— fdrake

• Subjectivities are more than roles, they become integrated capacities of a person which are exercised in how they live their life.
• Subjectivities are more than the application of an on-off property to a subject, like 'disabled' or 'traumatised'; they can inform and transform people in different degrees of similar ways; like episodic flashbacks vs more mundane intrusive memories; or in much different ways; like generalised anxiety vs dissociative disorder as comorbidities of PTSD.
• Subjectivities are to a large degree impersonal; they are composite patterns of behaviours, feelings and events which constrain individuals along a mode of variation. A person can be said to 'inhabit' the unfolding of PTSD just the same as they can inhabit walking; being a sufferer of PTSD or a walker respectively.

This is a great summary of the idea and helps alot to explain why thinking of subjectivities in terms of 'experiences' or consciousness is so wrong-headed - in fact perhaps the mistake to be avoided at all costs. Putting the idea in terms of a 'pattern', where what composes the pattern is behaviours, feelings, events, and capacities rightly strikes at the impersonality of subjectivity, in deep contrast to the first-person orientation of the vocabulary of experience. In fact one aspect of the non-overlap between experience and subjectivity is that our subjectivities are rarely grasped as such: we don't often (or at least, some of us are lucky enough not to have to) make our subjectivities the object explicit cognizance: in walking the street, I rarely grasp myself as a walker of the streets.

Things might be different for the wheelchair-bound however, whose kind of subjectivity does not so neatly coincide with the environment she negotiates. Her subjectivity becomes a problem of explicit reference: "I am not the kind of being who can walk up those stairs - how then do I get to where I need to go?"; The walker, on the other hand, might encounter a set of closed stairs, and the question put to him is: "what other stairs can I use?": his being, the kind of subjectivity that he is at that moment, is not put into question (this another way in which the question of subjectivities is an ethical and political one).

The PTSD example is another example where ones subjectivity becomes a problem for one: where the normal mode of operation (of living, as you say) intrudes upon the kind-of-being one is, historically and biologically informed. This may seem less political, but not necessarily; consider the questions: what kind of support is there for a PSTD sufferer in our society? What kind of educational and clinical resources are accessable for the sufferer so that he might know to better deal with his condition? Are there questions about the distribution of those resources along economic lines? (in which case class now becomes pertinant?). Is there a societal awareness of PSTD and efforts to destigmatize it? These very questions are inaccessable when approached from the angle of 'consciousness' and 'experience'; not so, I think, with suubjectivities.

There's simply no possible world where Wayfarer's statement was made in good faith, or without wilful ignorance: the rudimentary confusion between the diametric opposites of a conclusion and a premise, one that ignores the very first sentence of the paper; the idea that Rovelli is trying to 'smuggle in' the notion of the mind-independence of math when the literal point of the paper is to argue against it; the baloney claim that the paper is making a claim for 'what is real' when it explicitly disavows precisely that vocabulary; referring to a doubly-cited claim as 'smuggling'. And this in two sentences of a multi-paragraph post.

This to say nothing of the usual modus operandi of citing blurbs (that is, second hand, twice-removed, assertions that themselves contain no argument) that have zip all to do with the topic at hand - Einstein and Bohr?? - all the while spending the bulk of the post talking about an entirely different topic altogether - 'scientific' claims about 'objects' - and referencing nothing, not a jot, of argument from the paper under discussion. And then to conclude, after this tangle of complete irrelevancy that "So, I'm not convinced by Rovelli's argument" - its a morass of obfuscatory sophistry, and simply the latest in a long line of it. By all means comment on it; it will dilute the muck.

So, I'm not convinced by Rovelli's argument; in any case, his conclusion that mathematical Platonism says that mathematics is 'fully independent' is not at all the case. Here, you're seeing the assumption that 'what is real' must, by definition, be mind-independent being smuggled into the argument. — Wayfarer

Either you haven't read the paper you actually qualify as a clinical imbecile. Rovelli's take on MP is not a conclusion he reaches - it is literally the first line of the paper where it is given as a premise against which the argument unfolds. A premise, moreover, supplied with two citations to Penrose and Connes. If emblazoning the first line of your paper with an explicit definition together with citations counts as 'smuggling' its no wonder your entire post is an exercise in obfuscation, invoking irrelevant debates about QM along with blurbs of books you show no evidence of even having read. Muddy the waters elsewhere you intellectual cretin.

Well then he's not talking about the trivial world, which is the world where everything is true. — MindForged

Well yes, but thats not was ever under consideration and is, if I may, an artifact of you not yet having read the paper.

But then M isn't a possible world, it's an impossible world. Under most analyses, impossible worlds have no ontology (because then you're accepting the existence of a contradictory object). — MindForged

No, Rovelli's 'M' explicitly excludes contradiction: "Then the platonic world M is the ensemble of all theorems that follow from all (non contradictory) choices of axioms": It contains everything that is true under any choice of non-contradictory axioms (so yes, read the paper!).

All that's needed for math platonism is for the objects referred to and quantified over in maths to be real. — MindForged

Again, this isn't what Rovelli's paper is about - nor do I think it ought to be about. The question is explicitly about the independence of math from our intellectual activity. Rovelli - rightly, imo - does not say anything about what is or is not 'real', partly, I suspect, because the question of 'the 'real' causes more muddles than it solves. For my part, the metaphysical prejudice that equates the real with the Platonic is, I think horribly misguided, and simply bad philosophy through and through. I'm perfectly happy to accept the reality of math, with the caveat that what counts as 'real' needs to be rethought wholesale.

But irrespective of which one the universe does does have, the theorems about those systems are true about those systems — MindForged

But this is just tautological: theorems are by definition true (as distinct from hypotheses). You can't milk necessity out of analyticity. Or at least, you can't milk any non-trivial necessity out of it. The question of modality turns on something like: could math be otherwise? And again, the answer is a qualified yes - given what the world is, and how we utilize math for certain purposes, no, the math looks exactly as it 'should'. But without those constraints, in principle, math could well be - again, in principle - a whole bunch of junk: pure meaningless syntax unconstrained by the necessity provided by the world in which we live (which is to say: inseparable and thus not independent from it: this is the sense of contingency Rovelli is employing).

I think this is already starting on shaky grounds. What does "exist" mean here? Mathematically it would mean something like "provable" but if we're dealing with a possible world in which everything is provable, we're dealing with the Trivial World. A world without any coherent structure at all. — MindForged

I believe that's exactly the point: M would be entirely trivial. This is the dilemma that the paper poses for Mathematical Platonism: either M is trivial and has no structure whatsoever (and thus largely says nothing at all about our world), or, if M is not trivial in this way, then it cannot be independent from our intellectual activity. In either case Platonism is undermined because if the former, then it has no explanatory power, and if the latter, then it simply isn't Platonism.

I'm not really sure what his argument is supposed to be. Math platonism doesn't say math is universal in the sense he is assuming. I'd say I'm a mathematical pluralist, so I don't find myself committed to any particular math system as a matter of principle, but this doesn't preclude being a math platonist — MindForged

The paper's index of Platonism has to do with the independence of mathematics from human intellectual activity; part of this, in turn, has to do with the modal status of our math: contingent or necessary, and to what degree? Rovelli's answer is a kind of qualified contingency: our math is contingent ("Which tiny piece of M turns out to be interesting for us, which parts turns out to be \mathematics" is far from obvious and universal. It is largely contingent"), but this contingency in turn is premised upon the kind of beings we are, and the kind of things we encounter in the world, along with what we do with them - which lends our mathematics a kind of empirical necessity (Rovelli doesn't use that term, but I think it's appropriate in this context).

For this reason, Platonism is in a sense reductivist, though not in the way that a 'bottom-up' philosophy is. It is conceptually reductivist, not materially reductivist. The simplicity of the first principle is contrasted with the simplicity of elements out of which things are composed according to a 'bottom-up' approach. Whether or to what extent the unqualifiedly simple can also be intelligible or in some sense transcends intelligibility is a deep question within Platonism. — Wayfarer

I don't understand how you can read this passage - which I agree with almost entirely - and not think to yourself: "gee this Platonism business is just as shittily reductive as the materialist reductionism that I'm always moaning about". But of course you don't care about reductionism - you just want reductionism in the 'right way'.

I'm okay with prejudicial. Would even encourage more of it.

Et voila.

Well of course you would; you're demonstrably incapable of taking things in terms other than that which you've projected onto them from without.

I don't argue against irrelevancies that can't even get basic terms right.

Terminology is not terribly important — Pneumenon

"I want to have my own debate".

Have fun.

Right, so you want to have a debate over terms not employed by the paper... about the paper? Come back when you've read it and are prepared to actually do so.

All you dribbled off was some irrelevancies about 'abstractions not being real'; this being a phrase not even found in the paper. Come back when you've read it.

I'm not the one playing with labels.

When your picture of reality has so little to do with reality then so much the worse for that picture. "But you're not dealing with reality!"; You can keep your two-bit reality.

One might avoid both mistakes though recognizing that the phenomenon of convergence is a dynamical product of the enactment of the social practice of arguing for or against doing and/or believing things. The convergent phenomena are being constituted from within the enactment of dialectical reason by social beings rather than from without their historically situated lots of shared practices. — Pierre-Normand

Totally agree. Insofar as we are (mostly) beings that count, and employ counting to engage in certain behaviors, it's simply unsurprising that our counting systems will tend to converge around certain invariants. And as Rovelli remarks, the fact that we are beings that count has itself a strong element of sheer contingency: "The development of the ability to count may be connected to the fact that life evolved on Earth in a peculiar form characterized by the existence of “individuals”. There is no reason an intelligence capable to do math should take this form. In fact, the reason counting appears so natural to us may be that we are a species formed by interacting individuals, each realizing a notion of identity, or unit. What is clearly made by units is a group of interacting primates, not the world".

I don't think it's a matter of coincidence as well that in the sphere of evolution, convergence is sometimes also used as an argument for theistic ends - the usual "wow, look at all these eyes across so many different species, must be God at work!"; well, no, eyes are the product of the dynamics involved with the properties of light and animals that move, many of whom share similar environments (with animals in the depths of the ocean evolving no eyes - what a surprise!). There's a very real parallel with those who think that convergent aspects of math similarly reflect some grand transcendent design decoupled from the material universe, rather than behavior and environment: it's nothing less than intelligent design shunted into the field of mathematics. And it's all just as bogus. Math is the last, shrinking, refuge of a God deservedly driven out of everywhere else.

Also totally agree with you about the critique of 'naive empiricism': as you said it's just the mirror image of Platonic Idealism, both of which are totally utterly blind to the evolutionary and historical dynamics of shared practices - in the case of math - and shared ecological and developmental dynamics - in the case of evolution.

Doesn't the fact that basic mathematical truths are the same for anyone who can count demonstrate that they're independent of particular thinkers? — Wayfarer

It's like saying: wow, look at all these various languages that have nouns! Guess Nouns must be Platonic Entities. It's reasoning made for and by idiots.

I am understanding these 'subjectivities' as human experiences, or interactions with the world we live in — Pattern-chaser

I'm loathe to talk about subjectivities in terms of 'experiences', which reeks of a mentalistic vocabulary that I'd prefer to be expunged if at all possible. I'd say that subjectivities inform experiences, but are in no way reducible to them.

In any case, the sense in which Platonism says that numbers (etc) are independent of particular minds, is simply based on the observation that they are the same for anyone capable of counting. — Wayfarer

And? The unarticulated premise here is that this mutual recognition entails 'independence'. But this is clearly nonsense. That people recognize words - and especially non-referential words like 'and' and 'is' - does not entail any ostentatious, overblown metaphysics of Platonic Is's and And's- it simply entails that we've learnt how to use a language, like the slightly-less-than-dim animals that we are.

As for neo-Thomism being the last refuge of Greek philosophy - all the better that it's drawing its last, dying breaths. The sooner we forget about hot mess that is Greek philosophy and it's intellectual spawn, the better.

Yeah, that was the passage I had in mind when Janus mentioned it. That, and, loosely connected, Voltaire's critique of Leibniz's best-of-all-possible-worlds.

The problem for Platonists is that they have failed to, and apparently cannot, explain in what sense the purported Platonic objects exist, or are real, in some way other than the familiar concrete (human mind independent) existence or reality of sense objects (or at least of whatever gives rise to them), and the familiar ideal (human mind dependent) existence or reality of the contents of thought, emotion and perceptual experience, — Janus

Yep. All you end up getting are these miserable negative non-specifications that are more than happy to specify what Platonic entities are not, all the while dodging the question by saying that 'oohh its so hard to explain'. It's a cheap rhetorical go-to that feeds right into the elitist, exclusionary, and cultish tendencies that span all of Plato's thought. No wonder that it ends up, in its later, Christian incarnations as negative theology and cultic mysticism: making a virtue out of intellectual failure (which also helps explains Neitzsche's diagnosis of nihilism which runs an intellectual line from Plato right through to Christianity: "man would rather will nothingness than not will.").

Yes these kinds of objections to Platonism occurred quite early on in the form of questions such as "But is there a perfect form of the turd, or the pile of vomit?". — Janus

This is a really nice historical point! Totally didn't think of that.

Although I hadn't found the time to comment, I had very much enjoyed the OP. — Pierre-Normand

Thanks! It's really very introductory, and in fact so-called 'critical theory' and 'cultural theory' is full of this stuff: 'what kind of subjectivity does such and such a culture produce?', or 'what kind of subjectivity does such and such a technology foster?', together with questions like 'what limits and opportunities do these productions (of subjectivity) impose or enable?'. It's an approach that connects very deep questions of philosophy right to contemporary (or even historical ones), in a way that you get a feel for how philosophy can be pressing and not simply some detached reflection on eternal questions. Foucualt is probably the name that stands at the start of this approach, and I think it's very exciting that you can find resonances in authors like Varela and Bitbol.

Right, but I'm asking if there is a human junkyard of abandoned math, whether constructed or discovered. Because the argument turns on most of math being a junkyard. I'm asking whether this is a hypothetical, or actually historical. — Marchesk

I think this is a great question, and I think it's important to show that, if most of what could-be-math is junk, then we've come across that junk before. One example that I think fits the bill is John Wallis' proof that all negative numbers are - or rather can be construed as - greater than infinity (the reasoning is simple, and I summarized it in a previous post). The upshot of Wallis' proof is that the number line (which Wallis invented), which normally looks like this:

-∞ < ... < -1 < 0 < 1 < ... ∞

can look like this:

0 < 1 < 2 < ... < ∞ < ... < -2 < -1

The thing about this is that there's nothing particularly 'wrong' with this way of ordering the integers (here's a paper that fleshes it out in modern terms). The reason math doesn't opt for Wallis' construal of the number line - and his conception of infinity - is because Cantors' constural of it (now the canonial treatment of infinity) is much more productive. Wallis' number line is 'junk math'.

In a physicsforum post that discusses the paper, a commentator makes a point that's almost identical to Rovelli's with respect to Dirac that I quoted earlier: "when Dirac wrote in his book: 'principles of quantum mechanics' that the derivative of Log(x) should contain a term proportional to a so-called 'delta function' that he had just invented out of thin air a few pages back, was complete nonsense too."
(source); Compare Rovelli: "Dirac, in his book, is basically inventing linear algebra in the highly non-rigorous manner of a physicist. After having constructed it and tested its power to describe our world, linear algebra appears natural to us. But it didn't appear so for generations of previous mathematicians".

The reason it's not very easy to come up with examples of junk-math is precisely because it's... junk math. No one cares for it, and no ones cares to pursue it because its largely useless.

That said, another, perhaps less pertinent example might be geometrical definitions of infinity (i.e. definitions that rely on intuitions about physical space), which in turn relied on the fuzzy concept of the infinitesimal. Until the invention of non-standard analysis in the 60s (which provided a rigorous way of understanding the infinitesimals) mathematicians made a huge effort to understand infinity on a strictly arithmetic basis (i.e. without reference to physical space), because the logical foundations of 'geometrical infinity' were not considered to be secure. In that time before those foundations were secured, one could say that the concept of infinity teetered on the edge of 'junk math' - being 'saved', ultimately, because it's so damn useful.

https://arstechnica.com/science/2018/10/bogus-homeopathy-data-published-in-top-journal-sparks-outcry-facepalms/

"Editors at a respected scientific journal are reconsidering their decision to publish a study, which claims that a homeopathic dilution of poison oak can reduce pain in rats, after online critics pointed out that the study is rife with bogus, sloppy, and low-quality data. The study—titled “Ultra-diluted Toxicodendron pubescens attenuates pro-inflammatory cytokines and ROS-mediated neuropathic pain in rats”—was published September 10 in Scientific Reports, an open-access journal run by the Nature Publishing Group".

Better shut down science before its too late.

Lots of irrealists about math make this argument. "Well, it's not useful, so these abstractions aren't real." Of course, the reality of an abstraction would only depend on its utility to us if the abstraction were not independently real to begin with. — Pneumenon

But no one but you is talking about 'real'. There's something very insidious about the idea that unless something is eternal and timeless it can't be real. Part of the necessity of re-evaluating Platonism is to block its usurpation of what counts as real: denying that math exists apart from humans is equally to insist that reality is far more interesting than the bland, white-padded wall picture of it painted by Platonists.

So his argument is that the Platonic world of math doesn't exist because it is... uninteresting? — litewave

Uninteresting in the sense that it does not even count as mathematics; not 'uninteresting, but still mathematics'. Rovelli's other example, of linear algebra, makes this clearer:

"When Heisenberg wrote his famous paper he did not know linear algebra. He had no idea of what a matrix is, and had never previously learned the algorithm for multiplying matrices. He made it up in his effort to understand a puzzling aspect of the physical world. This is pretty evident from his paper. Dirac, in his book, is basically inventing linear algebra in the highly non-rigorous manner of a physicist. After having constructed it and tested its power to describe our world, linear algebra appears natural to us. But it didn't appear so for generations of previous mathematicians. Which tiny piece of M turns out to be interesting for us, which parts turns out to be "mathematics" is far from obvious and universal. It is largely contingent."

The fact that linear algebra even is considered mathematics is because of it's interest to us. The question is ask is about 'paths not taken' (or even, as the history of math is littered with, paths-once-taken-but-now-largely-abdondoned, like geometrical definitions of infinity, as distinct from algebraic definitions of infinity): paths that 'populate' the world of M, and which have no power at all to describe anything about our world, and thus are dismissed as not-math. As fdrake rightly points out, the counter-argument to the supposed 'unreasonable effectiveness of math' is to point out that the vast majority - in fact almost everything that could have possibly been math (all the useless junk in M), sans the tiny sliver of what we currently consider to be math - of what might be math is completely useless and is totally and utterly 'ineffective'. It's as if, having had a suit tailored and refined over more than two millennia, one is surprised to find that it fits so damn well, and then to declare: this suit must be eternal and Real! It's intelligent design masquerading as math.

Very cool. I'll definitely check out his stuff.

Let me add that, here on Earth, we have the Pirahas of the Amazon rainforest who don't have any use for natural numbers, not even the number 1, nor of the existential or universal quantifiers (which Hume, I think, argued were required for grounding the practice of counting). — Pierre-Normand

Just quickly, on this - Do you know if this is something that is in Daniel Everett's discussion of the Piraha language? I ask because I think there's a deep and little explored connection between grammar and math and I'm looking everywhere for resources on this, even though I've yet to read Everett's book.

Mm, I'm of a know-thy-enemy type as well. You fight cancer by studying it rigorously and prodding it incessantly. The Sophist remains one of my favorite philosophical works.

So, Sellars's pragmatism is inimical to Plato, in that sense. But it still retains, from Plato (and through Kant), the idea that intellectual reflection can reveal to the intellect its own a priori forms — Pierre-Normand

Surely, if one squints hard enough one can see Plato in anything - which is not necessarily a bad thing (Deleuze: "The task of modern philosophy has been defined: to overturn Platonism. That this overturning should conserve many Platonic characteristics is not only inevitable but desirable".) And the Plato I have in mind is more the Plato who valorizes eternity, who rejects becoming, and poses infantile questions.

There's a famous essay by Arendt ("Tradition and the Modern Age"), where she characterizes our age as one that has effected a series of 'turning-operations' or 'inversions' upon tradition, marked by the names of Kiekregaard, Nietzsche, and Marx:

"Against the alleged abstractions of philosophy and its concept of man as an animal rationale, Kierkegaard wants to assert concrete and suffering men; Marx confirms that man's humanity consists of his productive and active force, which in its most elementary aspect he calls labor power; and Nietzsche insists on life's productivity, on man's will and will-to-power. In complete independence of one another none of them ever knew of the others' existence they arrive at the conclusion that this enterprise in terms of the tradition can be achieved only through a mental operation best described in the images and similes of leaps, inversions, and turning concepts upside down".

One of her conclusions is that these turning-operations can never be sucessful, because they take place on the same terms as those they aim to invert; so of Marx, she writes: "Turning the tradition upside down within its own framework, he did not actually get rid of Plato's ideas, though he did record the darkening of the clear sky where those ideas, as well as many other presences, had once become visible to the eyes of men". Arendt's point, among others, was that what needs to be inverted are not simply the philosophical 'positions' as it were, but the very terms in which those positions are posed: the whole framework. Otherwise you remain stuck with those same terms, even as you reject them (Heidegger will thus talk of a 'twisting-free' of Platonism, and Blanchot of a 'step not beyond' (Le pas au-delà) metaphysics, each of which tries to do more than simply 'do the opposite' of Plato or metpahysics).

So the sense in which Wittgenstein 'inverted' Plato needs to be carefully understood. I think that Wittgenstein did more that just a simple inversion of Plato (in Arendt's sense): he rejected more than just Plato's answers (as if simply inverting the priority of matter and idea): he rejected Plato's very questions. Plato's inane obsessions over 'what is Beauty?' 'What is Justice?' and so on are all renounced as awful ways of even approaching the questions. The blog post I linked to doesn't quite make this point, but I think it's important to insist upon. But yeah, the history of philosophy is full of these kinds of inversions - but it's important to pay close attention to how they are enacted.

So your response might be that the full explanation is both our phenomenal experience and the corresponding scientific explanations. Both of which make up the real. — Marchesk

No. Explanation isn't a lego-house where you stack bits on other bits. Things are more complex than this. Without going into it, the point is simply that science does not play a subsumptive role with respect to explanation. At their limit, the 'laws' of science establish nothing more than limits in certain domains; everything else is fair game. Anyway, this is far beyond the OP.

But then what is science doing when it uses mathematical language to form it's explanations of the world? — Marchesk

Depends on how you understand the range of 'explanation'. If you think science exhausts the claim to explanation, then this strikes me as a reductive reading, unwarranted imposed from without, of what the sciences do.

It is literally what you quoted and said 'this is what science does'. So you don't even know what you're quoting, that's not my problem.

Ordinary matter is made up of atoms to small for us to see, mathematical equations are heavily used to explain physical and chemical interactions, there are aspects of QM which cannot be visualized or explained in ordinary language without invoking metaphysical interpretations, GR has counterintuitive implications for space and time, and so on.

But more than anything, our sensory modalities are left off as perceiver dependent properties. The scientific image is devoid of smell, sound, color, etc. — Marchesk

This is all irrelevant. The question is about subsumption under abstraction. This is just fluff.

How do they? You made the claim.

Only problem with this is that the hard sciences do exactly that. — Marchesk

No, they do not.

In lieu of an effort on my part, this blog post gets the general gist of it right, I think:

"Wittgenstein inverts the antiquated western metaphysical tradition which places the essential before the actual: the abstract is an abstract from the present material world. Thus the task of attempting to reach the real via a process of intellectual abstraction, or via an examination of linguistic forms, is doomed before it starts. The real is present before us - in analysing it and refining it into its (apparently) general essence we are not approaching the truth of the matter, the "real" which is concealed by the corruptible form of the actual, we are in fact becoming increasingly lost in the sterile imagination.

... Plato's attempt to essentialise the world and perceive the 'real' behind the phenomena is, to Wittgenstein, fundamentally misguided. It is the phenomenal which is the real and if we desire to understand it we cannot subsume it under some abstract system. The abstract can only be an etiolated version of the real; it is the real, once we have nullified the differences, the vibrancy, the temporality of actual existence. What we consider essential in things is in fact a statement of human value, and should not be mistaken for a quality in things themselves. The attempt to do so confuses and denigrates both the nature of scientific enquiry and the role of human value in thought."

http://ayinsrazor.blogspot.com/2009/07/wittgenstein-on-plato.html

Platonism is philosophical cancer.

I was just thinking earlier that I can think of few philosophers who were quite as diametrically opposed to Plato than Wittgenstein. And if one thinks of the nominalistic proclivities of Quine, Davidson, Sellars, and their disciples, it's hard to argue that analytic philosophy as a whole is Platonic in its overall orientation (which is not to say there aren't plenty of Platonically oriented analytics, but only that there's plenty of variation within the field).