I agree that it is a good thing that the idea of a 'realm of forms' has fallen out of favour. I do not go to the other extremity of holding to nominalism, and saying that universals reflect only the human mind and nothing beyond that. Some people do not seem to see any alternative apart from one or the other extremity.

If I am identified as the man who wears a red cap, it does not follow that I always wore a red cap, or always will wear a red cap. — Janus

Didn't say it did. Didn't say it didn't. It need not follow that you always wore one, or always will. That is irrelevant to the argument made. If you are identified as the man who wears a red cap, and you are not wearing a red cap, then the identification is false.

To keep it on point...

If you are existentially contingent upon wearing a red hat, then it only follows that thought and belief are necessary for your very existence.

Red hats are existentially contingent upon thought and belief. You are existentially contingent upon red hats. You are existentially contingent upon thought and belief...

I agree that it is a good thing that the idea of a 'realm of forms' has fallen out of favour. I do not go to the other extremity of holding to nominalism, and saying that universals reflect only the human mind and nothing beyond that. Some people do not seem to see any alternative beyond one or the other extremity. — Janus

True.

Note that the position being argued does not suffer...

The same applies to humans using language; and nothing in Aristotle's definition necessitates otherwise. So, the idea that the conclusion that being human is "existentially dependent" upon using language is a corollary of Aristotle's definition is false. I've explained why, and I won't explain it again. If you don't accept it then show me where I went wrong in showing you where you went wrong.

That may be true, but nor does Aristotle's position suffer...

I mean, my point is really that, for example, whether humans are distinguished by being the only animal that uses language, or the only anthropoid with opposable thumbs and scant body hair; it does not follow that humans are existentially dependent on language, opposable thumbs or scant body hair. If they evolved to lose the opposable thumb and become covered in hair they would still be human, in other words.

I addressed a specific claim. It was a definition statement of 'X' by an author. It is the only definition statement of 'X' given by the author. It is, therefore, the only thing to ground further contemplation upon with regard to casting a critical eye upon the definition.

You objected to my analysis, and later sided with the author. Your objection, however, was not based upon what the author said. My analysis was. The author said 'X'. I showed that 'X' suffered reductio. I further argued that 'X' was false.

You're claiming that the author's definition does not suffer from reductio. I presume you're also claiming that the author's definition is not false. Your evidence for that has been something other than the author's definition.

So...

You have not shown that the argumentative form is invalid. You have not objected to the author's definition. You have not directly addressed the argument I've offered, in terms of validity or terms of truth. Your claiming that the author's definition does not suffer a reductio. I presume you're also claiming that the author's definition is not false.

Your evidence for that is something other than the author's definition.

That's the best I can do.

Hope it helps.

****Need offering flower emoticon****

Don't take it too far now...

I've yet to see a complete rendition of Aristotle's definition of being a man or being a universal. I'm basing my argument upon what is at hand here.

Show me Aristotle's stuff, and we'll get past that part.

;)

I mean, my point is really that, for example, whether humans are distinguished by being the only animal that uses language, or the only anthropoid with opposable thumbs and scant body hair; it does not follow that humans are existentially dependent on language, opposable thumbs or scant body hair. If they evolved to lose the opposable thumb and become covered in hair they would still be human, in other words. — Janus

I agree with all this.

If we changed the definition accordingly. Problem is, we're doing philosophy here. Changing a definition in mid-debate is a bad move, an invalid objection.

If humans are ontologically defined by using language, having opposable thumbs, and having scant body hair, then all humans use language, have opposable thumbs and have scant body hair...

Or...

The definition is wrong. Pick one. You can't have your cake and eat it too, here. Either the definition is wrong, or being human is existentially contingent upon language.

The author said 'X'. I showed that 'X' suffered reductio. I further argued that 'X' was false. — creativesoul

Yes, but that the author actually meant what you say he must have meant is merely your interpretation. I think I have shown that it is open to a wider interpretation.

These are flexible 'average' definitions, though. Someone could be irrational, mute, incredibly hairy and born without thumbs, and yet still be human. You are insisting upon an unnecessary rigidity of interpretation.

The definition is right as far as it goes, in other words; but exceptions must be allowed for.

You're out of options...

See ya around.

don't think that's right. Again, I think you attribute far too much significance to the notion of the individual. It was barely present in classical philosophy. Individuals only exist because they are expressions of the universal. — Wayfarer

I really don't know what else to tell you, except to read some Aristotle. Did you read the quote I put on the other thread? The individual is central to Aristotelian philosophy. From his law of identity, which refers to a thing, through "substance" which refers to the individual, through his physics, which employs matter and form to account for the fact that individual things change, through his biology which assumes the soul, to account for the existence of a living body; and his metaphysics, where he states that the important question for metaphysicians to ask, is not why is there something rather than nothing (in the general sense), but why is this thing, the thing it is, and not something else.

And as I argued in the other thread, Aristotle derived this perspective from Plato. You know Aristotle was a student of Plato. The difference is that Plato came to the importance of the individual towards the end of his life, in his later philosophy, so it forms more of a conclusion to his philosophizing, whereas Aristotle takes the importance of the individual as a starting poinmt. With Plato, all his early material focuses on universal Ideas. It's after the Republic, where he sees the need to assume "the good", that he starts to shift his attention toward the creation of individual things.

Notice first, that Plato speaks of "the good", and this is commonly misrepresented in modern presentations of Platonism, as the Idea of good, or the Form of good. You can see that this misrepresentation changes the nature of "the good" from an individual to a universal. But the good is necessarily an individual, as "the ideal". And this is the conclusion he reaches at the end of The Republic, that there is necessarily a perfection to any idea, which is the Ideal. Positing the perfect idea, the Ideal, allows that we can all have a different idea of what "just" means, while there is still, "the Ideal" idea of just, somewhere that we haven't yet grasped. This is very important, because the fact that we all have different ideas concerning things like "just", is a major problem for those who claim participation, i.e., that the idea we each have of "just" is a participation in an independent universal. How can our ideas be a participation in an independent universal when our ideas of the very same thing are so different?

Once Plato gets to the Ideal, the whole structure of idealism must be turned around, inverted. The independent Idea can no longer be conceived of as a universal, because it is necessarily a particular, the perfect, the ideal, and this is where the Neo-Platonists derive the One. For Plato though, by the end of The Republic, he proposes an Idealist structure of a double representation. There is a divine Idea, of "bed" for example, (we could say God's idea of bed), which is the perfect idea of what a bed is. The carpenter attempts to copy this ideal, with his own idea of the best bed, then proceeds to build a bed in representation. So we have two levels of representation. The human mind produces the universal, which is an attempt to represent the divine idea. what is apprehended as the perfect universal. With the use of the universals which the human beings have created, they proceed to produce individual objects. Notice how the entire structure starts and ends with individuals. The divine, "Ideal" bed is an individual. The products produced by human beings are individuals. The "universal" is a medium between these two particulars, the ideal particular, and the material particular which the human being creates.

Why would you consider something that is made op of parts to be a unity rather than a multiplicity? — Janus

It is dictated by the statement "something made up of parts". To call it "something" indicates that it is one, unity. if we called it a group of things, rather than "something", then it would be a multiplicity.

Look at the symbol, "5". Depending on how you choose to interpret this you could choose that it signifies one number, the number 5, which is a unity of parts, or you could choose that it signifies a multiplicity. However, the rules of interpretation which are required for mathematical proceedings. dictate that we interpret it as one unit. That is the essence of the symbol "5", that this particular multiplicity exists as one unit, represented as 5, so it is treated within mathematics as one unity. That's how it must be interpreted. If "5" were interpreted as a multiplicity, then each object within that multiplicity would have to be dealt with individually, and the mathematical process would be thwarted. So "5" represents a unity not a multiplicity, because this is what is required for proper mathematical proceedings.

Boundaries are notoriously imprecise, so it seems we cannot rely on them to define what counts as a discrete thing. Say a discrete thing is an individual; the etymology of 'individual' is 'not divisible', and yet something made up of parts can be divided into those parts, or may even be able to be arbitrarily divided. Would you say you ceased to be an individual if I cut off your arm, for example? — Janus

I don't really see the meaning of the question here. To remove a part from a whole makes that part no longer part of the unity, but it is an individual on its own. To remove my arm from me makes me less, in size for example, as an individual, but still an individual. But my arm is also an individual now. Notice that examples like this are just exercises in interpretation. We might disagree on interpretation, so we'd have to discuss to see what exactly is meant by the example. If we have "5", and we remove "1", we then have "4", and "1". 4 is not the same as 5, but they are both unities.

I haven't read up much on mereology, but as far as I know it is a contentious field; so I'm not convinced there would be an unambiguous "mereological principle" that could be relied upon. Now I can say, for example, that my body is a unity of discrete parts, so what kind of "unity" is that, if not a functional unity? And to think of unity in functional terms would seem to be thinking in terms of systems rather than entities. — Janus

That is exactly the point, just precisely what the mereological principle might be is of contention, but that does not negate the fact that one is needed to account for the existence of unities, if we are to give any unities the ontological status of real existence. That it is contentious indicates that we do not even know what a unity is. If we deny the need for such, then unities are illusions, and all we have is multiplicities. But sense information tells us that we have individual objects, unities, and they are real. Furthermore, if there is nothing real to account for unities then the assumptions of mathematics, that 5 is a unity, for example, are completely ungrounded. Unity is the basic assumption of numbers.

Of course we do commonly speak and think mereologically, if that is just taken to mean something like "in terms of parts and wholes". But we are here questioning whether or not that thinking, on analysis, remains unambiguous. I don't think we can fairly claim that it does. — Janus

That what "unity" refers to , or what it is, remains ambiguous, gives a rational foundation for doubt and skepticism with respect to all mathematics, and the entire epistemological system, which is grounded in the identity of the individual. Until we know what it means to be a unity, and validate the reality of a unity, then all knowledge based in the assumption of unity (including all mathematical knowledge) can be considered to be unsound.

If we deny the need for a mereological principle we end up with apokrisis' systems approach. As a whole, or as a part, are two different ways of looking at the same thing. Whether it is related to a larger thing or to smaller things, determines whether it is a part or whether it is a whole. This denies the need for a mereological principle to account for unity, but a unity is just an arbitrary designation relative to one's perspective. — Metaphysician Undercover

It makes mereology emergent rather than fundamental. So yes, ontically it gets the story the right way around. It explains how hierarchical organisation can arise in nature.

The problem I have with this, which I am trying to explain, is that if you place the opposing limits, within the same category, as "the continuous spectrum" which is assumed to be within that category, then these limits are not real. — Metaphysician Undercover

Well yes. A “category” is thus unambiguously defined in terms of what it is not. Being is shaped by its complementary limits. The polar extremes create an actual range that then allows the third thing of some particular or individuated position on a spectrum of possibility.

Ideas are mind-dependent.

Ideas are existentially contingent upon thought and belief.

Some ideas talk about things that we discover.

These things are not existentially contingent upon being discovered. — creativesoul

So all ideas about things are mind dependent and some ideas about things are mind independent.

Seems legit.

It is dictated by the statement "something made up of parts". To call it "something" indicates that it is one, unity. if we called it a group of things, rather than "something", then it would be a multiplicity. — Metaphysician Undercover

I disagree with this. An arbitrary collection of disparate, unrelated things is a multiplicity, but then so is a collective of functionally interrelated things, such as for example, the human body. We say the human body is a functional unity insofar as it consists of parts that work together to achieve self-regulation. A human body is constantly changing, so it is not one and the same thing from one second to the next, Its identity is not a matter of an isolated instant presence, but is the idea of one unique ever-changing spatiotemporal activity.

So we have two levels of representation. The human mind produces the universal, which is an attempt to represent the divine idea. what is apprehended as the perfect universal. With the use of the universals which the human beings have created, they proceed to produce individual objects. Notice how the entire structure starts and ends with individuals. The divine, "Ideal" bed is an individual. The products produced by human beings are individuals. The "universal" is a medium between these two particulars, the ideal particular, and the material particular which the human being creates. — Metaphysician Undercover

How does this story work when we are talking about nature? Humans can invent notions about beds (and what use God would have for a bed is a mystery). But where is this double representation deal when it comes to an oak tree or a river?

Does the ur-oak tree and ur-river exists as a particular ideal in God’s mind? And how particular would it be, given variety seems an essential part of natural things? (Natural law always seems to have maximum generality according to scientific discovery at least.)

Then in what sense is material nature trying to make an ideal oak tree or ideal river? How is universality the medium connecting two individual representations. Does nature employ a mind when it produces its paler imitations of the divine ideal?

I really don't know what else to tell you, except to read some Aristotle. The individual is central to Aristotelian philosophy. — Metaphysician Undercover

I have read enough of the sources to believe that your interpretation is incorrect. The law of identity doesn't have anything to do with individual identity as such, it's about logic.

Look at the symbol, "5". Depending on how you choose to interpret this you could choose that it signifies one number, the number 5, which is a unity of parts, or you could choose that it signifies a multiplicity. However, the rules of interpretation which are required for mathematical proceedings. dictate that we interpret it as one unit. That is the essence of the symbol "5", that this particular multiplicity exists as one unit, represented as 5, so it is treated within mathematics as one unity. That's how it must be interpreted. If "5" were interpreted as a multiplicity, then each object within that multiplicity would have to be dealt with individually, and the mathematical process would be thwarted. So "5" represents a unity not a multiplicity, because this is what is required for proper mathematical proceedings. — Metaphysician Undercover

Your account needs to say something exact about why fiveness can be regarded as a unity. The continuity has to be explained on logical grounds, not simply treated as a matter of mathematical fiat. A meaningless convention.

Crucial to the notion of fiveness is that it is a permutation symmetry. The five parts that compose the whole can be swapped around without making any difference to their total number. The set has cardinality but not ordinality. And fiveness, in representing pure cardinality/complete lack of ordinality, thus can become itself an ordinal part. It can be placed after fourness and before sixness.

So even when dealing with a paradigmatic conception of atomistic discreteness - the integers or whole numbers - the dialectical logic of metaphysics applies. The fundamental story is the triadic one of a symmetry breaking.

The story goes that in the beginning is some higher state of symmetry - a vagueness or firstness. Then you get a symmetry breaking - the separation towards two mutually opposed bounds of possibility. Then finally you get the arrival at some equilibrium balance - the arrival at a limit to the symmetry breaking which is itself a return to a symmetry. Like a completely thermalised gas of ideal particles, a symmetry is restored in that while the particles continue to move about freely, the changes in position no longer make a difference. They express a permutation symmetry so far as the macroscopic or universal properties of the system go.

So the arc of development is the triadic one of symmetry, symmetry breaking, arrival at a balance where breaking ceases to break and so symmetry again rules.

If we are talking about our conception of numbers, we can see how we go from some conception of absolute unbroken unity - the One - to a conception of the many, the brokenness of multiple ones, and eventually arrive at a permutation symmetry in the sense of the many sets of ones where the internal arrangement makes no difference to the macroscopic state of the set. Five is five, regardless of how it’s composing ones are shifting about and swapping places.

But then ordinality emerges as a new property of this cardinality. The symmetry can be broken by a ranking in terms of some new concept of relative size. Some permutation sets are bigger or smaller than others.

Next stop, some conception of infinity that restores a new level of symmetry, finds a limit to counting sequentially. Counting now becomes a difference that can’t make a difference. Countability just becomes a generic macroscopic property of a counting system. Talk of individual acts of counting make no more sense than worrying about the microstates of a thermalised ideal gas.

Being existentially contingent upon language and being a language construct are not equivalent. — creativesoul

The basic point is that the capability came first (i.e., animals evolved with the capability for language/rational thought). At some later point that capability was recognized and represented in language.

For the realist about universals, that capability is real independent of whether it is represented in language. Whereas for the nominalist, that capability is real only to the extent that it is represented in language. Essentially it comes down to whether universals are considered to be discovered or created.

BTW by rational animal, Aristotle was referring to a general capability (i.e., humans are capable of acting rationally or irrationally in addition to being instinctive animals). See the Wikipedia entry for the general idea or, for a more nuanced sense, try Matthew Boyle's article, Essentially Rational Animals.

I think Ernst Cassirer's definition is also apt here:

man, for many philosophers both ancient and modern, is the "representational animal," homo symbolicum, the creature whose distinctive character is the creation and manipulation of signs - things that stand for or take the place of something else. — W. J. T. Mitchell

Edit: animal symbolicum definition due to Cassirer, quote is Mitchell's.

The law of identity doesn't have anything to do with individual identity as such, it's about logic. — Wayfarer

Even in logic, it is for reasoning about the particular. It axiomatically secures the PNC and LEM.

But then how is the principle of identity itself secured, except in distinction to the notions of vagueness and generality?

So here we now have the principle of indiscernibles - the idea that there are differences that don’t make a difference. A can now equal A to the measurable degree that someone agrees nothing essential is changed by the finer detail.

A man is still a man so long as his functional unity isn’t compromised too much by a missing arm, a micro-penis, or deaf-muteness.

All through this thread, MU and creative show how badly metaphysics can go astray in presuming identity as brute fact rather than being relative to some principled degree of indifference.

Mathematical thought has no problem specifying what counts as indiscernible, as I just explained with the entropic notion of a permutation symmetry.

So there is no real excuse for perpetuating a simple minded atomism or reductionism when it comes to the laws of thought. To apply predicate logic to issues of holistic metaphysics is always going to come up short.

Metaphysics has irreducible triadic complexity for a reason. That is how an immanent nature can bootstrap into being.

All through this thread, MU and creative show how badly metaphysics can go astray in presuming identity as brute fact rather that being relative to some principled degree of indifference. — apokrisis

Agree. A = A isn't about whether a particular instance of A 'is equal with itself', which seems absurd to me.

Again, the passage from the metaphysics that I cribbed off Wikipedia:

The whole thing, such and such a form in this flesh and these bones, is Callias or Socrates; and they are different owing to their matter (for this is different), but the same in species, for the species is indivisible.

The passage from Thomistic psychology that I have quoted previously

if the proper knowledge of the senses is of accidents, through forms that are individualized, the proper knowledge of intellect is of essences, through forms that are universalized.

So here is a statement of matter-form (hyle-morphe) dualism - the form is universal, the same in all things of similar type, in fact, what makes perception of 'similar type' possible, not to mention the ability to quantify or count.

The material difference is accidental, i.e. this particular man happens to be Socrates or Callias. The higher intellect sees the immaterial form, the lower mind receives the sensory impression.

So in my understanding, this is a clear pre-cursor to Cartesian dualism - actually you can see how Descartes derived his basic schema from this, but then radically altered it by conceiving of res cogitans as something self-existent; whereas in A-T dualism, matter and form are always part of a single whole, even if they have recognisably different aspects (although I suppose at the end of the day, it is simply 'body and soul'.)

But, intuitively, what it means is that 'nous' is 'what perceives the meaning of things ' - the faculty which sets humans apart, being able to think and communicate abstractly, as per the Cassirer quote above.

An arbitrary collection of disparate, unrelated things is a multiplicity, but then so is a collective of functionally interrelated things, such as for example, the human body. — Janus

Again, you are saying the same thing. By designating it a "collection", you have declared that it is one whole, a collection. So it is fundamentally a whole. If you remove the designation of "collection", then you have a "multiplicity" and either this multiplicity is a bounded whole, or we'd have to consider that it is infinite. It's simply the way that our language works, we refer to things, wholes, and it's very difficult to get out of that paradigm, because everything then becomes unintelligible.

It makes mereology emergent rather than fundamental. So yes, ontically it gets the story the right way around. It explains how hierarchical organisation can arise in nature. — apokrisis

The "right way around" as you assert. But I've demonstrated to you, in a number of different ways, in a number of different threads, that your ontology is backward, because it is illogical. You put the part as prior to the whole, but this is logically impossible. It seems intuitive to you, for some strange reason, that organization has emerged from complete disarray, but this is demonstrably unintelligible.

How does this story work when we are talking about nature? Humans can invent notions about beds (and what use God would have for a bed is a mystery). But where is this double representation deal when it comes to an oak tree or a river? — apokrisis

This is the structure which Plato produced to explain the existence of ideas, and ideas are demonstrated to us by human beings. How Ideas relate to natural things was developed later by the Christian theologians in the theories concerning creation.

Does the ur-oak tree and ur-river exists as a particular ideal in God’s mind? And how particular would it be, given variety seems an essential part of natural things? (Natural law always seems to have maximum generality according to scientific discovery at least.)

Then in what sense is material nature trying to make an ideal oak tree or ideal river? How is universality the medium connecting two individual representations. Does nature employ a mind when it produces its paler imitations of the divine ideal? — apokrisis

I think that the general sense of this would be that the Form of the individual thing exists in God's mind prior to it's material existence, such that the ideal Form is the cause of the thing's existence. This does not necessitate determinism, as God's will is free. Under these principles, which are more religious than Platonic, though they may be derived through Neo-Platonism, the material thing follows the immaterial Form of the thing, like a representation of it, and the universal, as the human conception follows the material thing as a representation. But it's complex, because human beings create things as well, and in the act of creation, the human being produces an idea or form, and the material object follows from this, just like God's creation in nature.

Your account needs to say something exact about why fiveness can be regarded as a unity. The continuity has to be explained on logical grounds, not simply treated as a matter of mathematical fiat. A meaningless convention. — apokrisis

That's the way "5" is regarded in mathematics. It is the number five, a single unity. It is not regarded as "fiveness", it is regarded as a collection of five, a unit of five. If this were not the case, then 1, 1, 1, 1, 1, would have the same meaning as 5. But they do not have the same meaning, the former is five separate ones, while the latter is five united as one. So two plus three is equal to 5, but it is not the same as five. This is what I learned in grade school. Johnny has two apples, and Bobby has three apples. We describe this as a group of three (3), and a group of two (2). This is not described as five (5). But if we put them together (add them), then we have five (5). A group of three and a group of two is different from a group of 5.

The point being, that unity is implied by "5" when the symbol is used within the mathematical system. It is a mathematical fiat, but it is not meaningless convention it is a very useful convention. The fact that it is useful says something about the reality of unities.

Crucial to the notion of fiveness is that it is a permutation symmetry. The five parts that compose the whole can be swapped around without making any difference to their total number. The set has cardinality but not ordinality. And fiveness, in representing pure cardinality/complete lack of ordinality, thus can become itself an ordinal part. It can be placed after fourness and before sixness. — apokrisis

You call this "crucial", but I think it's irrelevant. What is at issue is the unity. It is self-evident that the members of the unity are treated as being "equal", or the same, because what is being dealt with here are values. Because 1 and 1 and 1 and 1 and 1 are all of the same value, and the entire system is a system of values, then they are the same. But the values united, as 5, is not the same thing as the five individual values, 1 and 1 and 1 and 1 and 1. Whether the values are united as one, or they are separate, makes a difference.

So here we now have the principle of indiscernibles - the idea that there are differences that don’t make a difference. A can now equal A to the measurable degree that someone agrees nothing essential is changed by the finer detail. — apokrisis

I think you misunderstand the principle of indiscernibles. It actually indicates the exact opposite of what you claim here. It indicates that we cannot disregard any differences in our designation of identity. Because it states that if there are no differences between what appears as two distinct things, then they are necessarily one and the same thing. So we must account for all differences or else we might mistakenly identify two distinct things as one and the same thing.

All through this thread, MU and creative show how badly metaphysics can go astray in presuming identity as brute fact rather than being relative to some principled degree of indifference. — apokrisis

Identity is a brute fact, that's exactly how the law of identity was stated by Aristotle, a thing is the same as itself. This means that any thing has an identity proper to itself, and this is not relative to anything.

the general sense of this would be that the Form of the individual thing exists in God's mind prior to it's material existence, such that the ideal Form is the cause of the thing's existence. — Metaphysician Undercover

So does God imagine trees in general, or the particular kinds of trees like oak and larch, or even each particular tree, such as all the individuals in an oak forest? Is there any limit to the particularity of his generality? Or alternatively, any limit to the generality of his particularity?

This is what I learned in grade school. Johnny has two apples, and Bobby has three apples. We describe this as a group of three (3), and a group of two (2). This is not described as five (5). But if we put them together (add them), then we have five (5). A group of three and a group of two is different from a group of 5. — Metaphysician Undercover

So do you think grade school philosophy of maths is sufficient for the questions raised here? Hmm, okay....

But the values united, as 5, is not the same thing as the five individual values, 1 and 1 and 1 and 1 and 1. — Metaphysician Undercover

And the reason for that unity is....some kind of continuity? They were all scattered and part, now you have collected them altogether so they can be tallied within the one act of counting? They are not a disunity. Or something like that. :P

Because it states that if there are no differences between what appears as two distinct things, — Metaphysician Undercover

You meant, no essential difference.

Identity is a brute fact, — Metaphysician Undercover

Of course it is. :)

So does God imagine trees in general, or the particular kinds of trees like oak and larch, or even each particular tree, such as all the individuals in an oak forest? Is there any limit to the particularity of his generality? Or alternatively, any limit to the generality of his particularity? — apokrisis

each mode of contingency, in turn, represents the possibility of something different from what we see in each subsequent mode of necessity. The very possibility that, in time, we can open the window or make some other alteration in reality is a case where we deal with the contingency of present time and our ability to bring about some new possibility. What this adds up to for universals is that as forms of necessity they represent the rules and guideposts that limit and direct possibility: Universals represent all real possibilities. Thus, what Plato would have called the Form of the Bed, really just means that beds are possible. What would have seemed like a reductio ad absurdum of Plato's theory, that if there is the Form of the Bed, there must also be the Form of the Television also (which is thus not an artifact and an invented object at all, but something that the inventor has just "remembered"), now must mean that the universal represents the possibility of the television, which is a possibility based on various necessities of physics (conditioned necessities) and facts (perfect necessities) of history. — Kelly Ross

Meaning and the Problem of Universals

So all ideas about things are mind dependent and some ideas about things are mind independent.

Seems legit. — apokrisis

Try again apo...

Mirror, mirror...

Cool. Thanks for the actual Aristotle stuff...

I'll check it out and get back with ya.

8-)

By designating it a "collection", you have declared that it is one whole, a collection. So it is fundamentally a whole. If you remove the designation of "collection", then you have a "multiplicity"... — Metaphysician Undercover

I cannot see any reason why you would think "collection" implies "one whole", whereas "multiplicity" does not.

For example take the collection ( in the sense of 'set') of things in this room; they do not form a whole in any but the associative sense that they happen to all be in this room. I could equally refer to them as ' the multiplicity of things in this room'. Multiplicities or collections need to be functional or relational unities in order to qualify as wholes.

What this adds up to for universals is that as forms of necessity they represent the rules and guideposts that limit and direct possibility: Universals represent all real possibilities. — Kelly Ross

It’s not hard to understand a constraints based approach to these hoary old chestnuts.

But I would add that universals represent the real possibility of a difference.

A universal is a generality and thus the potential for an act of particularisation or individuation. And a strong universal is talking about a dichotomous-strength difference. One that is bounded by mutually definitional limits.

A Pekingese is a dog. A dog is somewhat different from a wolf or fox, and rather more different than a rat or a cat. But the differences are weak or vague. A dog isn’t different to other animals in some absolute sense. So to call a dog a universal is rather a stretch.

A universal really ought to be speaking of properties we would predicate of being itself. The real business of metaphysics was working out the most basic possible divisions of nature - the symmetry breakings that could have got it going like discrete vs continuous, flux vs stasis, chance vs necessity, one vs many, matter vs form, etc.

So does God imagine trees in general, or the particular kinds of trees like oak and larch, or even each particular tree, such as all the individuals in an oak forest? Is there any limit to the particularity of his generality? Or alternatively, any limit to the generality of his particularity? — apokrisis

It is particulars which I was talking about. I think I went through this with you on another thread. It is necessary to conclude that the Form of each individual thing precedes its material existence. This is necessary because the existence of material things is contingent. When a material thing comes into existence, we have to account for the reason why that particular thing, and not some other thing is the thing which came into existence. Therefore the Form of the thing must be prior to the thing's material existence, as the reason why the thing is what it is. It is a formulation of the principle of sufficient reason. Your metaphysics of emergence seems to oppose the principle of sufficient reason.

And the reason for that unity is....some kind of continuity? — apokrisis

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I wouldn't equate unity with continuity at all, they seem quite incompatible. The symbol "5" refers to one discrete unit, or it means a group of 5 discrete individuals. I do not see how you can impose "continuity" on this concept.

I cannot see any reason why you would think "collection" implies "one whole", whereas "multiplicity" does not. — Janus

Collection; a group of things collected together. Multiplicity: a great number. Whole: all there is, entire, complete. Do you see how "collection" implies a finite group, with completion to that group, a whole. All there is of that group is in that collection. On the other hand, "multiplicity" implies no such wholeness, or completion, it may even be infinite.

For example take the collection ( in the sense of 'set') of things in this room; they do not form a whole in any but the associative sense that they happen to all be in this room. — Janus

Of course the collection forms a whole, it is the whole of "things in this room", all there is, entire, complete. Any set is a whole, by definition. Here's what Wikipedia says is Cantor's definition of set:

"A set is a gathering together into a whole of definite, distinct objects of our perception [Anschauung] or of our thought—which are called elements of the set."

I could equally refer to them as ' the multiplicity of things in this room'. — Janus

Yes, you could equally say that there is a multiplicity of things in the room, but that is to say something completely different. As a collection, or "set", the things in the room are referred to as one object. As a multiplicity, the things in the room are referred to as numerous objects.

A universal really ought to be speaking of properties we would predicate of being itself. — apokrisis

I'm focussing on the sense in which logical laws, real numbers, and so forth, comprise the laws of thought. They dictate or are constitutive of our ability to understand. The mistake is to then believe that therefore that they're existing things. They're not existent as phenomena - number can only be grasped by a mind capable of counting, but is the same for any such mind. That's why I think what is 'intelligibly real' is different to what is 'empirically real'. So it would be a mistake to say that the objects of mathematics are phenomenal objects; they're actually 'noumenal objects', i.e. real objects of thought.

In a recent discussion about objectivity as the criterion for 'what is truly the case', it occured to me that you have to be numerate to work out what is objectively the case. In other words, arriving at an objective result relies on numerical analysis to derive the generalised picture of whatever object of analysis you're dealing with. But numerical analysis is not objective insofar as it is purely deductive. You can validate your calculations against the results, but the calculations themselves are purely logical or deductive. And often enough a deductive result might even reveal some imperfection in the experimental set-up or the way the results were interpreted, again showing the predictive traction that mathematics provides.

It seems to me a valid distinction and a way of focussing on what the debate is about.