We can maintain that mathematical objects are mind-independent, self-subsistent and in every sense real, and we can also explain how we are cognitively related to them: they are invariants inour experienceconsciousness
Mathemarical concepts for Husserl are no more ‘real’ than the spatial objects we interact with in the world. — Joshs
Physicists, probably more than anyone else in science, are obsessed with simplicity, unification and "naturalness," and not without reason, because this attitude has accompanied spectacular advances in physics over the past two centuries. But how philosophically justified is it? And how sustainable? I suppose that goes to the question of the proverbial "unreasonable effectiveness of mathematics." — SophistiCat
Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades.
The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: observation has been unable to confirm mindboggling theories, like supersymmetry or grand unification, invented by physicists based on aesthetic criteria. Worse, these "too good to not be true" theories are actually untestable and they have left the field in a cul-de-sac. To escape, physicists must rethink their methods. Only by embracing reality as it is can science discover the truth.
In his later Ideas for a Pure Phenomenology and Phenomenological Philosophy (1913), Husserl develops the method of eidetic variation. Eidetic variation consists of a series of mental acts that aim to grasp an invariant, ideal, non-sensory object that serves as a substrate to a range of experiences. The same object is given across this range of experience and we experience its self-samenesss. Husserl suggested that this method would serve to sharpen our conceptual grasp of ideal objects, and Tieszen argues that this method is in fact close to the actual procedure employed in modern geometry. In abstract sciences, Tieszen writes, "objectivity and invariance go hand in hand" (p. 89), and invariance is best understood as givenness. An ontology of abstract objects, then, should rest on the elements of Husserlian epistemology.
Husserl called his position "transcendental" phenomenology, and Tieszen makes sense of this by claiming that it can be seen as an extension of Kant's transcendental idealism. The act of cognition constitutes its content as objective. Once we recognize the distinctive givenness of essences in our experience, we can extend Kant's realism about empirical objects grounded in sensible intuition to a broader realism that encompasses objects grounded in categorial intuition, including mathematical objects.
The view is very much like what Kant has to say about empirical objects and empirical realism, except that now it is also applied to mathematical experience. On the object side of his analysis Husserl can still claim to be a kind of realist about mathematical objects, for mathematical objects are not our own ideas (p. 57f.).
This view, Tieszen points out, can preserve all the advantages of Platonism with none of its pitfalls. We can maintain that mathematical objects are mind-independent, self-subsistent and in every sense real, and we can also explain how we are cognitively related to them: they are invariants in our experience, given fulfillments of mathematical intentions. The evidence that justifies our mathematical knowledge is of the same kind as the evidence available for empirical knowledge claims: we are given these objects. And, since they are given, not subjectively constructed, fictionalism, conventionalism, and similar compromise views turn out to be unnecessarily permissive. The only twist we add to a Platonic realism is that ideal objects are transcendentally constituted.
We can evidently say, for example, that mathematical objects are mind-independent and unchanging, but now we always add that they are constituted in consciousness in this manner, or that they are constituted by consciousness as having this sense … . They are constituted in consciousness, nonarbitrarily, in such a way that it is unnecessary to their existence that there be expressions for them or that there ever be awareness of them. (p. 13).
I am of the view that inner as opposed to outer, objective aspects of 'reality' are important here in the tradition of human understanding. Science, similarly to religion may be embedded in mythic understanding. What do you think, especially in relation to the concept of myth? As far as I see it is a topic involving dialogue between ancient philosophy, as well as anthropological thinking and research. How may the development of ideas about 'gods' or one God be understood in the history of religion and philosophy? — Jack Cummins
In a nutshell, 'mathematical platonism' would suggest people have experienced these higher realities and found mathematics to be existing within them. — Tzeentch
During his Manichaean period Augustine’s attention had been focused on the external corporeal world. His thinking had consequently been bound by sensory experience: he could conceive only what he could form a sensory image of. Platonism, however, admonished him to abandon the corporeal world and turn inward, using the eye of his own rational soul. When he did so, he discovered an astonishing new realm. The incorporeality, immutability, and eternity that characterize purely intellectual thought are the clues that led Augustine, by stages, to the divine nature itself.
Augustine begins by establishing a hierarchy that sorts into general categories and ranks the natures that comprise the universe: existence, life, and understanding:
Therefore the nature that merely exists (and neither lives nor understands) ranks below the nature that not only exists but also lives (but does not understand) – the soul of the non-human animals is of this sort. This nature in turn ranks below the nature that at once exists, lives, and understands – for example, the rational mind of the human being. (lib. arb. 2.6.13)
His strategy will be to argue that there is a nature that ranks above the rational mind of the human being, a nature that he will identify as divine (lib. arb. 2.6.14, 2.15.39). In order to discover it, he ascends the hierarchy of natures, turning attention first from bodies (the first and lowest-ranking category in the hierarchy) to the soul (psuche, the nature constitutive of both the second and third categories), and then within his own soul from the sensory (found in both human beings and the non-human animals) to the rational: “a kind of head or eye of our soul ... which does not belong to the nature of non-human animals” (lib. arb. 2.6.13).11
Having ascended as far as reason – that which is highest in us – he focuses on reason’s distinctive perceptual capacities and the distinctive sorts of objects they put us in contact with, the objects of pure thought. By way of example, Evodius, Augustine’s interlocutor in the dialogue, first suggests that they consider “the structure and truth of number,” by which he means arithmetical facts and relationships of the sort expressed by such truths as “seven plus three equals ten” (lib. arb. 2.8.20–21). Augustine himself adds the example of the indivisible mathematical unit that is the foundation of all number. He later introduces into the discussion a collection of a priori evaluative and normative truths such as “wisdom should be diligently sought after,” “inferior things should be subjected to superior things,” and “what is eternal is better than what is temporal” (lib. arb. 2.10.28). He thinks of these truths as constitutive of wisdom itself and therefore normative for anyone who would possess it. Moreover, anyone who is able to contemplate them will recognize their truth. Examination of these various examples leads Augustine to three conclusions: intelligible objects of these sorts are independent of our minds, incorporeal, and higher than reason. Put briefly, the main lines of his reasoning are as follows (lib. arb. 2.8.20–12.34):
1. Intelligible objects must be independent of particular minds because they are common to all who think. In coming to grasp them, an individual mind does not alter them in any way, it cannot convert them into its exclusive possessions or transform them into parts of itself. Moreover, the mind discovers them rather than forming or constructing them, and its grasp of them can be more or less adequate. Augustine concludes from these observations that intelligible objects must exist independently of individual human minds.
2. Intelligible objects must be incorporeal because they are eternal and immutable. By contrast, all corporeal objects, which we perceive by means of the bodily senses, are contingent and mutable. Moreover, certain intelligible objects – for example, the indivisible mathematical unit – clearly cannot be found in the corporeal world (since all bodies are extended, and hence divisible). These intelligible objects cannot therefore be perceived by means of the senses; they must be incorporeal and perceptible by reason alone.
3. Intelligible objects must be higher than reason because they judge reason. Augustine means by this that these intelligible objects constitute a normative standard against which our minds are measured (lib. arb. 2.5.12 and 2.12.34). We refer to mathematical objects and truths to judge whether or not and to what extent our minds understand mathematics. We consult the rules of wisdom to judge whether or not and to what extent a person is wise. In virtue of their normative relation to reason, Augustine argues that these intelligible objects must be higher than it, as a judge is higher than what it judges. Moreover, the intrinsic nature of these objects shows them to be higher than reason. They are eternal and immutable; by contrast, the human mind is clearly mutable. Augustine holds that since it is evident to all who consider it that the immutable is superior to the mutable (it is among the rules of wisdom he identifies), it follows that these objects are higher than reason.
...By focusing on objects perceptible by the mind alone and by observing their nature, in particular their eternity and immutability, Augustine came to see that certain things that clearly exist, namely, the objects of the intelligible realm, cannot be corporeal. When he cries out in the midst of his vision of the divine nature, “Is truth nothing just because it is not diffused through space, either finite or infinite?” (FVP 13–14), he is acknowledging that it is the discovery of intelligible truth that first frees him to comprehend incorporeal reality. — Cambridge Companion to Augustine
Popper's "Third world" differs from Plato's world of forms in that it is entirely an artefact of language and culture and is thus constantly changing. This is in contrast to the changeless world of Plato's forms. — Janus
There really is privileged metaphysical structure; we're just not sure about the terms to use. — J
You seem to be suggesting that one of these logics is correct. — Michael
Your view seems to be a form of transcendental idealism, which is about how we understand reality fundamentally through mental ideas (and cognitive pre-structures) and thusly is a form of epistemic idealism---not ontological idealism. — Bob Ross
A human being is a part of the whole, called by us "Universe", a part limited in time and space. He experiences himself, his thoughts and feelings as something separated from the rest — a kind of optical delusion of his consciousness. The striving to free oneself from this delusion is the one issue of true religion. Not to nourish the delusion but to try to overcome it is the way to reach the attainable measure of peace of mind. — Albert Einstein, Letter of Condolence
There is no scientific evidence for dualism - verifiable separability of mental stuff and physical stuff. It is also not metaphysically parsimonious and borderline incoherent. So which is it? Mental stuff or physical stuff? — Apustimelogist
To say the world is made of experience in the same way as houses are made of bricks also doesn't avoid the hard combination problem... — Apustimelogist
The second objection (to idealism) is against the notion that the mind, or ‘mind-stuff’, is literally a type of constituent out of which things are made, in the same way that statues are constituted by marble, or yachts of wood. The form of idealism I am advocating doesn’t posit that there is any ‘mind-stuff’ existing as a constituent in that sense. — Wayfarer
You can believe that numbers and other abstracta really and truly exist without being a mathematical platonist. You merely assert that they exist because we have created them, and they will cease to exist if we also cease. — J
Do mathematical objects exist in some exotic realm, awaiting discovery? — jgill
And it has changed character from a descriptive and predictive tool to an enormous game, unbounded in some aspects, with recently formulated foundational rules. — jgill
I've always thought of these little critters as part of the metaphysics of mathematics — jgill
rather I am expressing skepticism towards those who would claim mathematics is 'objectively real', and also pointing out the contradiction in the term 'mathematical platonism'.
Does that make sense? — Tzeentch
If Platonism seems to ‘undercut’ empiricism, it does so only by occupying the opposing pole of the binary implicating both physicalism and platonism within the same tired dualistic subject-object metaphysics. — Joshs
see both numbers and physical things as pragmatic constructions, neither strictly ideal nor empirical, subjective nor objective, inner nor outer, but real nonetheless? — Joshs
Some scholars feel very strongly that mathematical truths are “out there,” waiting to be discovered—a position known as Platonism. It takes its name from the ancient Greek thinker Plato, who imagined that mathematical truths inhabit a world of their own—not a physical world, but rather a non-physical realm of unchanging perfection; a realm that exists outside of space and time. Roger Penrose, the renowned British mathematical physicist, is a staunch Platonist. In The Emperor’s New Mind, he wrote that there appears “to be some profound reality about these mathematical concepts, going quite beyond the mental deliberations of any particular mathematician. It is as though human thought is, instead, being guided towards some external truth—a truth which has a reality of its own...”
Many mathematicians seem to support this view. The things they’ve discovered over the centuries—that there is no highest prime number; that the square root of two is an irrational number; that the number pi, when expressed as a decimal, goes on forever—seem to be eternal truths, independent of the minds that found them. If we were to one day encounter intelligent aliens from another galaxy, they would not share our language or culture, but, the Platonist would argue, they might very well have made these same mathematical discoveries.
“I believe that the only way to make sense of mathematics is to believe that there are objective mathematical facts, and that they are discovered by mathematicians,” says James Robert Brown, a philosopher of science recently retired from the University of Toronto. “Working mathematicians overwhelmingly are Platonists. They don't always call themselves Platonists, but if you ask them relevant questions, it’s always the Platonistic answer that they give you.”
Other scholars—especially those working in other branches of science—view Platonism with skepticism. Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something existing “outside of space and time” makes empiricists nervous: It sounds embarrassingly like the way religious believers talk about God, and God was banished from respectable scientific discourse a long time ago.
Platonism, as mathematician Brian Davies has put it, “has more in common with mystical religions than it does with modern science.” The fear is that if mathematicians give Plato an inch, he’ll take a mile. If the truth of mathematical statements can be confirmed just by thinking about them, then why not ethical problems, or even religious questions? Why bother with empiricism at all?
Massimo Pigliucci, a philosopher at the City University of New York, was initially attracted to Platonism—but has since come to see it as problematic. If something doesn’t have a physical existence, he asks, then what kind of existence could it possibly have? “If one ‘goes Platonic’ with math,” writes Pigliucci, empiricism “goes out the window.” (If the proof of the Pythagorean theorem exists outside of space and time, why not the “golden rule,” or even the divinity of Jesus Christ?) — What is Math?
Mathematical platonism has considerable philosophical significance. If the view is true, it will put great pressure on the physicalist idea that reality is exhausted by the physical. For platonism entails that reality extends far beyond the physical world and includes objects that aren’t part of the causal and spatiotemporal order studied by the physical sciences.[1] Mathematical platonism, if true, will also put great pressure on many naturalistic theories of knowledge. For there is little doubt that we possess mathematical knowledge. The truth of mathematical platonism would therefore establish that we have knowledge of abstract (and thus causally inefficacious) objects. This would be an important discovery, which many naturalistic theories of knowledge would struggle to accommodate. — SEP, Platonism in the Philosophy of Mathematics
Reducing truth to a binary seems to edge us towards primarily defining truth in terms of "propositions/sentences" and, eventually, formalism alone, and so deflation. This is as opposed to primarily defining truth in terms of knowledge/belief and speech/writing.
The key difference is that, in the latter, there is a knower, a believer, a speaker, or a writer, whereas propositions generally get transformed into isolated "abstract objects" (presumed to be "real" or not), that exist unconnected to any intellect. Such propositions are true or false (there is no gradation) simpliciter. Such a view seems to require some dubious assumptions. — Count Timothy von Icarus
The essential unity of the thinker with the thought, the knower with the world, can only be shown by rejecting, as Kimhi does, the idea that a proposition can be true or false in the absence of some context of assertion. — J
Sebastian Rödl — J
everything that makes you you... — praxis
The problem of base load power isn't just corporate propaganda. — ssu
However, the "hard question" remains : by what physical process does a brain construct a worldview? — Gnomon
In that case, is natural Matter their substitute for belief in a super-natural Ideal realm? — Gnomon
"Thus materialism is the attempt to explain what is immediately given us by what is given us indirectly." — Gnomon
In fact, what we regard as the physical world is “physical” to us precisely in the sense that it acts in opposition to our will and constrains our actions. The aspect of the universe that resists our push and demands muscular effort on our part is what we consider to be “physical”. On the other hand, since sensation and thought don’t require overcoming any physical resistance, we consider them to be outside of material reality. It is shown in the final chapter ('Mind, Life and Universe') that this is an illusory dichotomy, and any complete account of the universe must allow for the existence of a nonmaterial component which accounts for its unity and complexity. — Pinter, Charles. Mind and the Cosmic Order: How the Mind Creates the Features & Structure of All Things, and Why this Insight Transforms Physics (p. 6). Springer International Publishing. Kindle Edition.
I see the concept of the 'middle way' as a principle for careful thinking, but wonder how may be it seen as as a basis for ethics? How useful is the idea? — Jack Cummins
Of all systems of philosophy which start from the object, the most consistent, and that which may be carried furthest, is simple materialism. It regards matter, and with it time and space, as existing absolutely, and ignores the relation to the subject in which alone all this really exists. It then lays hold of the law of causality as a guiding principle or clue, regarding it as a self-existent order (or arrangement) of things, veritas aeterna, and so fails to take account of the understanding, in which and for which alone causality is. 1
It seeks the primary and most simple state of matter, and then tries to develop all the others from it; ascending from mere mechanism, to chemistry, to electricity, to the vegetative and then to the animal kingdom. And if we suppose this to have been done, the last link in the chain would be animal sensibility—that is, knowledge—which would consequently now appear as a mere modification or state of matter produced by causality. Now if we had followed materialism thus far with clear ideas, when we reached its highest point we would suddenly be seized with a fit of the inextinguishable laughter of the Olympians. As if waking from a dream, we would all at once become aware that its final result—knowledge, which it reached so laboriously, was presupposed as the indispensable condition of its very starting-point, mere matter; and when we imagined that we thought 'matter', we really thought only the subject that perceives matter; the eye that sees it, the hand that feels it, the understanding that knows it.
Thus the tremendous petitio principii (= circular reasoning) reveals itself unexpectedly; for suddenly the last link is seen to be the starting-point, the chain a circle, and the materialist is like Baron Münchausen who, when swimming in water on horseback, drew the horse into the air with his legs, and himself also by his cue. The fundamental absurdity of materialism is that it starts from the objective, and takes as the ultimate ground of explanation something objective, whether it be matter in the abstract, simply as it is thought, or after it has taken form, is empirically given—that is to say, is substance, the chemical element with its primary relations. Some such thing it takes, as existing absolutely and in itself, in order that it may evolve organic nature and finally the knowing subject from it, and explain them adequately by means of it; whereas in truth all that is objective is already determined as such in manifold ways by the knowing subject through its forms of knowing, and presupposes them; and consequently it entirely disappears if we think the subject away. 2
Thus materialism is the attempt to explain what is immediately given us by what is given us indirectly. All that is objective, extended, active—that is to say, all that is material—is regarded by materialism as affording so solid a basis for its explanation, that a reduction of everything to this can leave nothing to be desired (especially if in ultimate analysis this reduction should resolve itself into action and reaction). But ...all this is given indirectly and in the highest degree determined, and is therefore merely a relatively present object, for it has passed through the machinery and manufactory of the brain, and has thus come under the forms of space, time and causality, by means of which it is first presented to us as extended in space and active in time3. From such an indirectly given object, materialism seeks to explain what is immediately given, the idea (in which alone the object that materialism starts with exists), and finally even the will from which all those fundamental forces, that manifest themselves, under the guidance of causes, and therefore according to law, are in truth to be explained.
To the assertion that thought is a modification of matter we may always, with equal right, oppose the contrary assertion that all matter is merely the modification of the knowing subject, as its idea. Yet the aim and ideal of all natural science is at bottom a consistent materialism. The recognition here of the obvious impossibility of such a system establishes another truth which will appear in the course of our exposition, the truth that all science properly so called, by which I understand systematic knowledge under the guidance of the principle of sufficient reason, can never reach its final goal, nor give a complete and adequate explanation: for it is not concerned with the inmost nature of the world, it cannot get beyond the idea; indeed, it really teaches nothing more than the relation of one idea to another. — Arthur Schopenhauer, World as Will and Representation
I agree that consciousness is a natural process — Joshs
Kant correctly recognized that taking a strictly materialist stance depends on an idealism, since the very notion of a mind-independent object covertly smuggles in all the subjective apparatus needed to have an object appear before a subject. So realism and idealism are not opposites but versions of the same subject -based thinking. — Joshs
if you want to get beyond the realism-idealism, fact-value split, you have to be able to see value WITHIN matter, not separate from it and alongside it. — Joshs
"So in our understanding of the Universe we should recognize the existence of something other than matter. We can call that something spirit, but if we do we should remember that in Buddhism, the word "spirit" is a figurative expression for value or meaning. We do not say that spirit exists in reality; we use the concept only figuratively". — Three Philosophies, One Reality — Gnomon
