared to the point of origin. I don't see how you can deny that. — Gary Enfield

You haven't in the slightest addressed any of the criticisms that have preceded this facade, so let me quell this particular tension with a literal example:

Imagine that we were tracing two, celestial bodies - A and B, situated at a vast distance from one another (in excess of billions of light-years) - by observing how the absolute distance between them, expanded.

With simplicity in mind, let's visualize a discerned expansion equivalent to $3ct$, in a time interval demarcated by $t$.

If one were to undertake a cursory aftermath of that observation, they might partake in:

$v = \frac{ds}{dt} = \frac{3ct}{t} = 3c;$

When the expansion's symmetric:

$v_{A} = v_{B} = \frac{3c}{2} = 1.5c$.

Is this, by any chance, what your 'speed-of-light violation' construct is accorded sustenance by?

If so, here's an exposition discrediting it - and if not, we can continue quarreling incessantly.

$v = \frac{ds}{dt}$ doesn't suffice herein - since it doesn't attain the velocity of a body on the fabric it's ensconced in, if the fabric migrates too.

Anyone can analogize this idea; if you're seated in a car - and the car's careening at a 100 miles per hour - are you characterized by the same velocity, from within the car? Einstein's constraint is tantamount to asserting that with the car as one's stationary reference frame, one can't exceed c.

If this is how you initiate, I've got to wonder what your ulterior motives are. Way more dissing than is warranted by the circumstances. I'm only beginning to get into the mathematical core of cutting edge physics, so my ideas of proportion and correlation are primarily qualitative, but they are drawn from books by respected physicists who I presume didn't make an error that flagrantly misguides readers. Theories associated with the speed of light are at the fringe of my knowledge, and this post is as speculative as I've attempted at this site, so consider it an effort to learn more than a proposal of something I believe is definitive. As for the theory of relativity, I'll think about it and do some reading. — Enrique

Admittedly, that may have been an imprudent sentence to commence with - and I apologize for its brazen nature. I was merely seeking to pinpoint (falsifiably) that there may exist an inconsistency between the two paradigms you've sought to coalesce. Qualitative arguments are meritorious too; since I'm not matriculated into any form of higher education in Physics, I've also found them of tremendous utility.

The probability wave concept I'm employing is just that the predicted proportion of behavior within a reference frame at the quantum scale, whether construed in terms of position, momentum or whatever, models the average amount of energy within that reference frame relative to the rest of the wave function. Maybe time contraction because matter of lower frequency (energy) moves or spreads faster in some way? Not my expertise, but if someone wants to critique that definition, go for it! — Enrique

That's a novel postulate, and I concede to not being adequately attuned to the subject - in order to partake in a thorough deconstruction.

I do have one, minor qualm nevertheless: what does the phrase 'proportion of behavior' imply, precisely? How are you contextualizing it in a reference frame? I ask, since wave-functions aren't interchangeable with waves - one can't move across them, as one might with the latter (unless one apprehends their probability amplitudes as the QM analogs to normative crests and troughs).

What I can contribute, is a quantitative formulation - that may, or may not be associated with the qualitative hypotheses that precede it (in a fragmentary fashion):

$\triangle E \triangle t \geq \frac{h}{4 \pi }/E \triangle t \geq \frac{ \hbar }{2}$

This is, ubiquitously (as I'm certain you're familiar), the energy-time equivalent to Heisenberg's Uncertainty Principle. What it suggests, is that quantum states are (predominantly) transient, and are not characterized by definitive energy thresholds. Their observed energy thresholds, however, are by definition predicated on the frequencies of their states - which, in turn, are the inverse of how long they sustain itself for.

When you're unearthing QM time contraction, is this the interrelation you're endeavoring to bring to the fore - or is it instead, purely relativistic and non-experimental? If the former doesn't assuage the proposal, do contemplate reading with regards to the Dirac Equation - as the exercise may underpin your ideas in the framework, that formalizes them.

Thank you, I really appreciated your explanation. This last part 'suggestive trajectory to how 'likely...', it's tricky to me, 'cause in my language the translation of likely and probable is the same, so looks like not going further from the initial point. But adding this information 'suggestive trajectory...' was enough to make think a little more. — denis yamunaque

Quite truthfully, after engaging in this discussion, I'm not sure I understand probabilities as well as I thought I did.

You're right - I haven't been able to further your initial argument. Personally, I don't know if one can.

Mathematically, one can always devise one sophistication upon another.

Philosophically, however - determining what exactly likelihood entails, is a genuine conundrum.

What, conceptually, is probability? What is something being likely to happen? — denis yamunaque

Statistical probability is (for all necessary objectives) a formalism, that underlies the intuitive notion of a 'likelihood' (as you've discussed).

I mean, we assume that if an event has probability of 99,9% of happening, it means that if we simulate the conditions, each 1000 times the event would occur next to 999 times. But that's not a fact, since nothing really prohibits the complement of the event, with probability of 0,1% of keep continuously occurring through time, while the first event, with almost 100% of probability never happens. — denis yamunaque

You've identified precisely why probabilities aren't exhaustive, in and of themselves - they don't preclude the complement of an event (or an event itself), irrespective of how unlikely (or likely) they exert themselves to be. Unless they're of an unequivocal certainty (0 or 1), they shouldn't be conflated with assertions of certainty - or its lack, thereof.

Probabilistic interpretations, nevertheless, often 'suggest' that an assertion - of likelihood - is of practical utility in a decision-making paradigm (or likewise, not).

In this particular analogy, one can formalize a probabilistic construct with a binomial distribution for the complement of a 'significantly probable' event - denoted by $B (1000, 0.001)$, in the characteristic form $B (N, p)$.

You might be acquainted, in some measure, with the following sequence of reasoning:

For any elective integer $K$, wherein $0 \leq K \leq 1000$, there exists a discernible probability that conducting 1000 iterations of an arrangement, will result in $K$ complements to an event.

Specifically, if $P (N, K, p)$ illustrates the likelihood of an outcome (under the purview of a sample space) with an affiliated probability $p$, emerging on $k$ occasions after exactly $N$ iterations - then a canonical inference entails:

$P (N, K, p) = \binom{N}{K} [p^{K}] [(1-p)^{{N-K}}]$

Repurposing this expression, by virtue of the aforementioned system's $n$ and $p$ constituents suggests:

$P (1000, K, 0.001)= \binom{1000}{K} [0.001^{K}] [0.999^{{1000-K}}]$

0.001 is an imperceptible ratio, but is nonetheless fathomable. For instance, when $a = 1000$ (an indescribably anomalous iteration set), $P (N, K, p) = 0.001^{1000}.$

This might be misleading, unfortunately - since singular or incremental probabilities are nearly always inconsequent.

One may consolidate (or assimilate) the singular probabilities of $K$ variable iterations, across the discrete interval $a \rightarrow b,$ in order to accumulate superior likelihoods. Naturally, this engenders a binomial cumulative distribution - for a complement to manifest anywhere between $a \leq K \leq b$, when a probabilistic event is undertaken with $N$ distinctive iterations.

What if one were to redefine (for argumentation) $N=1000,$ to $N=1000^{100}$ - whilst $a$ and $b$ were unchanged? We'd witness an inconceivably larger number of operations (or iterations), therefore bolstering the likelihood of spectating a particular outcome across a specific interval of frequencies.

In answering your question, probability - schematically - is merely a suggestive trajectory to how 'likely' an event should be construed as being. It's neither infallible, nor overly authoritative; it exists solely to guide.

Droves of atheists (and anti-theists) renunciate merely the social consequences of organized, religious structures - as opposed to the (indeterminate) metaphysical assertions, that the structures themselves declaim.

Well, I was contemplating how we maybe able to both numericize and geometrize philosophy because we do to talk of philosophical "landscapes" and, for me, that's an open invitation for mathematicians to get involved in philosophy. In addition, the divine is closely linked to the concept of infinity; philosophy, my friend, is a mathematician's paradise. — TheMadFool

That's an enthusing idea, but what does numericizing and geometrizing Philosophy entail, precisely? We can't ascribe predetermined quantities to abstract ideas, mediate them, and pretend we're ingeniously resolving a confluence between two, disparate epistemologies.

On the notion of Infinity: that's certainly a mathematically inclined concept. Its converse (infinitesimals) was of significance, if I'm not mistaken, in Newton's Calculus - prior to being discounted in exchange for Limits. Nonetheless, the mathematical Infinity is rigorously constrained to an array of mathematical consequences, and doesn't trivially extend outside them.

Mathematicians may be (but often aren't) predisposed to undertaking philosophical discussions - but solely in a fashion, that is adherent to quantitative frameworks. Aside from Kurt Gödel, very few others (to my knowledge) have willfully lent themselves to that cause; David Hilbert might constitute an exception.

Hilbert's Program may be the most consecrated (and valuable) mathematical interpretation of a philosophical edifice, in that it rigidifies several constructs of finitary reasoning, consistency and meta-logic.

It isn't as though the chasms that separate quantitative and qualitative disciplines are untraversable, either; it's only that they should (ideally) be traversed with forethought, and two-sided significance.

Ernst Mach, for instance - a proponent of the famed Mach's principle, was commemorated for path-breaking discoveries in both Physics and Philosophy.

I never foresaw a page-long explanation, but it was most certainly worth it.

I'm affixing the entirety of it herein, with a few observational comments - for it definitely simplifies the overarching rigor of the subject, and necessitates a read.

'First of all, when I say "proved", what I will mean is "proved with the aid of
the whole of math". Now then: two plus two is four, as you well know. And,
of course, it can be proved that two plus two is four (proved, that is, with the
aid of the whole of math, as I said, though in the case of two plus two, of
course we do not need the whole of math to prove that it is four). And, as
may not be quite so clear, it can be proved that it can be proved that two plus
two is four, as well. And it can be proved that it can be proved that it can be
proved that two plus two is four. And so on. In fact, if a claim can be proved,
then it can be proved that the claim can be proved. And that too can be
proved.'

What this predominantly suggests, is that if an assertion can be proved, then one may also (successfully) prove that it can be proved, in a recursive manner. I don't know why this bears veracity, especially in a formalized system characterized by a certain degree/class of arithmetic. Will you able to shed any light, on this matter?

'Thus: it can be proved that two plus two is not five. Can it be proved as well
that two plus two is five? It would be a real blow to math, to say the least, if
it could. If it could be proved that two plus two is five, then it could be
proved that five is not five, and then there would be no claim that could not
be proved, and math would be a lot of bunk.

So, we now want to ask, can it be proved that it can't be proved that two plus
two is five? Here's the shock: no, it can't. Or, to hedge a bit: if it can be
proved that it can't be proved that two plus two is five, then it can be proved
as well that two plus two is five, and math is a lot of bunk. In fact, if math is
not a lot of bunk, then no claim of the form "claim X can't be proved" can be
proved.'

Does this (the latter) entail the crux of Gödel incompleteness, insofar as contradictions are concerned?

Here's a simplistic, non-technical sequence of rationalizations - identical to the ones in the exposition above (it doesn't consist of any jargon - inclusive of languages, theorems, proofs or axioms).

1) Hypothetically, there exists a statement A (2+2=5).
2) A's negation can be proven.
3) Ideally, A should not be provable.
4) Unfortunately, one can't prove, that one can't prove A.
5) If 4 holds true, then one can simultaneously prove A (since A must demonstrate a specific truth value).
6) Therefore, there exists an inconsistency between 2 and 5, implying that certain truths will necessarily remain unprovable.

Have I significantly misapprehended the argument, or is it at all substantive?

'By the way, in case you'd like to know: yes, it can be proved that if it can be
proved that it can't be proved that two plus two is five, then it can be proved
that two plus two is five.'

Interpreting this sentence, is harder than accruing a mastery over all of Mathematics.