I'm mainly antagonistic to the Cartesian take on "res extensa" being utterly severed from mind stuff due to the former having extension in space but not the latter. — javra


And do smells necessarily have extension in space? — Count Timothy von Icarus


The question raised here is an interesting one, and I also take trouble with the split of res extensa and res cogitans. — Lionino

Apropos to directional smell, turns out research does evidence directional, else stereo, smell in humans. Given that most other mammals have a keener sense of smell than we do, I by this then infer that smell is generally directional, and, hence, spatial, in most lifeforms that are equipped with this physiological sense.

To be free, one must overcome the shackles of instinct, desire, and circumstance. How is this accomplished? In The Phaedo and Book IV of The Republic, Plato argues that this can only be accomplished by having our soul unified and harmonized by our rationality. Why should our rationality be "in charge?" Why not have reason be a "slave to the passions," as Hume would have it? — Count Timothy von Icarus

A well written OP. You’ve touched upon passion vs. reason. Here only want to present the case that Hume’s stipulation that “reason is a slave to the passions” is not necessarily contrary to the overall gist of the OP, at least as I currently interpret the OP.

It can be upheld that whereas passions in themselves always addressed ends (passions always being in some way wants and that wanted being the end pursued), reasoning (even when human reasoning is construed to be a part of the universal logos) will always strictly be a means toward the ends pursued—including potentially those ends of discerning what is true or, else, the end of a maximal eudemonia.

Hence, without any held ends, reasoning is useless and thereby devoid of meaning. On the other hand, ends held and pursued without reasoning can be likened to a headless chicken’s moving to and fro (this metaphor here primarily addressing the inability of obtaining the ends pursued in the absence of any and all reasoning).

At which point lesser lifeform’s reasoning changes from reasoning that is in some way human-like in being consciously appraised to being purely that of the universal logos (which applies to rocks and to automata alike) is of course not something that can be definitively delimitated. That aside, were there to be a universal logos, it than stands to the reason here presented that it too would hold its own end toward which it only serves as a means. For example:

The OP references the Platonic notion of the Good. Here, a somewhat subtle but important change in focus can be found occurring between Platonism and Neoplatonism: wherein, tmk, the first addressed the Good as that upon which all else is contingent on (only implicitly at best upholding that the Good is to be pursued as an end), the latter furthers this by explicitly framing the Good as also being that which is to be pursued as end in the form of henosis with the One. In at least this latter conceptualization, then, the universal logos is not equivalent to the Good / the One but is that which emanates from it and which is reconciled in it—with logos being here considered the intermediary between soul, nous, and highest level of reality: the One. My point here being, in this case as example, the logos (universal reasoning) is still a means toward the One, with henosis (unification with the One) being of itself a passion: here again making reasoning subordinate to (end-driven) passion(s), albeit at a more universal level of contemplation.

Going back to Plato as you’ve mentioned in the quote, reasoning here is also only a means to the end of freedom and the related eudemonia that results from a unified and harmonized soul. The want for this end is then a passion, to which reasoning is then again subservient to.

I know its not a definitive argument and there are alternative ways of interpretation. All the same, that reason is subordinate to passion—either on an individual basis or on a global scale—seems to me an important observation, and one which in no way contradicts the authority of reasoning per se. Granted, to avoid radical relativism, these very observations would then need to be embedded within the very metaphysics here addressed: wherein “the Good” is an absolute end (and is absolute in so being).

I'll leave it there, but for now I think it's worth considering how much our society is driven by appetites (consider the electorate's response whenever consumption must decrease) and passions (consider the fractious, tribal political climate), as opposed to its rational part and how this constricts freedom of action on implementing ethically-minded policy. — Count Timothy von Icarus

This implicitly presumes that individuals are goal-driven and hence hold desires that they want satisfied. In which case, the question isn’t one of whether reasoning is subservient to passion but, instead, whether the reasoning being employed satisfies the very core passions addressed. Judging by the ever increasing rates and depression, suicide, and related issues, they give no indication of so doing.

p.s. This is a topic that gets complicated very easily by our having predominant passions to subordinate passions. But I find that it is precisely reasoning which facilitates all our subordinate passions optimally satisfying our predominant passion(s). Again, serving as a means toward (desired) ends.

What would you think if I told you I'd seen such things? — Janus

Since you asked: I'd think it a hallucination, or at the very least as not having anything to do with what can take place in the objective world, this due to my core metaphysical commitments. I'm certain I'd think this even if I myself were to "see" such things. Other's might not so interpret, but that would be due to their disparate core commitments.

I don't think any of this has much to do with metaphysics. — Janus

OK, thanks for sharing. But then we do disagree on what metaphysics is. My view being in general accord with this:

Metaphysics is the branch of philosophy that studies the fundamental nature of reality. This includes studies of the first principles of: being or existence, identity, change, consciousness, space and time, necessity, actuality, and possibility.[1] — https://en.wikipedia.org/wiki/Metaphysics

... which to me fits in well enough with the answer I just provided to your question above regarding core metaphysical commitments (that, again, can be unconsciously held and thereby not be consciously analyzable worldviews but, instead, in part being - as you say - "habitual expectations based on what has been encountered and observed in the course of one's life"). I get it, you hold a different semantics and views and thereby find it important to assert that you disagree. But that, of itself, again doesn't warrant my view being egregious.

Got a few lightbulbs to change (metaphorically speaking) such that philosophizing right now will be a bit too distracting - so I'll be signing off for the time being.

While I’m here, getting back to the OP:

Metaphysics might be viewed as being in part comprised of discerning just how many philosophers it takes to change a light-bulb - tricky issue because many, if not all, will sit about endlessly debating the topic.

Else, it might be viewed as those aspects of ontology universal to all beings which facilitate both the possibility of the light-bulb being changed and the possibility of debating the issue without end - aspects that objectively are irrespective of one’s beliefs on the matter, if any.

I so far like this generalized appraisal; though, of course, other perspectives - some of which will disagree - are possible.

I don't find any of this surprising and I don't think professed worldviews tell us much. — Tom Storm

Yea, my point being about the same.

OK. Thanks.

As an example, though I do not uphold the claim of "no atheists in foxholes", I do have evidence that some atheists no longer act according to their atheistic principles in dire situations. Although of course disagreements can abound regarding this, to me this does illustrate that sometimes one's professed worldview - while in no way being a lie - can in some ways be self-deceptive when put the test, so to speak. But this is one example among potentially many.

Thanks again for your views, though.

The two don’t have to be in conflict. — Joshs

This can be in full accord to "not necessarily equating". To be clearer, do you find that hypocrisy in what is maintained in praxis and what is professed via propositions cannot occur and, if so, due to what reason(s)?

I am thinking that it is only in the philosophies that came after Hegel and were strongly influenced by him that we get an articulation of metaphysics as comparable to worldview. That is, as an overarching framework of intelligibility that orients us to the world and ties all its aspects together in a global unity, but that in most cases is held naively, unconsciously. — Joshs

In many a way I agree, but how would you account for discrepancies such as these:

I’ve met self-proclaimed non-spiritual atheists that uphold this metaphysical worldview but are in practice superstitious and affirm things like “your car was broken into today because you weren’t cordial to person A last week” or, as an example of the flipside, self-proclaimed Christians that adhere to all ritual aspects of their faith and uphold this metaphysical worldview while at the same time in practice being in many a way atheistic (e.g., they fear - and hence innately believe - death to be a cessation of being; or else don’t believe in the occurrence of spiritual realities in the here and now, as contrasted to occurring for biblical figures (e.g., “burning bushes” are OK biblically but not in reality that is lived); etc.) - this to not address the grave hypocrisies in ethical principles relative to Jesus Christ’s teaching that often enough occur (the ontology of values being in many a way metaphysical).

Here, there seems to me to be a professed and defended metaphysical worldview that is explicitly maintained which is in at least some ways in direct contradiction to the metaphysical beliefs/principles implicitly maintained.

Because of examples such as these, I don’t then necessarily equate a being’s often unconsciously occurring Umwelt (for lack of a better word) to - in the case of humans - the self-professed worldview which is consciously upheld and maintained.

I don't know, I don't know what examples you are referring to — Janus

This is mouth dropping to me. I'll highlight them for you:

For just one example, were one to witness billiard balls randomly fall through solid table tops or else hover in midair, one would hold a confirmation bias in line with one’s core ontological understanding as to what is in fact possible. Most would assume it to either be stage magic or tricks of the eye precisely due to this confirmation bias. Whether or not miracles can occur is again determined by one’s core ontology’s confirmation bias. — javra

Having done that, have a nice day.

Can you provide for your contention that people cling to “some core conviction regarding the nature of the world via which we assimilate all novel information"some "meaningful justification" for "outside of “it doesn’t sit well with my own intuitions”"? — Janus

Are the examples I just provided to this very effect rationally or empirically in any way contradictory to - or else do they in any way not cohere to - reality as we all know it?

But if you're in search of infallible proof I've none to give.

Can you explain the difference? — Janus

For one thing, a metaphysical worldview is a strictly conscious construct which is itself pivoted upon - and hence not equivalent to - some core conviction (or core set of convictions to be more precise) regarding the causal, spatial, temporal, etc. nature of the world, the latter often enough not being consciously analyzable in fully explicit manners the way that the metaphysical worldview is.

No empirical or logical grounds can be adduced to support or deny the contention. It comes down to how you see people and whether in this particular connection you see uniformity or diversity. — Janus

OK. So your contentions that it is an egregious - by which I understand “outstandingly bad” - generalization comes down to an opinion that you can provide no meaningful justification for, outside of “it doesn’t sit well with my own intuitions”.

Moreover, I take any and all ontological understanding - be it consciously upheld or else unconscious - to in itself be metaphysical in nature. Whereas from what I’ve so far perused of your expressed perspective you take it mean something akin to anything out of the ordinary in relation to ontology. This, of itself, would make a large difference in what I myself stated.

For just one example, were one to witness billiard balls randomly fall through solid table tops or else hover in midair, one would hold a confirmation bias in line with one’s core ontological understanding as to what is in fact possible. Most would assume it to either be stage magic or tricks of the eye precisely due to this confirmation bias. Whether or not miracles can occur is again determined by one’s core ontology’s confirmation bias.

But there are innumerable examples - many very different due to very different core ontological beliefs that can be held in theory if not also in practice.

And again, in the absence of evidence that people go about life in the complete absence of core ontological beliefs - if not consciously maintained than unconscious - around which they assimilate new information such that they hold a confirmation bias to these very core beliefs, your decrying my perspective egregious is, basically, completely unwarranted.

Read more carefully what I actually wrote and you might find I never once mentioned that we cling to “metaphysical worldviews” but to “some core conviction regarding the nature of the world via which we assimilate all novel information [...]" - which in my lexicon are quite distinct propositions.

Thanks for the corrections.

Was it approximately 1000 pages or closer to about 360? — TonesInDeepFreeze

Bad online reference apparently. Yes it now seems to be the latter.

Was the axiom of reducibility used in the proof? — TonesInDeepFreeze

A best inference on my part, The axiom was indeed introduced in PM according to this reference. Haven't been able to verify if it was used to prove 1 + 1 = 2.

Let me know if you find these well received corrections make a change in what I uphold in that post: to paraphrase, that some more basic aspects of mathematics give all indications of being universal while other more developed maths do not.

[...] In pursuit of this accelerated post-Singularity future, any harm they’ve done to the planet or to other people is necessary collateral damage. It’s the delusion of people who’ve been able to buy their way out of everything uncomfortable, inconvenient or painful, and don’t accept the fact that they cannot buy their way out of death. — Joshs

Thanks for that! :up: The whole article reverberates quite well with me.

As what I find to be a somewhat humorous apropos to what's here quoted:

One’s death - irrespective of what one assumes one’s corporeal death to this world to imply ontologically - can be ultimately understood to be the “obliteration of one’s ego” (whether one then no longer is or else continues being only being a possible appended issue). Taxes on the other hand - something that many, especially those who are rich, are also morbidly averse to - are when symbolically addressed “one’s contribution to the welfare of a community/ecosystem/whole without which the community/ecosystem/whole would crumble” (be it a tyranny, a democracy, or any other politics when it comes to the monetary contribution of taxes per se).

At least when thus abstractly understood, I can jive with Franklin in that death and taxes, as much as they might be disliked, are sooner or later both certainties for individuals partaking of a societal life and, hence, for humans - transhumanist of otherwise.

Not an argument I'm gonna defend. Just an opinionated observation to be taken with a grain of salt.

Can we make progress in understanding and navigating the world by continually revising this scheme, without having to declare the earlier versions ‘false’? — Joshs

Tricky question in so far as I too am a construcitivst in many a sense, though by no means a radical relativist.

I'll use the notion of scientific progress as an example: to me, there can be no such thing - to include no Kuhnian paradigm shifts that in any way improve anything of our understanding - without there being an objective reality to be progressed toward via scientific investigations - one that is in and of itself true. (Granted, this to me requires a different metaphysical approach than either that of physicalism or of any notion entailing an Abrahamic deity as ultimate reality, to list just two.)

So appraised, while the Newtonian understanding of the physical world was and remains quite pragmatic for everyday purposes, it is nevertheless a false understanding of the physical world. This just as much as declaring the the sun revolves around the Earth is pragmatic for everyday purposes (such as is implied in sunrises and sunsets) but nevertheless false.

In the absence of a functional theory of everything regarding physicality, the same too can be hypothesized of the theory of relativity as it currently stands (nevertheless granting many a variation in its interpretation).

To me, then, if progress is in fact made from understanding A to understanding B, this then entails the (non-fabricated) truth that B is a better understanding than is A. That, though, does not then entail that understanding B is the (objectively) true understanding (if this notion is in any way intelligible). But it does entail that understanding A was then in some way faulty - and, in so being, it can then in this sense be declared false. This will however extend beyond a strictly bivalent notion of truth-value (for me, one that however still makes no use of dialetheism; one that nevertheless acknowledges partial truths, along with different vantages of reality to which these pertain).

Complex topic, but I think that summarizes my view. In short, if progress is in fact made, one's formerly held but now discarded understandings will be far more false - falser - that will be one's currently maintained understanding.

That is, if we drop the notion of truth as a valid assessment of our utterances in favour of the will to power or some such, we are endorsing the powerful, reinforcing their hegemony.

Post modernism cannot speak truth, therefore it cannot speak truth to power. — Banno

Well, to my best understanding, post-modernists can speak fabricated truth to powers that likewise fabricate truths - without there being any right or wrong to it. It's one interpretation of the "Will to Power".

I personally view fabricated truths as deception - be it self-deception or otherwise - if not outright lies. But that's just me.

I suppose my own "axis mundi" consists of – begins with – the principle of non-contradiction (PNC). — 180 Proof

:grin: :up: Yup, it forms part of my axis mundi as well. :smile:

In other words, both the non-pomo left and the far right believe in the non-relativist objectivity of scientific truth. They just disagree on what constitutes the proper scientific method for attaining objective truth. Postmodernists, on the other hand , disagree with both of these groups on the coherence of their various ideas of objective truth. — Joshs

I'm having a hard time understanding this. To not be presumptuous, can you clarify the following:

According to radical relativism, is the "scientific method" which produces the claim that dinosaurs walked the earth along humans on a par to rather distinct, also termed "scientific method" that produces the claim that humans did not exist when dinosaurs roamed the earth?

Secondly, are both just mentioned claims of objective truth of equal value in their being socially constructed truths that nevertheless compete for dominance within society?

Lastly, if postmodernists do not believe in there being correct facts - else expressed, do not believe in objective (rather than fabricated/created) truths - how do postmodernist resolve the contradictory nature of the two just stipulated claims?

I think this is an egregious generalization—all I can think of to say in response is "speak for yourself". — Janus

As you've expressed in a post elsewhere last time we chatted, you don't care what I think. All the same:

1) I am speaking for myself: it's my established worldview. (Right up there with you not being a p-zombie.)

2) On what rational or empirical grounds do you affirm that what I previous expressed is "an egregious generalization"? (Hint: that "I don't like it" is not such a justification.)

There’s this saying: one can (try to) lead a horse to water, but …

We all consciously or unconsciously cling to some form of what Mircea Eliade termed an axis mundi when more abstractly appraised—some core conviction regarding the nature of the world via which we assimilate all novel information, without which we would loose our bearings, around which all of what we interpret to be the world pivots, and which, because of all this, we either implicitly or explicitly consider to be sacred (at the very least in relation to ourselves). To some this is the Abrahamic deity, to others it is scientism, to yet others it is the conviction that there are no correct facts, or otherwise some notion akin to the Platonic or Neo-Platonic notion of “the Good”, and so on and so forth. And we all hold confirmation biases in terms of this personal, typically implicitly maintained, axis mundi.

There is no convincing another that their own axis mundi is incorrect without the other being able to replace it with what they find to be a better axis mundi—one which accounts for the entire body of knowledge and values they already possess in addition to all new information they might be exposed to.

Or at least so I so far find. And so disagreement among humans on many but the most concrete of interpersonally experienced facts can be found.

But then this too is in itself a metaphysical perspective of sorts.

Are these aggressive anti-philosophy beliefs being promulgated in universities these days? — Gnomon

While it is likely that in some yes and in others no, I have no idea as to the overall reality of the matter. Opinionated as they might be, I doubt that others would know either in the absence of any impartial research regarding this topic.

I respect many of your views, but:

But it is one thing to claim that they ignore or distort facts , it is quite another to assert that they have taken radical relativists to heart and think that there are no correct facts. [...] They tend to be metaphysical, or naive, realists about both ethical and objective truth. — Joshs

How is that not blatantly incongruous (this in non-dialetheistic systems, if it needs to be said)?

Where “truth” is understood as conformity that which is actual/real/factual, that “the truth that ‘there is no truth’ is itself and affirmed truth” is not true on account of having no truth-value—and that one must be learned in many an authority figure to comprehend this—certainly seems post-modernistic to me. And, here, truth is whatever one wants to be true just in case one has the leverage, or power, to force the belief of its reality upon not only oneself but upon as many others as possible. Truth here can only be created in radically relativistic manners, rather than ever being the ontically uncreated waters in which we swim and breathe as psyches (this metaphorically speaking) and, on occasion, being that which can be discovered. In which case, this “metaphysical/naive realism regarding ethical and objective truths” wherein “facts can be and are ignored and distorted” is in perfect keeping with the radical relativism wherein there is no objective truths to speak of. This, again, granting a non-dialetheist reality.

For my part, in the world I live, most people need there being an unquestionable authority in their life. Most of those that then in one or another do away with the Abrahamic notion of an omni-this-and-that deity—which I find quite understandable on multiple grounds—will then turn to this nebulous term “science” as being just such an unquestionable authority. As a common enough example, for such people proclaiming “science says so” is to proclaim the unquestionable truth of that which is stipulated.

This is a gross misrepresentation of what the empirical sciences are. The vast majority of today's, for example, sciences regarding physics are, if fact, thoroughly entwined with a large sum of theoretical speculation—both inductive and abductive. There is zilch empirical about any interpretation of QM, regardless of what it might be. And when one takes a look at the nitty gritty of how we’ve arrived at today's QM, one will find a plethora of such inductive and abductive theoretical speculations regarding what in fact is. The proof that there is something objectively and fundamentally wrong with today's physics is that QM cannot be integrated into the theory of relativity in as is form so as to provide a theory of everything physical.

Science's only merit is that it can falsify those theoretical suppositions regarding that which can be empirically observed—this via empirical observations—and, by not falsifying, it can then to varying extents validate, but never “prove”, the theoretical suppositions in question.

This gross misunderstanding of science typically held by most people—these very same yet upholding science (hence, scientific inferences taken to be scientific knowledge) to be the de facto unquestionable authority regarding what is real—is, for example, readily witness in the popularized claim that “science has not proven human-caused global warming”. This being an utterly nonsensical claim, least of all because absolutely nothing of science is infallible and thereby beyond any and all doubt.

All that for now being placed aside, other than validating that it has a brain, science has nothing to say about whether or not a dog, for example, is conscious of anything, thereby holds a consciousness, thereby is a conscious being. It has no possible solution to the Sorites paradox. Nor does it have anything to say regarding the ontological standing of that which we all empirically perceive to be and label “the physical world”. In keeping with a long list of pertinent issues that science can only remain silent on is that of whether or not the universe is foundationally meaningless. Any position held on all of these many issues then being entirely metaphysical claims.

Which in a way brings me full circle to this:

Because, for one example, there’s nothing wrong with a bunch of lemmings actively swimming their way toward a climate change catastrophe in today’s status quo metaphysics of a meaningless universe. — javra

To deny the importance of any and all metaphysics is to be (bluntly expressed) ignorant of one's very own suppositions (be they culturally inherited or else arrived at by oneself) regarding what reality in fact is and consists of. Which, however, is not to then claim that all such suppositions are of equal value; some such being valueless, e.g., being the brain in a vat constructed by another brain in a vat constructed by another, this ad infinitum, though plausibly conceivable as a metaphysical possibility, is devoid of any value regarding, for example, what I should best do with my life or else how I should best understand value theory and, hence, the values by which I and others live our lives.

The idea of 'truth-value realism, which is the view that mathematical statements have objective, non-vacuous truth values independently of the conventions or knowledge of the mathematicians' is I guess what I am am exploring too. — Tom Storm

This hinging on the bifurcation I initially mentioned in my original post, here’s a simple argument for (some) mathematical statements having such "truth-value realism":

Regardless of ontological approach (materialism, idealism, dualism, pluralism, and so forth), that quantity occurs in the world is a fact. Secondly, the cognition of quantities can only occur via mathematical semantics (this irrespective of their symbolic representation, if any). Therefore, some mathematical statement (namely, those which can be mapped onto the empirically know world) have "objective, non-vacuous truth values independently of the conventions or knowledge of the mathematicians".

This conclusion, however, will directly ground mathematical thinking in the metaphysics of identity as foundation, for quantity can only occur with the occurrence of individuated identities (i.e., units, aka unities of that being addressed), and these are not always as intuitive as they might at first appear (the Sorites paradox as one easily expressed example of this).

At any rate, the only way I see of disparaging this stated conclusion is by disparaging the reality of quantity in the world.

These are far more abstract conceptualizations than that which I was addressing: the semantic which we, currently, in our culture, symbolize by "1" being universally equivalent to the semantics we convey in English by the phrase of "a unity".

So that "one unity and another unity will be equivalent to two unities" is then a universal staple of all mathematical cognition: in all humans as well as in lesser animals.

Hence, my question was intended to be specific to whether you find the semantic of "a unity"/"1" to be arbitrary and thereby not ubiquitously universal?

Asking whether math is different in other cultures is like asking whether chess is different in other cultures. — Lionino

Not sure what you mean by this. Chess has a long history and has had changes over time in different cultures. For example:

1200–1700: Origins of the modern game

The game of chess was then played and known in all European countries. A famous 13th-century Spanish manuscript covering chess, backgammon, and dice is known as the Libro de los juegos, which is the earliest European treatise on chess as well as being the oldest document on European tables games. The rules were fundamentally similar to those of the Arabic shatranj. The differences were mostly in the use of a checkered board instead of a plain monochrome board used by Arabs and the habit of allowing some or all pawns to make an initial double step. In some regions, the queen, which had replaced the wazir, or the king could also make an initial two-square leap under some conditions.[64] — https://en.wikipedia.org/wiki/Chess#1200%E2%80%931700:_Origins_of_the_modern_game

Does that to you then imply that something like 1 + 1 = 2 is constructed within specific culture contexts, such that the quantity "1" is arbitrary rather than ubiquitously universal?

does this point to maths being more arbitrary than we think? — Tom Storm

While I’m no math wiz either, I think (else presume) I know enough about maths to express the following (may I be corrected where appropriate):

Some maths are universal in their semantics (however these semantics might be expressed symbolically, if at all so expressed).

From these universal maths then can and often do get constructed derivations which, as such, often enough don’t consists of the same universality of semantics in that which is derived, but are to some extent constructed.

For instance, the mathematical semantic here expressed by the symbol “1” can only be universal. The symbol “one” here holding the semantic of “a unity” (which can get rather metaphysical when getting into the metaphysics of identity theory). It is a universal not only to all humans but also to all lesser animals that can in any way engage in any form of mathematical cognition.

So something like the semantics to 1 + 1 = 2 can only be universal relative to all sentience that is in any way capable of any mathematical cognition regarding addition.

On the other hand, mathematics which are very advanced derivations of this and similarly universal maths—such as surreal numbers or the mathematics to qubits—will be in part contingent on mathematical factors whose semantics are not universal to all those who can engage in mathematical cognition. Such complex mathematics can then be argued to be in some way constructivist (if in no way speculative) and, thereby, to some extent culture-relative.

For example, the Principia Mathematica (written in 1910) is commonly known to take about a thousand pages to in part formally prove that 1 and 1 is in fact equivalent to 2. No such formal proof occurred previously in human history (obviously, this didn’t prevent humans from successfully applying the mathematics of 1 + 1 = 2). Yet, while everyone has always universally agreed that 1 + 1 = 2, the formal mathematical proof of the book by which this is established is not universally agreed upon without criticism. As one example of this, at least one of the axioms the book uses, its introduced axiom of reducibility, has a significant number of criticism—thereby not being universally apparent in the same way that 1 + 1 = 2 is but, instead, being a best reasoned supposition which was set down as axiomatic.

So, 1 + 1 = 2 is universal and hence not culture relative or in any way socially constructed. The formal proof that 1 + 1 = 2 is however not fully comprised of that which is universal and thereby in no way culture relative or socially constructed—but, instead, can be deemed to be in part constructivist in ways which imply the relativity of some of its mathematical semantics (however these are expressed symbolically).

More directly to the quoted question: The mathematical semantics of 1 + 1 = 2 is in no way arbitrary. But it’s formal mathematical proof in some ways is (albeit yet constrained to reasoned best inferences).

The proper answer to the quoted question should then be relative to those specific mathematical notions implicitly addressed. Overall, the answer is "no and yes," this at the same time but in different respects.

------

P.s. In large part posting this in a want to see if any more formally mathematical intellect would find anything to disagree with in what was here expressed.

This would satisfy my idea of perfection as that which can't be improve upon. — Tom Storm

OK. Understood. To be clear, my own vantage in this discussion wasn't concerned with the issue of whether circles are perfect in the sense you here specify - to me, we both so far have given all indications that we both accept they are - but, rather, whether perfect circles are subjectively perfect (as you seem to have so far repeatedly upheld) or else objectively perfect. But its not the most pivotal of issues to me.

In seeing you've started a new thread on the issue of mathematics, best of luck in your investigations.

But you are quite right to say that a perfect circle and a unicorn have little in common. A perfect circle is a mathematical abstraction, while a unicorn is a mythical creature. The unicorn relies upon open an open ended imaginative discourse, while the circle's properties are defined mathematically. — Tom Storm

Almost makes it sound as though the perfect circle - being here a mathematical abstraction delineated by its mathematical definition and, hence, not occurring to anyone prior to any such formal definition of it - is purely a construct of human imagination. This rather than being apprehended by understanding as something that objectively is (again, this in non-physical manners).

But, if so, then – via pi and so forth – so too is all our modern scientific knowledge of quanta nothing more than concoctions of human imagination. This rather than being discoveries (however imperfect) regarding the way the world in fact is.

Which to me would kind of relate to those magical unicorns you bring up: this being magical thinking with global efficacy.

But it may also lead to unicorns — Tom Storm

Ha. Not that I agree (e.g., there is no one universal exemplar of the perfect unicorn), but, if so, it can then likewise also lead to unicorn based technologies we all live by and universally agree upon.

Nice. I hear you but i don't think this is all that useful a formulation. We can find any number of minds to agree and visualise a unicorn but it still doesn't make it true. In this way we can also have objective accounts of ghosts and UFO too. Not sure what the word objective adds to this understanding. — Tom Storm

Just wanted to point this out:

All can however only provide the exact same example of what a perfect circle is epitomized by. And from this universality of agreement in understanding among all sapience then gets derived things such as the number pi. — javra

By entailment: If a perfect circle is no more objective/true/real than is a unicorn, then the number pi is no more objective/true/real than is a unicorn. If the number pi is no more real than is a unicorn, then neither is the Heisenberg uncertainty principle (which in part relies upon use of pi) any more real than is a unicorn. If the Heisenberg uncertainty principle (which is a fundamental concept to quantum mechanics) is no more real than is a unicorn, then much if not all of quantum mechanics is no more real than is a unicorn. And, if the latter is true, then all technology reliant on quantum mechanics is no more real than unicorns.

I know, it might be hard to follow - but it's not oriented at convincing you of anything.

Unless evidenced wrong, the just mentioned argument appears to me quite sound; in brief: If a perfect circle is no more real than are unicorns, then the reality of our quantum mechanics based technology is on par to the reality of unicorns.

Since unicorns are commonly taken to be fully fictitious/unreal, something then is quite amiss with claiming that perfect circles are not objective in a way that unicorns can never be.

OK. Thanks.

Glad to hear. :up:

IMO, the comparison case for all these theories should be the best/most popular theories in other camps, not naive realism, which is more a strawman than a real position. — Count Timothy von Icarus

I can get that, but then can you clarify what you make out of this statement - or else whether you find it erroneous - with emphasis on the highlighted portion:

In recent years, direct realists have wanted the perceptual relation to be entirely unmediated: we don’t achieve perceptual contact with objects in virtue of having perceptual experiences; the experience just is the perceptual contact with the object (Brewer 2011).This is the view that perceptual experience is constituted by the subject’s standing in certain relations to external objects, where this relation is not mediated by or analyzable in terms of further, inner states of the agent. — https://plato.stanford.edu/Entries/perception-episprob/#DireReal

I so far interpret it as expressing that our perceptions are in no way mediated by or else analyzable in terms of the agent's specific (even if this is only a perfect representation of the its species-specific) relations of "physiological senses - CNS capacities - resulting states of awareness" - these relations of themselves constituting the "inner states of the agent". I'll try to decompress this if needed, but I'm currently hoping it will make general sense to you as is. At any rate, how do you interpret the quoted statement?

I don't disagree with anything you wrote. However, contemporary versions of direct realism, intentionality theories, and phenomenological theories all explain the same phenomena. Each of these have their own problems, but it doesn't seem readily apparent that some have significantly worse problems than others. The result is that I would tend to say that "indirect realism can be made consistent with the empirical sciences," rather than "the empirical sciences confirm indirect realism," which would seem to imply that we can eliminate competing theories based on the empirical sciences. — Count Timothy von Icarus

This seems to me to hinge one what one means by "direct" and "indirect" realism, and I acknowledge that opinions can vary greatly. It's a bit lengthy, but here is an excerpt from SEP on the matter:

2.3.3 Direct Realism

Proponents of intentionalist and adverbialist theories have often thought of themselves as defending a kind of direct realism; Reid (1785), for example, clearly thinks his proto-adverbialist view is a direct realist view. And perceptual experience is surely less indirect on an intentionalist or adverbialist theory than on the typical sense-datum theory, at least in the sense of perceptual directness. Nevertheless, intentionalist and adverbialist theories render the perception of worldly objects indirect in at least two important ways: (a) it is mediated by an inner state, in the sense that one is in perceptual contact with an outer object of perception only (though not entirely) in virtue of being in that inner state; and (b) that inner state is one that we could be in even in cases of radical perceptual error (e.g., dreams, demonic deception, etc.). These theories might thus be viewed as only “quasi-direct” realist theories; experiences still screen off the external world in the sense that the experience might still be the same, whether the agent is in the good case or the bad case. Quasi-direct theories thus reject the Indirectness Principle only under some readings of “directness”. A fully direct realism would offer an unequivocal rejection of the Indirectness Principle by denying that we are in the same mental states in the good and the bad cases. In recent years, direct realists have wanted the perceptual relation to be entirely unmediated: we don’t achieve perceptual contact with objects in virtue of having perceptual experiences; the experience just is the perceptual contact with the object (Brewer 2011).This is the view that perceptual experience is constituted by the subject’s standing in certain relations to external objects, where this relation is not mediated by or analyzable in terms of further, inner states of the agent. Thus, the brain in the vat could not have the same experiences as a normal veridical perceiver, because experience is itself already world-involving. — https://plato.stanford.edu/Entries/perception-episprob/#DireReal

I then take the highlighted portion of this text to imply that the yellow flower's uniformity of hew as seen by humans is (for emphasis) the one true reality of the object - this such that a bee's experience of the flower as having a pattern of different hews is then incorrect / bad / illusory ... if not also somehow hallucinatory.

If what I experience is a direct access (one that is hence "not mediated by or analyzable in terms of further, inner states of the agent") to reality as it truly, objectively is, then the just mentioned conclusion so far seems to me entailed. If so, this then contradicts our scientific knowledge of reality/the world.

In which way would you find the just expressed to be inaccurate?

Lower animals certainly have the second type of concept, but it seems doubtful they have the first. — Count Timothy von Icarus

There's plenty of scientific evidence that some of them do. As one example I quickly found online:
Can Dogs Learn Concepts the Same Way We Do? Concept Formation in a German Shepherd

This not to even start discussing studies on the great apes.

I just wanted to illustrate that theories all have significant problems AND can be made consistent enough with empirical evidence that none of particularly "confirmed" above others — Count Timothy von Icarus

My use of the term "confirmed" was likely inappropriate. I meant in the sense of "strengthened" rather than of of "having an assured accuracy". That mentioned, contingent on the issue of what "direct realism" entails, as previously expressed, our scientific knowledge does contradict our human perceptions being the be-all and end-all to what the objective world consists of (edit: to be clear, this perceptually). In this sense, I then yet find our scientific knowledge to evidence, hence support, the view that direct realism as just described in this post is erroneous. Be it "quasi-" or otherwise, this then results in science supporting an indirect realism.

But maybe I've got my definitions wrong.

Spaciotemporal properties are aspects of the phenomena for Kant, or aspects of what we intuit. — frank

This is very unclear to me.

What I expressed in relation to Kant's take on space and time is simply that neither space nor time are of themselves phenomena for Kant. They are instead for him "pure (rather than empirical) intuitions". Here's an excerpt from IEP:

The most basic type of representation of sensibility is what Kant calls an “intuition.” An intuition is a representation that refers directly to a singular individual object. There are two types of intuitions. Pure intuitions are a priori representations of space and time themselves (see 2d1 below). Empirical intuitions are a posteriori representations that refer to specific empirical objects in the world. In addition to possessing a spatiotemporal “form,” empirical intuitions also involve sensation, which Kant calls the “matter” of intuition (and of experience generally). (Without sensations, the mind could never have thoughts about real things, only possible ones.) We have empirical intuitions both of objects in the physical world (“outer intuitions”) and objects in our own minds (“inner intuitions”). — https://iep.utm.edu/kantview/#SH2c

Phenomena for Kant are appearances - which I so far take to always be in one way or another empirical. And, hence, I so far take it that for Kant space and time - both being a priori representations that are then in no way empirical - are not phenomenal in and of themselves.

Which is not to then say that either pure or empirical intuitions are not representations for Kant.

If you find this interpretation mistaken, can you please back up your disagreement with references.

Do we know if a perfect circle can be realised? — Tom Storm

That's the hitch. A perfect circle is realized in this world by all minds which can comprehend it's, granted non-physical, being and, furthermore, all minds with sufficient comprehension will be able to thus realize an understanding of the exact same geometric form. Such that this understanding is objective. Not so with abstractions proper: ten people will provide ten different examples of what the abstraction "bird" is epitomized by: from a finch, to maybe an eagle, and so forth. All can however only provide the exact same example of what a perfect circle is epitomized by. And from this universality of agreement in understanding among all sapience then gets derived things such as the number pi.

Is pi a realized, actual, number that occurs in the real world? I'd myself say of course: it is not unrealized, nor a mere potential, nor a fictitious construct. In which case, so too must the objectively perfect circle then also be a given that is realized all the time in the real world. For there can be no number pi in the absence of the circle's actuality.

In short, the answer to this quoted question would be "yes", albeit not physically within matter.

But its getting a bit late for me. And, again, I've got nothing to sell. So I'll leave it at that for the time being.

Unless I'm mistaken, I think contradiction

in (non-dialetheistic) logic = necessary falsity;

in modal logic = necessary impossibility; and

in modal metaphysics = necessary ontic-impossibility (e.g. sosein)*. — 180 Proof

Yes, I fully agree with that. I was only addressing the issue that contradictory claims are not necessarily equally fictional ... as per my example of "the Earth is flat" and "the Earth is roughly spherical" being contradictory claims that are however not both fictional.

Have I said that objectively perfect things do not occur? I actually don't think this, so if you can find me saying it, I withdraw it. — Tom Storm

I did say "implicit assertion". Which is corroborated by the following.

My actual point is what evidence do we have and can anyone provide an example in the real world of such a perfect thing? Not an abstraction, not an argument, not a theoretical description: but an actual perfect thing. — Tom Storm

Abstractions are abstracted from concrete givens, and as far as I know there are no concrete examples of perfect circles. If the latter is then true, then perfect circles cannot be abstractions by definition.

That touched upon, whatever they might be conceptualized as being by you, are you saying that (perfect) circles do not occur in the real world, but only in fictitious worlds?

This being a philosophy forum where debates and disagreements unfold, I just find your implicit assertion that objectively perfect givens do not occur, else that there is no evidence for them occurring, to be irrational, that's all. Would have liked to see the reasoning to it. But so be it,

Someone else may buy it. — Tom Storm

I'm not selling anything, you. So to you an apeirogon is not an imperfect circle. Hard to comprehend, but fine. What then is an imperfect circle to you?