Once, I received a big protest from a female interlocutor because I a had used the word "he" . — Alkis Piskas

Once, a student came up to me after class and complained because I had used "she". As if just another example of women being blamed by men. I pointed out that I had been switching back and forth between 'he' and 'she' so as to be inclusive. If this had occurred more recently I might have used 'they'. I read somewhere that this was at one time accepted usage but fell out of favor.

One can make the argument that there is something like a space of all possible concepts. Like the rules of mathematical syntax. It is already defined which concepts can be formed and which cannot. — Heiko

The problem with this is that potential being is not actual or operational being, and so it cannot do anything -- like limit how we think.

If you want this space to be actual, then, since it is populated with concepts, there must be a super mind thinking it. (Concepts are beings of reason, existing only when actually thought.) You then need to explain how the super mind actually imposes its limitations on human minds. Further, if the concepts come from the super mind (or anything other than the reality instantiating them) they are not based in their instances, and there is no way to recognize a new instance when we encounter one.

On the other hand, if concepts are elicited by their instances, one mechanism explains both their genesis and their application to new instances. That conforms to experience and is also more parsimonious.

When it was made, the sexist connotation escaped notice. — Dfpolis

Most probably. I hope so! :smile:

Concepts are beings of reason, existing only when actually thought — Dfpolis

When I say "For every natural number X there exists a number X+1", does such a number exist for every natural number of your choice? It is widely accepted that, it does of course, because it must exist per definition of the natural numbers itself.

PS: Excuse this argument. Formality is the death of philosophy.

When I say "For every natural number X there exists a number X+1", does such a number exist for every natural number of your choice? It is widely accepted that, it does of course, because it must exist per definition of the natural numbers itself. — Heiko

The problem is confusing this kind of "existence," which has no ability to do anything, with metaphysical existence, which invariably can do something -- even if it can only make itself known. What does nothing is indistinguishable from nothing, and so is nothing.

So, what kind of existence is mathematical existence? It is not an actual, but a potential, existence. When we say "there exists a number X+1", we do not mean that X+1 actually exists, because if it did, we would be actually thinking a specific number. Why? Because numbers are concepts, and concepts actually exist only when we are thinking them. When we are not thinking them, they are potential -- able to be thought, but not actually thought. So, "there exists a number X+1" means that, for any natural number X, X+1 can be thought, and when it is, it will be a natural number. This potential is well-founded, but it is not actual existence -- not even actual mental existence.

I am sure that you realize that we cannot define anything into actual existence. All we can do is define them into mental existence (entia rationis).

I don't think that's what 'form' means. Socrates truly is the form 'man' but the form 'man' is common to all men. Likewise for forms generally. — Wayfarer

What we can determine is common to a species is not seeing what makes a substance become and maintain its being. As quoted before:

But the universal too seems to some people to be most of all a cause, and the universal most of all a starting-point. So let us turn to that too. For it seems impossible for any of the things said [of something] universally to be substance. For first the substance of each thing is special to it, in that it does not belong to anything else. A universal, by contrast, is something common, since that thing is said to be a universal which naturally belongs to many things. Of which, then, will it be the substance? For it is either the substance of none or of all. And it cannot be the substance of all. — Metaphysics, 1038b9, translated by CDC Reeve

To look for causes of substances composed of matter and form cannot be done by simply identifying components. Whatever is bringing them into existence, and maintaining them while they do, is a principle beyond those components:

But in fact, as has been said, the ultimate matter and the shape are one and the same, the one potentially, the other actively, so that it is the same to look for what is the cause of oneness or what is the cause of being one.946 For each thing is a one, and what potentially is and what actively is are in a way one. And so there is no other cause here, unless there is something that brought about the movement from potentiality to activity. Things that have no matter, though, are all unconditionally just what is a one. — Metaphysics,1045b20, translated by CDC Reeve

This unity is not what is meant by a universal that can be named. In so far as we can talk about substance that makes each unique. The need for analogy points to a limit of our experience:

What we wish to say is clear from the particular cases by induction, and we must not look for a definition of everything, but be able to comprehend the analogy, namely, that as what is building is in relation to what is capable of building, and what is awake is in relation to what is asleep, and what is seeing is in relation to what has its eyes closed but has sight, and what has been shaped out of the matter is in relation to the matter, and what has been finished off is to the unfinished. Of the difference exemplified in this analogy let the activity be marked off by the first part, the potentiality by the second. — ibid. Θ 6 1048a35–b6

We have been given some ratios to work with but are far from seeing how it works in individuals.

So, what kind of existence is mathematical existence? — Dfpolis

Mathematical platonism says that intelligibles such as number are real even if not existent, being the same for all who think. Mathematical ratios and relationships are deeply embedded in the fabric of the cosmos, hence the 'unreasonable efficacy of mathematics in the natural sciences'.

Thanks again for those passages. The point that I'm disputing is this:

. So a material object is a combination of form and matter, and that form is proper and unique to the particular object, complete with accidents. — Metaphysician Undercover

I don't think that each particular is an instance of a unique form (and as an aside I don't recall in anything I've read from Aristotle, which is not much, any reference to 'material objects' - rather the arguments are usually couched in terms of 'particulars', meaning, 'particular beings'.) But the salient point of the dispute is, is each individual an instance of a unique form? I say not, that the form 'man' is common to all men, that is why it is a universal.

The problem is confusing this kind of "existence," which has no ability to do anything, with metaphysical existence, which invariably can do something -- even if it can only make itself known. What does nothing is indistinguishable from nothing, and so is nothing. — Dfpolis

Sorry, I have to counter this with an out-of-context Hegel quote

Nothing, however, is only, in fact, the true result, when taken as the nothing of what it comes from; it is thus itself a determinate nothing, and has a content.

I take this to say: in the moment you actually choose a number X for a "natural number" (as per definition) we have a "determinate nothing" X+1 as we know the rules to construct it. So it seems the "problem" is actually choosing a "natural number X" - and not X+1 which is already implied by the choice.

So if we'd define a concept of "concept" which allowed for deduction or implication of another concept - like e.g. we said "every concept has an opposite", then someone asked for a concept fitting out definition of "concept" has already - though indirectly - determined the real opposite when answering.

A problem seems only to exist when answering bleem for the number X...

When I say "For every natural number X there exists a number X+1" — Heiko

If we are still talking about Aristotle then there is no natural number "X". An number is always a number of something, a number of what it is that is being counted. The shift to symbolic notation occurs later.

For first the substance of each thing is special to it, in that it does not belong to anything else. — Metaphysics, 1038b9, translated by CDC Reeve

As I understand this, in simplest terms, one ousia or being is not any other. The translation "substance' easily misleads us unless we keep in mind that a substance means a particular being. It can also be misleading if we think of a substance as being of a thing, as if they are not the same.

But the salient point of the dispute is, is each individual an instance of a unique form? I say not, that the form 'man' is common to all men, that is why it is a universal. — Wayfarer

Qualities and parts all men share as attributes do not show us the cause of why we share them. That is how I read the text I quoted. Do you see another way to understand those words?

It is clear that there must be a relationship between the "particular formation" of individuals and the way they can be recognized as members of a species. Otherwise, there would be no species or kinds. How to understand that is a major hot potato in Aristotelian scholarship. But we don't have to get that deep into the pool to see that Aristotle objects to the language of participating in Forms because it starts with a general attribute and circles backs to itself:

" Of which, then, will it be the substance? For it is either the substance of none or of all. And it cannot be the substance of all."

If we are still talking about Aristotle then there is no natural number "X". An number is always a number of something, a number of what it is that is being counted. The shift to symbolic notation occurs later. — Fooloso4

I am sorry, I got carried away by the course of arguments. I haven't studied Plato or Aristotle in original, but I find the explanation of causes and causality in Heidegger's Essay "The Question Concerning Technology" quite informative.

What we call cause and the Romans call causa is called aition by the Greeks, that to which something else is indebted. The four causes are the ways, all belonging at once to each other, of being responsible for something else.

The cause formalis is just one contribution to the "thing".

First, I need to comment again on the translation of 'being' by 'substance' in Aristotle, which Joe Sachs criticizes here. Sachs says in reference to this mis-translation 'It is no wonder that the Metaphysics ceased to have any influence on living thinking: its heart had been cut out of it by its friends'.

So imagine if the passage you quoted above put 'being' in the place of 'substance'. It is not entirely accurate, but I think it conveys something which has been lost in the usual discussion of 'substance':

But the universal too seems to some people to be most of all a cause, and the universal most of all a starting-point. So let us turn to that too. For it seems impossible for any of the things said [of something] universally to be substance [a] being. For first the substance being of each thing is special to it, in that it does not belong to anything else. A universal, by contrast, is something common, since that thing is said to be a universal which naturally belongs to many things. Of which, then, will it be the substance being? For it is either the substance being of none or of all. And it cannot be the substance being of all. — Metaphysics, 1038b9, translated by CDC Reeve

I think the discussion of substance tends to slant the discussion, because it's natural to reify substance as something objectively existent (or more likely non-existent) and that this is at the basis of the difference between the Platonic and Aristotelian doctrine of forms.

I believe that Plato's doctrine of ideas requires an understanding that the 'ideas' or 'forms' are real in a different sense to the reality of phenomena. Betrand Russell says that universals don't exist in the sense that horses, men, tables and chairs do, but that they're nevertheless real - they 'subsist'.

Suppose, for example, that we are thinking of whiteness. Then in one sense it may be said that whiteness is 'in our mind'. ... In the strict sense, it is not whiteness that is in our mind, but the act of thinking of whiteness. The connected ambiguity in the word 'idea', which we noted at the same time, also causes confusion here. In one sense of this word, namely the sense in which it denotes the object of an act of thought, whiteness is an 'idea'. Hence, if the ambiguity is not guarded against, we may come to think that whiteness is an 'idea' in the other sense, i.e. an act of thought; and thus we come to think that whiteness is mental. But in so thinking, we rob it of its essential quality of universality. One man's act of thought is necessarily a different thing from another man's; one man's act of thought at one time is necessarily a different thing from the same man's act of thought at another time. Hence, if whiteness were the thought as opposed to its object, no two different men could think of it, and no one man could think of it twice. That which many different thoughts of whiteness have in common is their object, and this object is different from all of them. Thus universals are not thoughts, though when known they are the objects of thoughts. — Betrand Russell

I've bolded the significant point, which I think resolves many of these issues. So the 'idea of a man' is just that - but it doesn't exist, not in some 'ethereal realm' or 'Platonic heaven' - not that Plato himself is clear about that, but it became manifest in later (ancient and medieval) philosophy. I think the key idea is that of the intelligible object - something which is real, but only perceptible by reason, not by the senses. The idea or form is what is manifested in the physical form of man. Hence the simile in this post.

And that - realism regarding universals - is what was lost from the Western tradition with the ascendancy of nominalism over scholastic realism. That's why there can't be any conception that universals exist in a different sense to particulars - because that is an aspect of the conceptual space that is no longer available to us (cf. dfpolis 'post-Cartesian conceptual space')

Anyway, carry on.

//I should add that it's much easier to concieve of an idea of a form as 'the being of all' than it is as 'the substance of all' i.e. the individual is an instantiation of a singular idea. Every man exemplifies 'the idea of man'. I don't see how this presents great conceptual difficulties.

I take Sachs' and Kahn's point regarding how the use of 'substance' is misunderstood as a translation of einai and ousia. It is not germane to the distinction Aristotle is making in the text I quoted. Aristotle does not have Russell's problem about whether universals are real. Aristotle is saying that they are so real that we are tempted to think they explain what they do not.

Aristotle's objection to 'universals' understood as causes is its own objection to 'reification'. We encounter a world of beings and figure we have it all figured out by classifying those items properly. We have to classify and place things into relationships. We also have to find a way to find its limits while wondering what the heck is going on.

Anyway, carry on. — Wayfarer

Message received.

So, what kind of existence is mathematical existence? — Dfpolis

Mathematical platonism says that intelligibles such as number are real even if not existent, being the same for all who think. Mathematical ratios and relationships are deeply embedded in the fabric of the cosmos, hence the 'unreasonable efficacy of mathematics in the natural sciences'. — Wayfarer

Yet, to find the numbers, we have to measure nature, not intuit them mystically, as Plato believed. So, Aristotle's theory is far superior. There are no actual numbers in nature. There is discrete and continuous quantity. Discrete quantity is countable, eliciting actual number concepts. Continuous quantity is measurable, eliciting numerical value concepts.

If there were actual numbers in nature, then when we measured, we would invariably obtain those numbers -- for while a system can have many possibilities, it can only have one actual state. Special relativity and quantum physics show that measure numbers depend jointly on the system measured and the measuring process. Since different ways of measuring yield different results, the result is only potential (measurable) before measuring actualizes one of the possible results.

So, numbers are deeply rooted in nature, but not in the naive way Platonism imagines.

Yet, to find the numbers, we have to measure nature, not intuit them mystically, as Plato believed — Dfpolis

You're not even allowing for pure mathematics. Also for the role that mathematics has had in disclosing things about nature that we could never, ever deduce through observation alone. And I humbly suggest that it is your depiction of Platonism that is 'naive'.

It's significant that empiricist discussions of the nature of number tend to question how it is that humans even have a faculty that knows mathematical facts, because such facts are not, by definiton, empirical (discussed in e.g. The Indispensability Argument in Philosophy of Math)

Sorry, I have to counter this with an out-of-context Hegel quote

Nothing, however, is only, in fact, the true result, when taken as the nothing of what it comes from; it is thus itself a determinate nothing, and has a content. — Heiko

Nothing is not determinate, for if it had determinations, it would be something determinate -- something with properties.

X in your example is indeterminate as a number, but determinate as a concept, for it represents an arbitrary number of the type being discussed. And, specifying X specifies X+1. Still, neither exists (as a number) until it is specified and thought. And that is the point: mathematical "existence" is not actual existence, but a convenient shorthand for a certain kind of potential.

You're not even allowing for pure mathematics. Also for the role that mathematics has had in disclosing things about nature that we could never, ever deduce through observation alone. And I humbly suggest that it is your depiction of Platonism that is 'naive'. — Wayfarer

I spent some years studying pure mathematics, so I am unlikely to forget about it.

Being "pure" does not give mathematics any more existence than being applicable. For the most part, pure mathematics is abstracted from mathematical structures abstracted from nature. A small part is not, and is therefore hypothetical -- and we may not even know if it is consistent with the part that is abstracted.

Plato's view that there are actual numbers in nature, which is what I was talking about, is naive for the reasons I gave. It is also unnecessary, as abstraction provides an adequate account of most mathematics (see above). Further, it is psychologically naive. It provides no way in which we can (a) learn Platonic ideas, or (b) having learned them, no reason why what we "learned" should be applicable to scientific measurements. Aristotle's view, that numbers are based on counting and measuring operations ties them directly to scientific practice, and has survived the transition to modern physics -- being able to explain how we get different results depending on how and what we choose to measure. So, yes, mathematical Platonism is naive.

Where does he say that it is not properly a cause? — Fooloso4

Physics Bk 2, where he discusses causes. After describing the four senses of "cause" he says: "Such then is the number and nature of the kinds of cause." Ch. 3 195a. Then he distinguishes between those four which are "proper" causes, and incidental causes. 195a. Then at Ch. 4 he questions "in what manner chance and spontaneity are present among the causes enumerated". 195b. So he starts to describe the opinions of others. In Ch. 5 he discusses exactly what chance is, and makes the following conclusion.

Things do, in a way, occur by chance, for they occur incidentally and chance is an incidental cause. But strictly it is not the cause - without qualification - of anything; for instance, a house builder is the cause of a house; incidentally a flute player may be." — Physcis Bk 2, Ch 5, 197a 13 -14

Please notice Fooloso4, that he distinguishes between the four "proper causes" and what he calls "incidental causes". The word in your quoted translation is "accidentally". Chance is an incidental cause, therefore it is not a proper cause. I suggest you read the section, and figure out what he means by "incidental" because you seem to be totally ignoring this qualification.

It is relevant because at least part of your confusion seems to be based on the translation of the term ousia. — Fooloso4

Very clearly it is you who is confused.

It is not me but Aristotle who you are accusing: — Fooloso4

No, it is your pathetic interpretation which I am accusing

That is why I defined it for you. — Dfpolis

As I explained, your definition refers to nothing real because the additive are mixed with the subtractive What's the point in proceeding that way? You can define "abstraction" however you want, and produce a logical argument from this, but if there's nothing real which corresponds with your definition then it's just a false premise and your argument is unsound.

We do not "designate" species members. We find them, or don't. — Dfpolis

Of course we designate species members rather than finding them. We find things, and judge them to be of a specific species, thereby designating them as members of that species. The named species are categories for classification, we judge things and designate them as members of those categories. We do not come across things, and they say to us "I am of this specific species, you must place me in that category" Even if things did speak to us in this way, we would have to judge whether they were telling the truth or not. There's no way around the fact that we make a judgement which designates that the thing is of a certain species, and it is not the case that we simply "find" a thing to be of that certain species.

Not at all. We know they are different because they are not in the same place, and they cannot be in the same place because they are made of different stuff. — Dfpolis

This is backward. First, the same thing can be in different places, just not at the same time. The same thing being in different places is what validates the concept "motion". And, position is part of the formula, it is formal. If we state, as a formal principle, that the same thing cannot exist in two different places at the same time, then we have what we need to say that they are different. We do not reference "made of different stuff" at all. When we judge two things as different, we first reference obvious physical differences. If there is not obvious physical differences we might think that they are both made of the same stuff, aluminum steel, wood, etc.. Then we refer to spatial temporal positioning, and this tells us that the two things can't really be made of the very same stuff. But what makes the stuff different is something formal, spatial temporal position, not something material. Without form all matter would be the same thing.

The atomists proposed an indivisible stopping point, atoma. Aristotle roundly rejects the hypothesis of atoma, and answers instead that potential division is not actual division, so there is no actual infinite regress. — Dfpolis

That's right I agree here.

lso, will not find "prime matter" in Aristotle. It is an invention of the Scholatics, found in Aquinas, and confuses Aristotle's hyle with Plato's chora. (See my Hyle article.) — Dfpolis

No, we very much do find prime matter discussed in Aristotle's Metaphysics. He ends up rejecting it with his cosmological argument.

By "implies" I take it you mean that there is no text in which Aristotle actually says this. If there is, please cite it. — Dfpolis

Where he explicitly states this in "On the Soul", Bk1, when he addresses various different ideas about the relation between the soul and the body. He dismisses Plato's account of the circular motions of the heavens in Timaeus, starting with "Now, in the first place it is a mistake to say that the soul is a spatial magnitude." Then it is implied in Metaphysics Bk9 when he shows that there is necessarily an actuality prior in time to potentiality (cosmological argument). Since matter is potentiality, this actuality must be immaterial.

This is not Aristotle's position, and your reasoning is flawed for the reasons I gave. — Dfpolis

It appears like you have not read that part of "On the Heavens".

But the salient point of the dispute is, is each individual an instance of a unique form? I say not, that the form 'man' is common to all men, that is why it is a universal. — Wayfarer

So let me ask you, are properties part of a thing's form? If so, then how is it that different men have different properties yet they have the same "form", man?

Basically you're asking, How is it that all humans are homo sapiens yet with such a diversity of appearance?

Heidegger — Heiko

Heidegger is an important figure in helping to shape our current understanding of Aristotle. He taught a generation of students how to do a close reading of an ancient text, paying careful attention to the original language rather than relying on Latin translations.

You have either forgotten why the question of accidental causes arose or you are moving the goal posts. You claimed:

It is made very clear by Aristotle, that accidents are part of a thing's form ...

If the difference were not formal we could not perceive them as differences ...

So chance is not a cause at all, it's just the way we portray and represent our own ignorance. — Metaphysician Undercover

You went from denying that chance is a cause at all to saying it is not a proper cause to quoting Aristotle that it is an incidental cause.

That a man is skinny is not due to the formal cause. What it is to be a man is not to be skinny. If the skinny man becomes fat this is not due to the formal cause. He is the same man whether skinny or fat.

I see you went silent regarding the eternity and material of the heavens. It would have been better to have admitted you were wrong, but better to be silent then attempt to argue your way out. If only you had used such good judgment with the rest of your tendentious arguments. I think it is time for me to once again join the ranks of those here who, for good reason, ignore you.

As I explained, your definition refers to nothing real — Metaphysician Undercover

So, we always attend to every aspect of sensation and never prescind from some aspects to focus on others?

Of course we designate species members rather than finding them. We find things, and judge them to be of a specific species, thereby designating them as members of that species. — Metaphysician Undercover

We do not find them, we find them.

Consult a good dictionary. "Designating" is appointing, not judging. Appointing is an act of will, judging of the intellect. To rightly judge that a found organism is a member of a species, it must have properties that elicit the corresponding species concept. These properties are intrinsic to the organism, not willed by us in an act of designation.

First, the same thing can be in different places, just not at the same time. — Metaphysician Undercover

Pettifogging.

Without form all matter would be the same thing. — Metaphysician Undercover

I see you finally understood the texts I posted from the article I am working on. Matter (stuff) is the principle of individuation of form, and form is the principle of individuation of matter.

No, we very much do find prime matter discussed in Aristotle's Metaphysics. — Metaphysician Undercover

Do you have any text(s) to support this claim? You might mean that he is rejecting Plato's chora, but that is not "prime matter" in the sense used by the Scholastics.

Where he explicitly states this in "On the Soul", Bk1, when he addresses various different ideas about the relation between the soul and the body. He dismisses Plato's account of the circular motions of the heavens in Timaeus, starting with "Now, in the first place it is a mistake to say that the soul is a spatial magnitude." — Metaphysician Undercover

This is irrelevant to the issue at hand.

Since matter is potentiality, this actuality must be immaterial. — Metaphysician Undercover

This is equivocating on "matter." Proximate matter, "this flesh and bones," which is actualized by psyche, is not pure potency.

And that is the point: mathematical "existence" is not actual existence, but a convenient shorthand for a certain kind of potential. — Dfpolis

Which - in history - got apparent especially when a concretized potential invalidated the whole underlying concept.
Yet one could say that the mode of existence of x+1 changes, when x is determined.
For x=3432331, we get an x+1 for sure. I am just to lazy to write it down. It is completely predicted.
AND: I just hammered on the keyboard for x. It is just a stream of digits forming a number already too large to grasp. What would be meant by thinking a number?

Plato's view that there are actual numbers in nature, which is what I was talking about, is naive for the reasons I gave. — Dfpolis

I don't know if that is Plato's view. From everything I read, the basic tenet of mathematical Platonism is that numbers are real independently of any mind. They have a reality which is analogous to, but different from, material objects.

[Platonism is] the view that mathematics describes a non-sensual reality, which exists independently both of the acts and [of] the dispositions of the human mind and is only perceived, and probably perceived very incompletely, by the human mind. — Godel

From here

Heidegger is an important figure in helping to shape our current understanding of Aristotle. He taught a generation of students how to do a close reading of an ancient text, paying careful attention to the original language rather than relying on Latin translations. — Fooloso4

Well, not being able to judge the quality of such translations I am limited to saying I find his remarks interesting. Let me summarize and elaborate a little as I have taken some freedom of interpretation and application my self:

That, what makes a given thing the thing it is, is "caused" by 4 different moments. In Heidegger's words the thing owes itself to these four moments.
causa materialis - The material of which the thing is made or that makes up for it's body
causa formalis - The form or shape into which the the material was brought
causa finalis - The purpose of the thing - or - in a wider interpretation the relation of the thing to it's context
causa efficiens - which explicates or forges the thing as the thing it is. To me it seems possible to interpret this as calling a given thing names, taking into account or evaluating the other three causes. Yet Plato would object this as the thing "owes it's existence" to the causa efficiens.

I am moving the discussion of chance causes here

No doubt it will ruffle the feathers of those who desire a "just so" universe.