For me they apply to all forms, including fictional ones, and not only to that which is physical. That Harry Potter is not a unicorn is true - addresses a reality that stands in its own context of fictional concepts - this via the laws of thought, including the law of identity. — javra
We're right back to the initial problem. If we apply the law of identity to all forms, we see that universal forms cannot have an identity. And by that law, "identity" is something that "things" have, so we can use the law to exclude universal forms from the category of "things". This is the intent of that law, to distinguish two distinct types of form, and this is why Aristotle is properly called dualist. There is a categorical separation between primary substance and secondary substance. In your example, the "reality" you refer to is that of secondary substance. Not being "a thing", secondary substance has no identity.
"Oneness" can be readily defined as the state of being undivided, of being a whole. As to 1's infinite divisibility, remember that I take the concept of one to be a hylomorphic whole, a form endowed with constituents. But one constituent does not of itself equate to the given whole. A whole given is taken to be undivided as form, hence - for me at least - can be represented by the number 1. As one example, one horse can only be represented by the number "1", and not by any division. Yes, a horse can be divided into parts ad nauseam, all the way down into zero point energy. But its multiple parts are not the horse as a whole, which is in a state of being undivided. As a more abstract example, one grouping of two or more givens is, as a grouping, itself one whole. As one example, "animal" can be conceived of as a grouping of givens, yet the concept of "animal" is itself one whole - distinct, for instance, from the concept of "plant". — javra
The issue here, is whether the numeral 1 can represent a unified whole, which is not a physical object. In your example, I assume one horse is meant to be a physical object. As I explained when we refer to one horse, we are stating something about it, that it is one, so "one" is used as a property of that thing. Now you need to justify your assertion that the symbol "1" refers to a unified whole, independently of the object which is said to be one. My argument is that since there are numerous number systems, natural numbers, rational numbers, real numbers, imaginary numbers, and so forth, there are numerous different conceptions of "one", and no single mathematical system unifies these into one concept. Therefore one as a concept, is not a unified whole.
Again, the law of identity pertains to all conceivable givens, and not just those of physical reality. — javra
You don't seem to be grasping the fact, that when we apply the law of identity to forms which are other than material particulars, we are forced by the precept of that law, to exclude certain forms from the category of having an identity. This is because we can use language to refer things without any identity. You don't seem to be grasping the intent of the law, which is to prevent the situation where we assume that just because we can talk about it, it is a thing with an identity. You completely misinterpret the law if you claim that a fictitious thing has an identity, because the law of identity puts the identity of a thing into the thing itself, rather than what we say about the thing. The fictitious thing has no existence independent from what we say about it, therefore it cannot have an identity.
Sure, you can say that "the law of identity pertains to all conceivable givens", but unless you abide by that law, and acknowledge that some conceivable givens do not have an identity, then you step outside that law and you enter into hypocrisy.
One three-headed dragon - say one that a person saw in an REM dream - cannot at the same time and in the same respect be both green and not-green. This, to my mind, is so because it would then break with the law of identity. At any rate, a three-headed dragon holds an identity despite it not being a physical given. — javra
This is not a breaking of the law of identity, it is an issue with the law of non-contradiction. And, if we do not limit what we can logically predicate of a subject, to what is actually possible in the physical world, there is no need for a law of non-contradiction at all. If relevance to the physical world is completely unnecessary, why not allow all sorts of contradictions?
Hence, I maintain that awareness, and not that which is empirical, is fundamental to knowledge. — javra
"Awareness" implies being aware of something. I believe that being aware of the external is prior to being aware of the internal, and being aware of the external requires some form of sense. Of course this is a difficult issue to discuss logically because the terms are naturally slanted in my direction. To "be aware of" implies being informed, and this seems to refer to information from the external. But if we allow that information may come to us from an internal source, then ultimately the empirical is not fundamental. This is why Aristotle defined "the soul", as the first principle of actuality, or first form, of the living body. But if the soul is the first principle of actuality, and it is also the inner most thing, as well as the thing which is "aware", then there is nothing more inner that it could be aware of, and primary awareness is necessarily of the external.
Secondly, knowledge of metaphysical realities has nothing to do with whether or not these metaphysical properties occur. Same as with physical reality. Take a preadolescent child or a lesser animal as example. Their awareness operates via the law of identity without them having any knowledge of the law of identity. Or else take adult humans prior to Aristotle's formulation of the principle. They too where governed by the law of identity thought they had no propositional knowledge of it. — javra
I don't agree with this at all. I think it is incoherent, so perhaps I misunderstand. First, how could one have knowledge of something which is independent of whether that something occurs? If the something does not occur, yet someone is claimed to have knowledge of it, this is not knowledge at all. It is misunderstanding masquerading as understanding. Second, the law of identity is extremely difficult even for human beings to understand (as evidenced by this thread), it is set up as a defence against sophism. So I don't see how children or lesser animals could be applying the law of identity as a defence against sophism. I believe you continue to misrepresent "the law of identity".
That said, to me these metaphysical realities are intrinsic aspects of awareness - again, irrespective of whether the awareness addressed has propositional knowledge of them. We do not, and cannot, create them. We can only discover them. As such, we do not govern metaphysical realities, this just as we don't govern physical realities. We, as aware beings, are predetermined by the former. And, though in different ways, we are likewise determined - bounded/limited - by the latter. — javra
This is the pivotal point of how Aristotle applies the cosmological argument against Pythagorean Idealism (and some forms of Platonism). He analyzes what is involved in "discovering" such principles. Would you agree with Aristotle, that when the geometer produces geometrical constructs, and discovers geometrical principles, this is an act which is properly described as the mind actualizing the principles. The principles exist in potential, prior to being actualized by the mind.
Giving the game away, MU. No Platonist - or Aristotelian - worth his/her salt ink would say such a thing. — Wayfarer
You've already demonstrated how you misinterpret Aristotle. This is quite understandable because he has a massive volume of material and some is quite difficult. I was in the same position until I read Aquinas, and found that his interpretation of Aristotle was inconsistent with mine. Then I had to go back and read much of Aristotle (Metaphysics, On the Soul) all over again, some of which I had already read two or three times, to see what I was missing.
Have you looked at any of that material which I referred you to in Aquinas, how the human intellect is united with the body, and how this union with the body effects the way that the intellect understands? These principles are taken directly for Aristotle's "On the Soul". The intellect is a power of the soul, just like the other powers of the soul such as self-subsistence, self-movement, and sensation. As such, it operates through the means of the bodily organs. Therefore there is necessarily a privation in the knowledge which the human intellect holds. We can say that the bodily organs taint out knowledge because the intellect is dependent on them for the acquisition of knowledge.
If we ignore, or circumvent this reality, we can assert that the human intellect has direct access to the independent, immaterial Forms. But then we have no principles by which we might demonstrate that any claimed a priori knowledge is actually, truly deficient. We can understand this in Kantian terms. The a priori intuitions of space and time are responsible for the tainting of our knowledge. These are manifestations of the physical constitution of the human body, which serve as the conditions for any ideas, concepts, or knowledge in general. Unless we acknowledge that what Kant calls a priori intuitions are properties of the human body, and are therefore fallible principles rather than eternal, immutable, truths, we have no approach toward arguing the deficiencies of them.
Plato himself demonstrated the deficiencies of the theory of participation, which provides the ontological support for the independent Ideas of Pythagorean Idealism. This is why he turned to "the good" to support the existence of Ideas. Notice that it is "the good" which supports intelligible objects for Plato, not "the idea of good", as often represented. It is sometimes argued that Plato himself was not a Platonist, and this is due to the common misrepresentation of Plato's philosophy in modern discussion which produces the common notion of "Platonism". It is very important to approach this ancient philosophy, as much as possible, without bias, if one is intending to develop a true understanding.
It is the universal view of ancient philosophy that the 'empirical realm' which is taken by moderns as the sine qua non of the real, is in fact a treacherous illusion, which the hoi polloi do not see as their minds are contaminated by worldly passions, which blind them to the higher truths. The real can only be grasped by reason, and its truths are invariant and never subject to decay. Whereas everything in the sensory domain is subject to constant change and degradation through the ravages of time. — Wayfarer
In this passage you demonstrate significant ambiguity. The "empirical realm", if we use Kantian terminology, is phenomena. And this is how the mind apprehends the sensible objects. However, this refers to all ideas, and concepts which may be employed by reason toward apprehending truths. So all understanding is necessarily "a treacherous illusion" according to what you have stated. Therefore if a philosopher desires a true understanding, one must find a way out of this trap. The way out has been discovered by Plato, through the means of "the good", (implying final cause), and it has been developed by Aristotle, and carried forward by others like Augustine and Aquinas.
You ought to accept that "reason" refers to an activity, not a thing. It is carried out by the human intellect through the use of tools, ideas, and concepts. The human intellect is fundamentally deficient, necessarily so, because it is dependent on the human body. Therefore the ideas and concepts which the human intellect grasps are not the real, higher, invariant truths, which we might assume are out there somewhere. The things which the human intellect grasps receive their intelligibility relative to "the good", which is not necessarily the truth.