[PredatorOC]

As far as I know, a right triangle cannot exist in the material world. Even if you had three points and a perfectly 90° angle between two of those, a coherent line connecting the points is not possible as an atom is mainly composed of empty space. Thus an observer of only the material world cannot observe a right triangle. Yet we can abstract a right triangle and we can use that abstraction to explain and modify the material world. So does a right triangle exist? And if the right triangle does not exist, why is it applicable to the existing world?

[Vera Politica]

You can admit of 'existing' abstract objects by allowing quantification over them. Following Quine, (and early analytical philosophy) existence is not a property of any object but only the value of quantification. Let us write the following:

Fx: x is a right triangle

If we write (∃x)Fx we are saying there is at least one 'x' that has the property F (of being a right triangle in this case). If we allow quantification over 'x' with the property F, then we are committed to such an ontology (i.e. we admit to right triangles as abstract objects).

The idea here that is important is the Quine-Putnam indispensability argument. If abstract objects are required, in a scientific language, then we are committed to their abstract existence. Using this argument we could say that numbers are required in scientific language and therefore we are committed to their existence. (A philosopher named Hartry Field has bypassed this argument in his book Science without Numbers where he gave a nominalist account of Newtonian physics- i.e. he presented Newton's axiomatic system without the use of numbers, by only quantifying over space-time points and using advanced formal logic).

However, barring that numbers are used substantivaly (i.e. "The number of Jupiter's moons is 4" in mathematics and physics, we can actually give an adjectival definition of numbers that fixes their meaning in a context of a statement and doesn't commit us to an ontology including numbers. We would define the numbers adjectivally (i.e. "Jupiter has 4 moons"). To do this we define numerically definite quantifiers:

~ (∃[0]x)Fx (and so we have defined zero)
(∃[1]x)(Fx & (∀y)(Fy ⊃ x = y)) (and so we have defined one)

etc.

This definition has all sorts of problems.

[Potemkin]

So that's what philosophers do with their time, is it? I'd always wondered.

[Vera Politica]

So that's what philosophers do with their time, is it? I'd always wondered

Don't be so hasty to dismiss, Potemkin. These ontological arguments and disagreements have serious implications for the way we do Mathematics and Logic.
In any case what philosophers do depends on what they specialize in. Philosophy has become so technical that the field is now incredibly specialized.

[Potemkin]

Don't be so hasty to dismiss, Potemkin. These ontological arguments and disagreements have serious implications for the way we do Mathematics and Logic.
In any case what philosophers do depends on what they specialize in. Philosophy has become so technical that the field is now incredibly specialized.

I completely agree with you, Vera. I was just being somewhat flippant, as is my wont. It's my latent prejudice against analytic philosophy coming out.

[Vera Politica]

It's my latent prejudice against analytic philosophy coming out

Surprising considering you're from the UK, unsurprising considering you're a Marxist. Sadly (or not), I do characterize myself as 'analytic' rather than continental- although I do think the distinction shouldn't be as pronounced. I use this distinction only to say that I am quite interested in mathematical and scientific philosophy.

The distinction, I think, describes more the style of philosophy. Analytic philosophy tends to embrace scientific and mathematical techniques while continental philosophers tend to be hostile to them (and 'continental' undergraduates tend not to understand them). However, Analytic political philosophy is absolutely atrocious. What I dislike about the continental style is that it is too literary (this is besides the fact that it is painfully obscure - this is fine except in areas where it need not be).

What is it about analytic philosophy you dislike?

[Potemkin]

The distinction, I think, describes more the style of philosophy. Analytic philosophy tends to embrace scientific and mathematical techniques while continental philosophers tend to be hostile to them (and 'continental' undergraduates tend not to understand them). However, Analytic political philosophy is absolutely atrocious. What I dislike about the continental style is that it is too literary (this is besides the fact that it is painfully obscure - this is fine except in areas where it need not be).

I was trained as a physicist (MPhil in nuclear physics), so I am completely unimpressed by analytic philosophers' claims to be more 'scientific' or more 'objective' than their synthetic counterparts. Once you throw out everything in philosophy which is not 'scientific' or 'objective', you're left with something which may (or may not) have some practical value as an adjunct to science (except that most practicing scientists completely ignore it), but it will have no other value.

What is it about analytic philosophy you dislike?

Its scientism, basically. That, and the fact that it tends to be practiced by snobbish upper-class Englishmen.

[Vera Politica]

I was trained as a physicist (MPhil in nuclear physics), so I am completely unimpressed by analytic philosophers' claims to be more 'scientific' or more 'objective' than their synthetic counterparts. Once you throw out everything in philosophy which is not 'scientific' or 'objective', you're left with something which may (or may not) have some practical value as an adjunct to science (except that most practicing scientists completely ignore it), but it will have no other value.

I am not sure that analytical philosophers do make this claim - and I am also unsure how a degree in physics makes you hostile to their claims. It is common to see analytic philosophers who were previously trained in mathematics or physics. A distinct claim, however, (which I think is warranted) made by analytic philosophers is that philosophy is no longer a discipline different from the sciences but, rather, an extension of the sciences. Along with mathematics, it is an analytical method but deals with logic, propositions, etc. Historically, analytical philosopher simply believed they were clarifying scientific propositions and demarcating scientific from pseudo-scientific propositions. Philosophy, in this sense, was only a method of analysis that had no proper subject matter. I think there is some pull to this and most of the subject matter of philosophy has been, more or less, relegated to different scientific fields.

By 'mathematical' and 'scientific' philosophy is meant only the philosophy of mathematics and the philosophy of science (they are often used interchangeably). These fields tend to be treated better in analytic philosophy than they do in continental philosophy.

Moreover, to my knowledge,t he analytic/synthetic division has been largely discredited and I do not think that it would be appropriate to characterize continental philosophy as the 'synthetic counterpart' to analytic philosophy - although I know exactly what you mean.

Its scientism, basically. That, and the fact that it tends to be practiced by snobbish upper-class Englishmen.

True. The 'height' of analytic philosophy (by this I mean logical positivism) certainly warrants its 'scientist' label. Even so, there is much that can be salvaged from this period in terms of method (esp. techniques in formal logic) - and it is worth noting that not all analytic philosophers agreed on a particular philosophy of science.

As to the second point. I am neither upper-class nor English, so I hope you hold no grudges.

[Potemkin]

Philosophy, in this sense, was only a method of analysis that had no proper subject matter. I think there is some pull to this and most of the subject matter of philosophy has been, more or less, relegated to different scientific fields.

I think that's right. Philosophy has become emptied of content compared to its glory days, this content being hived off onto 'natural' philosophy, or modern science. To avoid the prospect of philosophy becoming completely irrelevant, the analytic philosophers seem to have attempted to take this process to its logical conclusion and reduced philosophy to an empty shell, a method of logical analysis and nothing else. From being the queen of the sciences, philosophy will become the handmaid of the sciences. This would be a rather pathetic fate.

By 'mathematical' and 'scientific' philosophy is meant only the philosophy of mathematics and the philosophy of science (they are often used interchangeably). These fields tend to be treated better in analytic philosophy than they do in continental philosophy.

Agreed. I am a great admirer of Schopenhauer's philosophical work, but when I read the chapters of The World as Will and Idea which deal with science and mathematics, I was hugely disappointed. He clearly hadn't a clue.

Moreover, to my knowledge,t he analytic/synthetic division has been largely discredited and I do not think that it would be appropriate to characterize continental philosophy as the 'synthetic counterpart' to analytic philosophy - although I know exactly what you mean.

Point taken.

True. The 'height' of analytic philosophy (by this I mean logical positivism) certainly warrants its 'scientist' label. Even so, there is much that can be salvaged from this period in terms of method (esp. techniques in formal logic) - and it is worth noting that not all analytic philosophers agreed on a particular philosophy of science.

And let's not forget the logical contradictions which 'Logical' Positivism tangled itself up in with its principle of verifiability.

As to the second point. I am neither upper-class nor English, so I hope you hold no grudges.

Just so long as you don't start smoking a pipe and wearing tweed jackets with leather patches on the elbows, we'll be alright.

[Vera Politica]

This would be a rather pathetic fate.

True - although pure logic would stand quite well on its own. That or some substantial paradigmatic shift tosses science into the dustbin of history.

[Agent Steel]

Just because something isn't a perfect right triangle, it is so close that the difference is negligible.

[Wellsy]

The part of reducing an object to the empty space between atoms relates well to the initial crisis of materialism upon the beginning of quantum mechanics.
But what one must keep in mind is the philosophical category of matter is defined in a way that doesn't leave it contingent on saying that the world is made up of specific kinds of matter otherwise one was persistently at risk of future discoveries.
http://www.autodidactproject.org/other/bazhenov.html

One can say that to try to discover the relation of matter and mind has always been central to philosophy; it was tacitly implied in the realization that the answer to the question "what is matter?" was different from the solution of the basic issue of philosophy, i.e., was it to be precisely the understanding of the true character of matter as such, apart from its relation to consciousness?

Until the end of the 19th century the metaphysical concept of proto‑matter had never entered into a too obvious conflict with the progress of science. Yet at the turn of the 19th‑20th century, there came about the "modern revolution in physics." It was as if proto‑matter once caught by physicists was quickly eluding their grasp. What had been hitherto called matter was vanishing, only to be replaced by what was then known as electricity, ether, etc. The phrase "Matter has disappeared" became fashionable among physicists. In the physical parlance of the day the phrase meant in fact that what featured such and such properties and had thus far been known as matter was no longer there. Instead, something new became known, with new unusual properties, and no longer answering the previous definition of matter (matter is that and only that which displays properties P1 . . . Pn). The newly‑emerged something possessed the properties Pn+1, etc., but no longer possessed some of the properties P1 . . . Pn previously ascribed to matter.

From the viewpoint of Dialectical Materialism what disappeared was not matter, but the limit indicating the extent of our knowledge until then. But in order to make this deduction, it was necessary to change the very concept of matter and delimit clearly the properly philosophical purport of the concept of matter and the concept natural science has about the latter's structure. The error was precisely a lack of delimitation underlying the statements of idealist philosophers about the disappearance of matter, though no longer in the sense physicists had meant it. In the parlance of idealist philosophy "the disappearance" of matter meant a disappearance of objective reality, a disappearance of objective content from our scientific theories, a collapse of philosophical Materialism, "dematerialization of matter," etc.

These assertions have been repeated with unparalleled zeal for more than half a century, thus showing demonstrably the importance and significance of developing a new, dialectico‑materialistic concept of matter. As is known, Lenin's definition, to become classical in Marxist philosophy, reads: "Matter is a philosophical category denoting the objective reality which is given to man by his sensations, and which is copied, photographed and reflected by our sensations, while existing independently of them." [4]

To which the fundamental aspects of ontology has long been the absolute distinction between mind and matter of which for materialists, mind is derived from man's social activity in the material reality. When primacy isn't given to our social relationship to the world, then the supposedly eternal and absolute assertions of idealism show themselves transient when we change our world and make new discoveries.
To which I emphasize activity because it is perhaps the only epistemological position which can be consistent whilst asserting the objective existence of the world.
http://critique-of-pure-interest.blogspot.com/2011/12/between-materialism-and-idealism-marx.html

The fact that this intermediate status of qualia is rarely observed, has everything to do with the traditional opposition between idealism and materialism – precisely the opposition Marx wants to overcome in the first Thesis on Feuerbach. Because traditional materialism stresses one-sidedly the passivity of man with respect to nature, it can understand qualia only as secondary, ie as mere effects in consciousness caused by external objects. And because idealism, in contrast, stresses one-sidedly the (mental) activity of the human subject, it cannot understand qualia as coming from external objects. The result is that materialism and idealism, precisely because of their opposing positions (passivity vs. activity), come to a surprisingly unanimous opinion about the ontological status of sensory qualities: they are merely subjective and not objective. Thus the traditional contrast in philosophy between materialism and idealism has led to a systematic disregard of the true in-between status of sensory qualities. Marx was in a sense the first to rehabilitate that true status of the sensory by taking up a position between materialism and idealism. That seems to be one of the main reasons why Marx in the first Thesis on Feuerbach focuses specifically on sensation, that is, on “reality, sensuousness” which in traditional materialism “is conceived only in the form of the object or of intuition, but not as sensuous human activity, practice, not subjectively”. Marx’s point is therefore not that man as part of nature is a sensuous being, rather his point is that reality as such is sensuous, i.e. praxis, the reciprocal determination of subject and object that takes place in sensation. For Marx, the sensuous is the medium (ie the middle, the “between”) in which subject and object – man and nature – meet and determine each other.

The nature of thought forms is peculiar but it is essentially derived from the natural world and something from which we then use to grasp the natural world (hence valid truth of rationalism in criticism of empiricism). Just so happens that it develops socially as the aggregate of man kind's relations. We use language/signs to describe reality, but the reality necessarily precedes our description of it. Though we have gotten so abstract for such a long time that many lose sight of the reality for the alienation of language and words, treating words functionally as if they were reality.

But as I would say thought exists, then of course abstract objects exists, but they exist only as internalized thought forms based on our inherited understanding of such things developed in actuality.
We didn't merely percieve triangles, we were/are able to create them. In the same way that our concepts of colour are interwoven with our ability to create them for ourselves, so that they're no longer merely in-themselves but for us.
https://www.ethicalpolitics.org/ablunden/works/evolution-language.htm

Tool-making and tool use is a particularly significant phase in the development of practical abstraction. The rendering of human powers into objective material objects continues to drive the development of language to this day, with new words flowing into the language from the latest products of technology and going on to be normalised in use remote from the technological context in which the words originated. For example, “interface” arose in the context of development of new electronic devices in the military industry, but nowadays commonly refers to interpersonal and institutional relations.

Hegel (18o4) said: “The word is the tool of Reason.” Tool-making and tool-use, in which a concept has a specific material shape, constitutes abstraction in behaviour, the necessary condition for abstraction in thinking. Today’s tool is tomorrow’s word. The most impressive proof of this is the history of colour words, which shows that no matter how prevalent a colour may be in a community’s environment, historically, a word for the colour enters the language only when a community had learnt how to manufacture the colour.

[late]

One of the current ideas in the philosophy of science is that we create models of reality. No one asks if a model is true, or eternal, they just want to know how well it works.

This is a deliberate attempt to avoid the language of traditional philosophy. Or, as Pragmatists like to say, to say philosophical things using non-philosophical language.