Below are my continuing efforts to understand some important parts of your article:

Replicability is a type, rather than a token, property. We can never replicate a token observation, only the same type of observation. — Dfpolis

Thus, the consciousness impasse is a representational, not an ontological, issue. — Dfpolis

The consciousness impasse, the root of The Hard Problem, is a conflation of type replicability with token replicability, the latter being an impossibility.

Since humans are psychophysical organisms who perceive to know and conceptualize to act, physicality and intentionality are dynamically integrated. — Dfpolis

The above claim posits conceptualize and intend within an equation. Moreover, it implies the integral-holism of rational action. Sentient beings acting rationally are never bi-furcated across the partition of conceptual dualism. Objectivist-Physicalist science breaks the natural coherence linking sentient beings to creation. The Hard Problem is thus a problem of scientific methodology.

Ignoring this seamless unity, post-Cartesian thought conceives them separately – creating representational problems. The Hard Problem and the mind-body problem both arose in the post-Cartesian era, and precisely because of conceptual dualism. To resolve them, we need only drop the Fundamental Abstraction in studying mind. — Dfpolis

Descartes, acting the part of the villain (albeit unintentionally), spurred conceptual dualism: a categorical partitioning of mind and body; Polis, for remedy, argues the return to Aristotelian integralism-holism with respect to physicality-intentionality.

This tells us Aristotle’s agent intellect is the sin qua non component of Polis’ proffered solution to The Hard Problem.

The agent intellect is the self who does introspection: pattern recognition in response to present intelligibility; logical manipulation of information: deduction; inference; interpolation; extrapolation; inferential expansion; information combinatorics, etc.

Matter and form are logically distinguishable, but physically inseparable, aspects of bodies – another one-to-many mapping from the physical to the intentional. — Dfpolis

Key Questions -- Aristotelian awareness contains a physical component: Does agent intellect = self? Does agent intellect as self possess form? Does awareness possess boundaries?

For Aristotle, form and matter are not things, but the foundations for two modes of conceptualization. — Dfpolis

Form and matter are two modes of organization, viz., matter = extension/extendability; form = context/configurability.

Thus, the concept <apple> is not a thing, but an activity, viz. the actualization of an apple representation’s intelligibility. — Dfpolis

Herein activity = physical-intentional complex, viz., present intelligibility ⇔ sentience.

The essence of representation is the potential to be understood. — Dfpolis

Representation = present intelligibility.

Dualism is incompatible with the identity of physically encoded information informing the intellect and the intellect being informed by physically encoded information. — Dfpolis

Sensible-object_sense-organ complex: a swirling yin-yang of integral_holism; no discrete bifurcation.

An agent intellect is necessary because we actually understand what is only represented in brain states. Since neural processing cannot effect awareness, an extra element is required, as Aristotle argued and Chalmers seconds. — Dfpolis

Does the sensible-object_sense-organ complex generate Aristotle’s phantasm?> Yes, however, like a computer; it processes data, but there’s no self who comprehends what it’s doing; there’s no self who comprehends the present intelligibility of the data.

Key Question -- What happens if:

Abstraction is the selective actualization of intelligibility. — Dfpolis

becomes:

Abstraction is the reductive actualization of intelligibility. — ucarr edit

This question is based on my supposition (as influenced by your claim re: replicability) abstraction can only be of type and never of token; replication of token, by virtue of its definition, must always be an identity and thus cannot be an abstraction. An idea can never hold identity with a thing-in-itself. As, per Aristotle:

‘For the sense-organ is in every case receptive of the sensible object without its matter’ — Aristotle

The sense organ takes in the attributes of a sensible thing (form), but not its hyle (potential). It is the potential of a thing-in-itself to map to myriad configurations -- all of them individual instantiations of existence -- that abstraction to the logical cannot emulate.

Key question – Is abstraction, a subtractive process, necessarily a reductive process?

Key question – Can agent intellect generate anything other than abstractions?*

*Consider the inevitable sensory overload from blooming creation sans abstraction.

The Hard Problem of consciousness signals the need for a paradigm shift. — Dfpolis

The physical-conceptual complex of Aristotelian animism is a corrective reversionist paradigm. However, this reversionism is not retrograde because it meshes cleanly and closely with much of scientific understanding evolving henceforth from antiquity.

Yet one could say that the mode of existence of x+1 changes, when x is determined. — Heiko

Yes.

What would be meant by thinking a number? — Heiko

It depends on how we are thinking of it. If we are considering a few objects, it would be thinking the count of the objects. If we are considering a string of digits, it would be the count represented by that string, even though we cannot imagine exactly that many objects.

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. — Wayfarer

Yes, that is mathematical Platonism. There is a related kind of extreme realism, which holds that measured values pre-exist measurement. This was promoted by Plato when he speculated that nature is made of numbers, geometric figures, and/or regular polyhedra. Opposed to all of these forms of extreme realism is Aristotle's view that numbers are abstractions based on our experience with counting and measuring operations.

We could not apply mathematical concepts to nature unless natural objects were countable and/or measurable, and so elicit numeric concepts. Thus, we know that nature can elicit such concepts. Since nature can, there is no need for a supernatural world of ideal mathematical objects to explain our knowledge of mathematics.

This is not forgetting "pure" mathematics, as most of it is abstracted from, and so generalizes, the structures of applied mathematics. The remainder is hypothetical.

The notion of mathematical Platonism also has psychological problems, as I said. How do we know its structures. In my experience, I need an example to truly understand mathematical concepts. I think this is the experience of most mathematicians. The concepts are then abstracted from the example(s). Second, our best understanding of how the mind works is that it uses neurophysical representations of contents. Mathematical Platonism requires a different, spiritual, mechanism that has not been observed or experienced. If mathematical thought were brain-independent, brain trauma would not diminish our mathematical ability.

If we are considering a string of digits, it would be the count represented by that string, even though we cannot imagine exactly that many objects. — Dfpolis

I'm confused. Does the number 10^1000 exist or not? It is written there, but you won't find or be able to think that many things. "Thinking the count" just shift the question one level higher.

I'm confused. Does the number 10^1000 exist or not? It is written there, but you won't find or be able to think that many things. "Thinking the count" just shift the question one level higher. — Heiko

It does not exist in virtue of being written. The string "10^1000" exists. It is not a number, but a symbol capable of eliciting a number concept, specifically, the concept <10^1000>. When no one is thinking <10^1000>, the number 10^1000 does not actually exist. Still, it is capable of being thought and so is a potential number.

The existence of a number does not depend on our being able to imagine the corresponding number of objects. It depends on actively thinking the concept and knowing what the concept intends -- knowing how to recognize an instance were we to encounter one. "How" is by counting to 10^1000. Knowing this does not require actually counting to 10^1000. This could be reformulated in terms of the successor operation.

We are able to do what you said for every number that can be written and we know that we can do it. How then are there numbers that do not exist?

PS: The last question itself looks like a contradiction...

Mathematical Platonism requires a different, spiritual, mechanism that has not been observed or experienced — Dfpolis

Is that really so? The IEP article I've referred to on the Indispensability Argument for Mathematics says:

Some philosophers, called rationalists, claim that we have a special, non-sensory capacity for understanding mathematical truths, a rational insight arising from pure thought. But, the rationalist’s claims appear incompatible with an understanding of human beings as physical creatures whose capacities for learning are exhausted by our physical bodies.

Another essay says

Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something [i.e. number] existing “outside of space and time” makes empiricists nervous.

I interpreted these objections as simply a reference to rational thought itself. How do we know the proofs of mathematics? Through pure reason, I was always taught. Why it can't be explained in other terms, is because it the source of explanation, not something itself in need of further explanation, so in that sense, not able to be reduced. I think that's what drives many of the objections - the faculty of reason transcends empiricist explanatory paradigms. As the first passage says, it's challenge to physicalism.

I agree that the depiction of Platonism as holding there is a kind of 'ethereal realm' of abstract objects - the 'Platonic heaven' - is a dubious concept, and that the Aristotelian view is more realistic. But I still believe that Aristotle insists on the reality of universals - that they're more than simply mental constructions or names. As James Franklin says:

Aristotelians agree with Platonists that the mathematical grasp of necessities is mysterious. What is necessary is true in all possible worlds, but how can perception see into other possible worlds? The scholastics, the Aristotelian Catholic philosophers of the Middle Ages, were so impressed with the mind’s grasp of necessary truths as to conclude that the intellect was immaterial and immortal. If today’s naturalists do not wish to agree with that, there is a challenge for them. ‘Don’t tell me, show me’: build an artificial intelligence system that imitates genuine mathematical insight. There seem to be no promising plans on the drawing board.

The consciousness impasse, the root of The Hard Problem, is a conflation of type replicability with token replicability, the latter being an impossibility. — ucarr

The argument about token replicability is intended to meet the objection that first person observations (aka introspection) is not properly scientific because it is private. I am saying that it does not matter if an observation is public or private. It is scientific if it is replicable -- if other observations of the same type produce the same results.

Then, given that 1st person observations are not methodologically problematic, we can add data from them to data previously allowed by the Fundamental Abstraction (3rd person observations). This allows us to come at consciousness from both ends: using 3rd person data to investigate neurophysical mechanisms and the content they encode and process, and the 1st person experience of awareness of content to see how that (merely intelligible) content becomes actually known.

The above claim posits conceptualize and intend within an equation. — ucarr

I am not trying to equate conceptualizing with intending (in the sense of committing to) a course of action. I am saying that conceiving courses of action is a causal step in voluntary behavior.

The rest of the paragraph grasps my point. Rational behavior seamlessly integrates intentionality and physicality.

The agent intellect is the self who does introspection: pattern recognition in response to present intelligibility; logical manipulation of information: deduction; inference; interpolation; extrapolation; inferential expansion; information combinatorics, etc. — ucarr

The primary function of the agent intellect is to make what was merely intelligible actually understood. I think the brain does a lot of the processing of data -- holograpically encoding similar stimuli, activating associated contents and so on. Still, as I explained in the article, judgements require awareness of contents, and so involve the agent intellect. So, while association does not require the AI, judgement does.

"Self" is a problematic term. I would say that the AI is the self in the sense of being the center of our subjectivity, but not in the sense of being who we are, because we are psychophysical wholes.

Key Questions -- Aristotelian awareness contains a physical component: Does agent intellect = self? Does agent intellect as self possess form? Does awareness possess boundaries? — ucarr

The physical component of awareness is the neurophysiological encoding of the contents we are aware of. The intentional component is the agent intellect by which we become aware of those contents.

I think the agent intellect has a form/actuality, since it is a determinate power. It actualizes intelligibility, not some other potential.

Boundaries? That is a hard question. Normally the AI is directed to contents encoded in our brain, but in mystical experience it seems to have some awareness of God, at least in His agency. (This is a very complex subject. A good start, but only a start, is the phenomenology discussed by Bucke, James and especially W. T. Stace.)

Form and matter are two modes of organization, viz., matter = extension/extendability; form = context/configurability. — ucarr

That is why "matter" is a terrible translation of hyle. Hyle is defined as "that out of which." It is a potential for new form. So, it could be something extended like bronze or clay, but it can also be axioms that can be formed into theorems, the tendency for a seed to become a mature plant, or the potential of a tree to be a piece of furniture.

Herein activity = physical-intentional complex, viz., present intelligibility ⇔ sentience. — ucarr

Intelligibility is what allows objects to be known. It is an object's capacity to inform a mind. The activity here is thinking of apples. When we stop thinking about apples, the concept no longer exists, but the brain encodes the content of the <apple> concept in our memory. So we "know" it in the sense of being able to think <apple> again without sensing an apple.

Representation = present intelligibility. — ucarr

Yes.

here’s no self who comprehends the present intelligibility of the data. — ucarr

Exactly.

Abstraction is the reductive actualization of intelligibility. — ucarr edit

That depends on what you mean by "reductive." If you mean that we reduce the amount of information, we do. I said "selective" because I wanted to make the point that we "shape" our understanding of reality by actively choosing what to look at, and what to ignore.

An idea can never hold identity with a thing-in-itself. — ucarr

In a way and in a way not. We can never have exhaustive knowledge on a divine paradigm. We can and do identify with the aspect of the object that is informing us, because the object informing me is identically me being informed by the object. These are two ways of describing the same event -- a case of shared existence.

Key question – Is abstraction, a subtractive process, necessarily a reductive process? — ucarr

I am not sure what you mean by "reductive."

Key question – Can agent intellect generate anything other than abstractions? — ucarr

Its prime function is knowing. It is because it does not know exhaustively that it produces abstactions. In mystical experience it knows something undefinable, and so not limited by a de-finition.

The physical-conceptual complex of Aristotelian animism is a corrective reversionist paradigm. However, this reversionism is not retrograde because it meshes cleanly and closely with much of scientific understanding evolving henceforth from antiquity. — ucarr

this reversionism is not retrograde ... — ucarr

I am suggesting that we add to, rather than replace, the contemporary view.

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

No, I'm asking how you conceive of diversity of appearance between individual human beings, under Aristotelian conceptual space, as anything other than each person having a different form?

Suppose each person is composed of different matter. It is the way that the matter is arranged which is the cause of the difference in appearance isn't it? And this is the form. Different instances of matter might look the very same, if it's not arranged in different ways. The arrangement, or order, is the form which the matter has, and that is what looks different.

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. — Fooloso4

That the man is skinny is accidental to the form of "man", but it is essential to the form of "skinny man". So, yes skinny or fat is a formal cause under that qualification. However, it is only accidental in relations to "man" and therefore not a formal cause at all without that qualification.

You are not paying attention to how Aristotle defines "incidental", or "accidental" causes. They are only formal causes in relation to the necessary qualification. In relation to "man", skinny and fat are accidentals therefore not formal causes in relation to this form. In relation to that specific qualification they are formal causes. That's why Aristotle explicitly stated in the passage I quoted, that without qualification chance is not the cause of anything.

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. — Fooloso4

No, I saw that you were hopelessly lost, and you failed to provide the proper reference for your quote. I read the whole section and did not find it. So I concluded that you were being dishonest in your quote. If you provide the proper reference for me, where he concludes that there is a different type of body which is the substratum to all other bodies, I'll take a look at the context and explain it for you. Until then, you are just wasting my time, because I know Aristotle well enough to know that this is not Aristotelian.

We are able to do what you said for every number that can be written and we know that we can do it. How then are there numbers that do not exist? — Heiko

"Being able" means that we have the potential to do so. Numbers are actual only while being thought, because they are abstractions and so instruments of thought. Your argument shows that they all have the potential to be thought, not that anyone is actually thinking them.

Numbers are actual only while being thought, because they are abstractions and so instruments of thought. — Dfpolis

Sorry, I still do no understand what you mean by thinking a number. We have explored a few different directions and approaches already. I am afraid I simply will not get it. I'll stay with a formal argument:
The set of non-existing numbers has to be empty per definition. They are a contradiction in themselves.

Some philosophers, called rationalists, claim that we have a special, non-sensory capacity for understanding mathematical truths, a rational insight arising from pure thought. But, the rationalist’s claims appear incompatible with an understanding of human beings as physical creatures whose capacities for learning are exhausted by our physical bodies. — Wayfarer

I am sure that some make this claim. A claim is not an observation or an experience.

Again, consider how we apply conclusions to concrete cases. In order to apply some mathematical theorem to physics, I have to recognize that the case I am considering instantiates some mathematical concept, <MC>. For that to happen, my case must be able to elicit the concept <MC>, because if it did not, I could not see that it was an instance of <MC>. But, if it can elicit the concept in application, there is no reason it cannot elicit the concept de novo. Finally, if nature can elicit a new mathematical concept, a Platonic source for the concept is unnecessary.

How do we know the proofs of mathematics? Through pure reason, I was always taught. — Wayfarer

That is not how we know the relevant concepts. In kindergarten or 1st grade, you learned to count pennies, oranges, apples or whatever until you were able to abstract the act of counting or enumeration from what was being counted. So, you learned number concepts from experience. The same with operations such as addition, subtraction, etc. Geometry came from land measurement after the floods of the Nile. The Greeks developed harmonic analysis to work out astronomical epicycles. The idea of a limit came from medieval physicists trying to define instantaneous velocity; vector decomposition from medieval architects working out the forces on their buildings. At a higher level, the examples from which we abstract are number systems, vector spaces and so on that were earlier abstracted from physical systems.

Of course, when we look at a finished, axiomatized system, it looks like it sprang whole from pure reason. It did not.

As the first passage says, it's challenge to physicalism. — Wayfarer

What is a challenge to physicalism is the existence of conceptual knowledge, and the consciousness required to produce it. Abstraction cannot be a physical act, as many concepts can be founded on one physical representation.

I still believe that Aristotle insists on the reality of universals - that they're more than simply mental constructions of names. — Wayfarer

They have to be for the application of universals to reality to work. The answer is moderate realism, first hinted at by Peter Abelard. There are no actual universals in nature, but there is an objective basis for us forming them. All the instances of a universal idea must be able to elicit that idea. That capacity (intelligibility) is an objective property, but it is not an actual idea.

What is necessary is true in all possible worlds, but how can perception see into other possible worlds?

Possible worlds talk is a terrible basis for approaching modality. Modality needs to be based on actual experience, which is our only means of knowing.

The scholastics, the Aristotelian Catholic philosophers of the Middle Ages, were so impressed with the mind’s grasp of necessary truths as to conclude that the intellect was immaterial and immortal.

I think this is bad history. The arguments for immortality I know are not based on our grasp of necessity.

Numbers are actual only while being thought, because they are abstractions and so instruments of thought. — Dfpolis

Sorry, I still do no understand what you mean by thinking a number. We have explored a few different directions and approaches already. I am afraid I simply will not get it. I'll stay with a formal argument:
The set of non-existing numbers has to be empty per definition. They are a contradiction in themselves. — Heiko

You know the difference between thinking of 7, as when you are thinking of the seven dwarfs or the seven days of the week, and not thinking of 7. That is what I mean by thinking of the number 7. Similarly, for all the other numbers.

The set of potential numbers is not empty. It is all the numbers that could possibly be thought. The problem is that mathematicians reflect on mathematical, not ontological, problems. That makes them sloppy when it comes to thinking about existence.

If the set of non-existing numbers has to be empty per definition, and the set of potential numbers (numbers that could be thought but are not) is not empty, and what is only potential does not actually exist, how could potential numbers be non-existing? Clearly, some distinctions are required.

You know the difference between thinking of 7, as when you are thinking of the seven dwarfs or the seven days of the week, and not thinking of 7. That is what I mean by thinking of the number 7. Similarly, for all the other numbers. — Dfpolis

The existence of a number does not depend on our being able to imagine the corresponding number of objects. It depends on actively thinking the concept and knowing what the concept intends -- knowing how to recognize an instance were we to encounter one. "How" is by counting to 10^1000. Knowing this does not require actually counting to 10^1000. — Dfpolis

I simply do not understand. There are so many stars in the sky, so many corns of sand on the beach....
Mind you, when you have 7 things, you have 6,5,... as well.

I read the whole section and did not find it. — Metaphysician Undercover

Out of concern that others might be reading this and be misled, I will give you the benefit of doubt and not assume that your inability to find it is due to willful blindness.

De Caelo

These are direct quotes from the text, not my interpretation.

These premises clearly give the conclusion that there is in nature some bodily substance other than the formations we know, prior to them all and more divine than they. (269a 30)

And the concluding sentence of Book 1, part 2:

On all these grounds, therefore, we may infer with confidence that there is something beyond the bodies that are about us on this earth, different and separate from them; and that the superior glory of its nature is proportionate to its distance from this world of ours. (269b 14)

Mind you, when you have 7 things, you have 6,5,... as well. — Heiko

Yes, but it is not the number that you can think of that is actual. It is the number you do think of.

The point is that numbers are not things. They are thoughts, specifically concepts. Thoughts only exist as long as someone is thinking them. If no one is thinking them, they remain possible thoughts, but not actual thoughts -- and if they are number concepts, they are possible numbers, but not actual numbers.

Consult a good dictionary. "Designating" is appointing, not judging. — Dfpolis

I don't really care how you want to say it. We could use "designate", "stipulate", "appoint", or whatever similar word, they're all very similar and also all forms of judgement. Judgement is to use reason in making a decision. The fact of the matter is, that we appoint things to the category which is their species, they do not just naturally place themselves into these categories, they are appointed to the appropriate categories

These properties are intrinsic to the organism, not willed by us in an act of designation. — Dfpolis

No, I think that this is false. The essential properties of the species are intrinsic to the concept, but all internal properties, are intrinsic to the organism. Every internal property of an organism is intrinsic to that organism, and essential to it being the organism which it is, as part of what makes it the very thing which it is. That's what the law of identity is all about. And that is also why members of the same species often have contradicting intrinsic properties. What is intrinsic to the organism is not necessarily essential to the concept. Those are the accidents.

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. — Dfpolis

I'm afraid I do not understand you, because this makes no sense to me. Form is the principle of individuation, it is the means by which we distinguish one thing, object, or entity, from another. It makes some sense to say "form is the principle of individuation of matter", because form is how we distinguish the material existence of one object as separate and distinct from the material existence of another object, but I can't make any sense of "Matter (stuff) is the principle of individuation of form". I believe it is the human mind which distinguishes one form from another (individuates), so I would need some further explanation to understand what you are proposing.

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. — Dfpolis

I think the best place for you to look for Aristotle's discussion of prime matter is Metaphysics Bk 8-9. In BK 8 he discusses how matter relates to form, as the potential for change. Change is the existence of contraries in the same thing at different times. At Ch4 he discusses the possibility that all things come from "the same original matter". And, he discusses how some differences are attributable to different matter, and some are attributable to different form. He also mentions things which have no matter, unchanging, eternal things.

Moving into BK 9, he questions "potency", and starts with a question concerning the possibility of one primary kind of potency which is the originative source of change. By Ch-8-9 he explains why actuality is necessarily prior to potentiality, thus excluding the possibility that prime matter is something real.

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

I do not see the equivocation., the possibility of "pure potency" is ruled out by the fact that actuality is prior to potency so there is no equivocation. The actuality which is prior to matter must be immaterial. Read Bk 8-9 of Metaphysics, mentioned above, to get a handle on how Aristotle conceives of the eternal, as actuality (form) without matter.

These are direct quotes from the text, not my interpretation.

These premises clearly give the conclusion that there is in nature some bodily substance other than the formations we know, prior to them all and more divine than they. (269a 30)

And the concluding sentence of Book 1, part 2:

On all these grounds, therefore, we may infer with confidence that there is something beyond the bodies that are about us on this earth, different and separate from them; and that the superior glory of its nature is proportionate to its distance from this world of ours. (268b 14) — Fooloso4

OK, now I see what you're talking about. Thanks for the exact reference, I must have been looking in the wrong section.

This is very consistent with what I've been telling you. Notice in the first quote he says "these premises give the conclusion...". He is discussing the argument of the Pythagoreans, and as I said, that argument proves the reality of eternal circular motion. Aristotle cannot refute that argument on its own terms. To refute that argument Aristotle needs to propose his own premise, that whatever is a body, is composed of matter, and by other means he demonstrates that anything composed of matter cannot be eternal. In the argument from the Pythagoreans, there is a distinction between natural body and unnatural body. This distinction is what Aristotle ends up rejecting, with the proposition that all bodies consist of matter.

Notice the latter quote, from the end of the section, he has replaced "some bodily substance" with "something beyond the bodies". This is very consistent with what he writes in Metaphysics Bk 8-9, which I refer to above and what I've been arguing. He speaks of an actuality which is prior to potentiality. It is not a body because being prior to potentiality it cannot consist of matter. So it is properly immaterial, eternal, and being an actuality it is a form. So he effectively replaces the Pythagorean idea of unnatural, divine bodies which are moved in an eternal circular motion, with an immaterial actuality or form, which is prior to all bodily existence.

If no one is thinking them, they remain possible thoughts, but not actual thoughts -- and if they are number concepts, they are possible numbers, but not actual numbers. — Dfpolis

I get the metaphorical idea but think it is not logically sound (at least, as presented).
What I understand of the philosophy of mathematics is, that as the idea of a non-existing number is self-contradictory, we have to ditch the law-of-excluded-middle (tertium non datur), to avoid having to conclude that all numbers exist.
Then one can argue, that having shown non-existing numbers are self-contradictory does not mean existence of all numbers is (positively) given. I am not aware that Aristotle did take that route; this is done by constructivist mathematics. I am no too familiar with their philosophical argumentation but can say they surely follow their ideas with logical scrutiny.

That is the problem with older writings: Maybe they give insights into "more initial", "more naive" concepts but the handiwork is not up to par with modern standards. Why would Aristotle's work contain better, more precise insights than the works of the generations following him who could start where he stopped? It would sound pretty reactionary to assume that things got worse over time.

I see those nilly-willy argumentations all over the place

There is no adaptive advantage ...

This is not how evolution works. We can say that advantageous properties have a tendency to reproduce and hence become more common, but this does not mean that all surviving properties are advantageous.

... in being aware of a physically determined role, because such awareness is impotent.

Which does not allow for any conclusion whatsoever. The whole consciousness-thingy could be an accident and not a supreme telos. In fact, if conscious thought was a necessary side-result of "biological computational" activity leading to some behaviour the empiric observation would exactly be what it is.

In my eyes this is two logical unsound conclusions in just one sentence - which I can not really explain happening. Maybe this is where the telos, the final cause is? But what have I done to you?

We could use "designate", "stipulate", "appoint", or whatever similar word, they're all very similar and also all forms of judgement. — Metaphysician Undercover

None are forms of judgement. They are all acts of will, not intellect. To judge is to see the truth of some connection, not to make an arbitrary decision.

The fact of the matter is, that we appoint things to the category which is their species, they do not just naturally place themselves into these categories, they are appointed to the appropriate categories — Metaphysician Undercover

No, things do not place themselves in species, nor was that my claim. I said that species are defined by objective commonalities. We decide which commonalities define a category, but, having decided that, whether a new object is an instance of the category is an objective question, with a right and wrong answer.

hese properties are intrinsic to the organism, not willed by us in an act of designation. — Dfpolis
No, I think that this is false. The essential properties of the species are intrinsic to the concept, but all internal properties, are intrinsic to the organism. — Metaphysician Undercover

This is a confused, as it is on the basis of intrinsic properties that an organism fits or does not fit into one of the categories we have defined. If it has 6 legs and a segmented body, it is an insect. If it has scaled wings, it belongs to the order lepidoptera, etc.

And that is also why members of the same species often have contradicting intrinsic properties. — Metaphysician Undercover

Nothing can have contradicting properties. Either it has a property, or if does not.

What is intrinsic to the organism is not necessarily essential to the concept. Those are the accidents. — Metaphysician Undercover

We agree. The accidental notes of comprehension are abstracted away in forming our species concept.

I'm afraid I do not understand you, because this makes no sense to me. — Metaphysician Undercover

If we have two things with the identical form, they are two (different) in virture of being made out of different instances of stuff. If we take a batch of plastic and make different kinds of things with it, they are not different because they are plastic, but because they have different forms.

I believe it is the human mind which distinguishes one form from another (individuates), so I would need some further explanation to understand what you are proposing. — Metaphysician Undercover

Yes, the mind distinguishes objects. The question is what aspect of the object does the mind latch on to in telling two objects with the same form, or with the same kind of matter, appart? The distinction is not purely arbitrary, but has an objective basis.

By Ch-8-9 he explains why actuality is necessarily prior to potentiality, thus excluding the possibility that prime matter is something real. — Metaphysician Undercover

I agree that the notion of prima materia is not well-founded, but potentials not being primary or actual does not mean they are not real. There is a present basis for furture form.

The actuality which is prior to matter must be immaterial. — Metaphysician Undercover

Of course. It has to be. If that is all you are saying, I think we have been misunderstanding each other.

These premises clearly give the conclusion that there is in nature some bodily substance other than the formations we know, prior to them all and more divine than they. (269a 30) — Fooloso4

A bodily substance is not immaterial.

This is very consistent with what I've been telling you. — Metaphysician Undercover

It is not, but believe whatever you need to. I will leave it there.

These premises clearly give the conclusion that there is in nature some bodily substance other than the formations we know, prior to them all and more divine than they. (269a 30)
— Fooloso4

A bodily substance is not immaterial. — Dfpolis

Right. What MU won't accept is Aristotle's claim that there is "some bodily substance other than the formations we know". Why? I don't know. Maybe an inability to admit he is wrong. Maybe some need for things to be "just so". In any case, I think it points to the reason Plato wrote dialogues. The character of interlocutors, that is, psychology, is not separate from philosophy.

What I understand of the philosophy of mathematics is, that as the idea of a non-existing number is self-contradictory, we have to ditch the law-of-excluded-middle (tertium non datur), to avoid having to conclude that all numbers exist. — Heiko

Don't you find abandoning logic irrational? There is no need to ditch excluded middle if we recognize that numbers are concepts and their "existence" is normally potential rather than actual. Still, just as a builder is a builder when he is not actually (but only potentially) building, so a number can "be" a number when it is not actually being thought. Still, there is a difference in mode between potency and act.

they surely follow their ideas with logical scrutiny. — Heiko

Logical scrutiny is of no avail if you have already abandoned logic.

Aristotle does not provide a full-blown philosophy of mathematics. Instead, he shows in numerous ways that Plato's theory of Ideas is irrational (which is why the Neoplatonists placed exemplar ideas in the mind of the logos), and he observes that quantity in nature is either discrete or continuous, and so either countable or measurable. Thus, it is potential, rather than actual, numbers.

We are left to conclude that actual numbers result from counting and measuring operations. Further, as a rule, when an agent actualizes a potential, the result can be partially determined by the mode of actualization (e.g. when material is formed into a work of art). So, there is every reason to expect that the result of a measuring operation will depend as much on the details of the operation as on the object measured. This expectation is borne out in special relativity and quantum mechanics, where measure numbers depend on how the measurement is done. You might think this would not apply to counting, but it does. In approaching a herd, we choose whether to count animals, eyes, legs, or whatever interests us. So, counts do not pre-exist counting operations.

Maybe they give insights into "more initial", "more naive" concepts but the handiwork is not up to par with modern standards. — Heiko

To say that older work adheres to the laws of logic is hardly a criticism. Increased comprehension counts in a theory's favor. It is much better to preserve logic while explaining mathematics than to abandon logic while trying to explain it. I already showed that the idea that mathematics is the work of pure reason is historical nonsense. You are pointing out that it also involves logical nonsense.

When a general principle (such as Excluded Middle) is abandoned in one case only, that is Special Pleading -- a common fallacy. To abandon such a principle, one needs to show its intrinsic weakness. This can be done by deep analysis, or by providing other examples of its failure.

There is no adaptive advantage ...

This is not how evolution works. We can say that advantageous properties have a tendency to reproduce and hence become more common, but this does not mean that all surviving properties are advantageous. — Heiko

Quite true. Still, it shows that the surviving property is not explained by the evolutionary process, which was the claim I was arguing against. On the other hand, if consciousness is causally potent, then conscious organisms could have a reproductive advantage and be selected by evolution.

... in being aware of a physically determined role, because such awareness is impotent.

Which does not allow for any conclusion whatsoever. — Heiko

On the contrary, it shows exactly what I said above: that consciousness, whatever its origin, cannot be selected unless it can do something that allows it to be selected.

The whole consciousness-thingy could be an accident and not a supreme telos. — Heiko

You are attacking a straw man. I did not argue that it was "a supreme telos," or speculate in any way as to the origin of consciousness. I merely accepted consciousness as a contingent fact of nature.

If you want to argue that it "could be an accident," you need to define "accident" and explain how an intentional effect can instantiate that definition when physics (the presumed source of the "accident") has no intentional effects.

In fact, if conscious thought was a necessary side-result of "biological computational" activity leading to some behaviour the empiric observation would exactly be what it is. — Heiko

Sadly, we know that it is not "a necessary side-result of 'biological computational.'" If it were, we would necessarily be conscious of all biological computation, and, as I showed in my article, we are not.

The character of interlocutors, that is, psychology, is not separate from philosophy. — Fooloso4

I agree. I got thrown off the Aquinas list some years ago for making exactly that point, and refusing to retract it.

Don't you find abandoning logic irrational? There is no need to ditch excluded middle if we recognize that numbers are concepts and their "existence" is normally potential rather than actual. — Dfpolis

But you are contradiction yourself. Try to tell me what it _is_(contradiction number one) that is "potentially available" (we can predicate those potentialities that cannot exist as they would then be actual countable things) but not "actually there". What are you even talking about? That makes absolutely _no_ sense: You are doing for your potentials what you deny for the numbers. In your view the potentials are readily "at-hand" when needed to become numbers but - for some not understandable reason - not the numbers themselves.

Logical scrutiny is of no avail if you have already abandoned logic. — Dfpolis

Logical calculus has made serious progress over time. We can choose axioms as needed.

We are left to conclude that actual numbers result from counting and measuring operations. — Dfpolis

Which is where you should stop - here the speculation over "potential existing numbers" is completely absent. That is what sends you right to the platonic number space.

Further, as a rule, when an agent actualizes a potential, — Dfpolis

Right here. What get's realized? Where are those potentials? Are they really there / do they exist? Are you sure about them?

... in being aware of a physically determined role, because such awareness is impotent.

Which does not allow for any conclusion whatsoever.
— Heiko
On the contrary, it shows exactly what I said above: that consciousness, whatever its origin, cannot be selected unless it can do something that allows it to be selected. — Dfpolis

But why would it _need_ to be selected to be present? This is why the follow-up is not a straw-man in your case.

If you want to argue that it "could be an accident," you need to define "accident" and explain how an intentional effect can instantiate that definition when physics (the presumed source of the "accident") has no intentional effects. — Dfpolis

Say evolution wants fire for the warmth but not the smoke but yet has to live with it. Things can be perceived in different ways because they have different effects.
You can imagine how an animal or another human would feel because the experience is linked to the body. You can even imagine to be someone else but yet cannot imagine to be your own self?

Sadly, we know that it is not "a necessary side-result of 'biological computational.'" If it were, we would necessarily be conscious of all biological computation, and, as I showed in my article, we are not. — Dfpolis

I don't see the necessity. My computer and the software it is running has no reflection on all the transistors that change state, yet those generate output on the screen which is the effect of those state-changes.

For what purpose would you need to argue with evolution theory in first place?

These premises clearly give the conclusion that there is in nature some bodily substance other than the formations we know, prior to them all and more divine than they. (269a 30)
— Fooloso4

A bodily substance is not immaterial. — Dfpolis

Wouldn’t the claim of the existence of such a bodily substance be an empirical claim? If it’s a substance, then either it can be detected by scientific means, or it can be declared a false hypothesis.

Try to tell me what it _is_(contradiction number one) that is "potentially available" (we can predicate those potentialities that cannot exist as they would then be actual countable things) but not "actually there". What are you even talking about? — Heiko

Sure, easily. A set of 7 sheep has the potential to yield a 7 count, and so actualize the concept <7> in a person counting them. Still, the set of sheep having cardinality 7 is not the counting person having the concept <7>. So, the number can be potential (having a basis in the set of sheep), but not actual if no one thinking the count.

In your view the potentials are readily "at-hand" when needed to become numbers but - for some not understandable reason - not the numbers themselves. — Heiko

There is a difference between being countABLE (your "readily 'at-hand'"), and actually counted, eliciting an actual number concept in the person counting. Do you deny the difference?

Logical calculus has made serious progress over time. We can choose axioms as needed. — Heiko

No, what has changed over time is the meaning of "logic." Classically, logic was the science of correct (salva veritate) thinking. Modern logic is not concerned with thought, but with symbolic manipulation. Its concept of truth is an arbitrary value, not adequacy to reality.

The result of confusing these

Which is where you should stop - here the speculation over "potential existing numbers" is completely absent. — Heiko

two meanings can be seen in your claim. We cannot arbitrarily choose the thought processes that preserve truth. Some always do, and recognizing them is the basis of classical logic. Choosing to include or exclude an axiom cannot possibly change which thought processes preserve truth as adequacy to reality, and which do not. All it can do is define (hopefully) self-consistent abstract structures. I say "hopefully," because we cannot know most are self-consistent.

Boole wrote The Laws of Thought, as though thought was ruled by logical laws. It is not. We see illogical thinking everyday -- some of great consequence. There is no law that prevents me thinking the square root of 2 is a rational number, or that a circle can also be a square. Classical logic tells us how we must think if we want our thought to be consistent with reality. Because of this, the laws of classical logic reflect the nature of being. For example, the law of non-contradiction is based on the ontological fact that nothing can be and not be in one and the same way at one and the same time. If we think otherwise, our thought will not be applicable to being, and useless in life and in science, both of which are constrained by reality.

Finally, the exploration of symbolic structures, whether mathematical or "logical," has not dispensed with Aristotelian logic. Every application of a theorem involves a syllogism in Barbara. Suppose we have a theorem "A -> B". To apply it, we must recognize that we are dealing with an instance of A. So, the syllogism is:
All As are such that B follows.
The present case is an A.
The present case is such that B follows.

We are left to conclude that actual numbers result from counting and measuring operations. — Dfpolis
Which is where you should stop - here the speculation over "potential existing numbers" is completely absent. — Heiko

No, the countability and measureability (potencies) of the natural world were the basis of this conclusion -- reread what preceded this.

What get's realized? Where are those potentials? Are they really there? Are you sure about them? Contradiction! Fubar!! — Heiko

Once more: The countability and measureability of nature. Are you denying that discrete objects can be counted? Or continuous quantities measured? I am not sure what you are objecting to.

But why would it _need_ to be selected to be present? — Heiko

Again, I am discussing the claim that consciousness evolved. If you do not think it evolved, you can skip my response to that claim. I am content to say that it is present, but did not evolve.

Say evolution wants fire for the warmth but not the smoke but yet has to live with it. Things can be perceived in different ways because they have different effects. — Heiko

Of course, but that does not provide a naturalistic explanation. It just says we have no explanation, and I agree: there is no naturalistic explanation, so consciousness is ontologically emergent.

I don't see the necessity. — Heiko

"Necessary" was your term:

if conscious thought was a necessary side-result of "biological computational" activity leading to some behaviour the empiric observation would exactly be what it is. — Heiko

My computer and the software it is running has no reflection on all the transistors that change state, yet those generate output on the screen which is the effect of those state-changes. — Heiko

Yes. The difference is that we can completely explain everything we know about computers without assuming they are conscious, but we cannot do so for humans.