Is that (that it didn't remove your guess) a reason not to switch? Note that the computer in this case knows, as monty Hall does, what the right answer is, and always removes wrong answers. — unenlightened

For the millionaire scenario, the computer randomly removes two wrong answers from the set of three wrong answers. That selection is statistically independent of your (secret) guess, so the remaining two answers are equally probable.

I looked at the link. As far as I can tell with a cursory skim, it doesn't talk about two identical particles being in the same place at the same time while remaining two separate particles. — petrichor

It says that bosons can share the same quantum state (which includes position). Fermions can't share the same quantum state but they can still share the same position if some other property differs (such as spin state).

Note that there are interpretive issues about what position entails given Heisenberg uncertainty. But the general point is that two particles can be indistinguishable in principle and it is this feature that leads to quantum interference effects. For a nice example of this with two particles, see the Hong-Ou-Mandel effect (where the two particles enter the beam splitter at the same time and produce interference effects).

Physical objects cannot occupy the same space at the same time. Things that can occupy the same space at the same time are not called objects. It's as simple as that. — SophistiCat

Fundamental particles can occupy the same space at the same time. See identical particles.

I, at least, consider particles to be physical objects. Here's the conventional usage:

1. A material thing that can be seen and touched.

1.1 Philosophy A thing external to the thinking mind or subject. — Object (Lexico)

And here's the crucial part. If the computer, who randomly opens one of the other two doors you didn't choose, reveals the car, the program terminates right there, and starts again. If on the other hand, the computer opens one of the other doors, and by chance it is a goat, the program continues and you are given a choice to switch or not.

My question is, in this simulation of the Monty Hall show, with this extra random variation where the computer doesn't "know" which door contains the goat or car, but reveals a goat in one of the other doors by chance, is the probability still 2/3 that the other unopened door contains the car? Or does the probability change because of the extra random process? — Purple Pond

As I see it, you should be indifferent to keeping or switching in the modified game. My reasoning:

If you initially correctly pick the door with the car, then the computer will continue the game. However there is a 2/3 probability that you are initially incorrect. In those games, there is a 1/2 probability that the computer will open the door with the car and the game will be terminated. Then the same logic applies to the rerun games.

So if you play a game where you are asked to keep or switch, then that is one of the non-terminated games. Out of 300 games, you will (on average) be correct on 100 games that therefore continue, incorrect on 100 games that continue, and the remaining 100 games will be terminated and replayed. Of those replayed 100 games, you will be correct on 33, incorrect on 33, and 33 will be replayed. In this way, you will approach being correct on 150 games and incorrect on 150 games.

I would like comments on the following statements. It is about change.

Statement 1:

A circle is never the same as anything that is not a circle. Therefore, a circle is something that is never anything that is not a circle.

Statement 2:

Something existent is never the same as something non-existent. Therefore, something existent is something that is never non-existent. — elucid

As you probably know, accounting for change was a major issue for the ancient Greek philosophers. As Parmenides (and Plato and Aristotle) would have agreed, a circle never is and never can become a non-circle. Think of Plato's eternal and unchanging Forms.

Instead on Aristotle's account, it is particular things (form/matter composites) that are the subject of change. For example, a circular (inflated) car tire can become a non-circular (deflated) car tire. As the example shows, it is the car tire, a particular existent, that is the subject of change, not the form.

I'm going to do some reading and get back to you if that's alright. — Sunnyside

Sure. You may find this comparison of the various interpretations useful, of which de Broglie-Bohm theory and Many Worlds are the main deterministic interpretations.

You're saying measurement is non-deterministic, I take that to mean random, so maybe I'm asking the wrong question. Tell me if I've got this right: Everything up to a measurement is deterministic, then before a measurement the path splits and there are multiple versions of the same particle, then a measurement happens totally randomly and one of those particles becomes "real". Is that about right? — Sunnyside

Not quite - whether there are multiple versions and what is considered real is an interpretive issue. What is universally agreed on is more like this:

If you send a photon through a beam splitter, the quantum state evolution (according to the Schrodinger equation) is:

(1) Photon enters beam splitter
(2) Photon transmitted + Photon reflected

That's deterministic, with state (2) represented as a superposition of two simpler states. When the photon is measured at a detector, you observe just one of those simpler states, e.g.,

(3) Photon reflected

The Schrodinger equation doesn't give (3). Instead the Born rule predicts (3) with 50% probability. The measurement problem is concerned with what (2) means and what measurement involves such that (3) is observed.

I'm not a scientist but Newtonian physics applies at the quantum level. If I'm correct that means particles, their position and velocity, are deterministic in behavior. — TheMadFool

Classical physics and quantum physics are incompatible descriptions of the world. Though classical physics provides a good approximation in many macroscopic scenarios.

While a quantum state evolves deterministically (as a superposition of states), measurement is non-deterministic (returning a single definite state per the probabilities given by the Born rule). Explaining the latter given the former is known as the measurement problem.

Knowledge of initial states of particles can be used to predict their properties at some other time in the future.

We're physical, our brains are physical i.e. we're all made up of particles. That implies our brains are deterministic machines if you'll allow me to use that word.

If that's the case then freewill shouldn't exist. It's existence would violate the laws of nature and it would be a true miracle. This can't be. — TheMadFool

I think of it this way. Suppose Alice prefers tea to coffee. If Bob models her preferences accurately, then he will make successful predictions about what she chooses to drink. Yet his model is simply descriptive. The model does not determine what she will drink - Alice does.

Similarly scientists can construct equations that describe the behavior of particles and, in principle, any natural system, including human beings. Yet those equations, even if deterministic, are descriptive not prescriptive.

As long as human choice is considered to operate within the context of natural causality, then there is no miracle or unresolvable conflict. Human beings can make choices based on their preferences AND be described mathematically. If there is a conflict, then it is the math that needs to change to reflect the observed behavior - the math is not prescriptive.

Your post provides a good description of a simple system where it is reasonable to talk about what I have been calling "empirical determinism." My main point, however, is that as a system becomes more complex, it quickly becomes practically impossible to predict it's outcomes empirically. At that point, it no longer makes sense to talk about the system as determined in that sense. — T Clark

OK, you're deflationary about determinism. Which is to say we either have equations and procedures to make predictions about a system, or we do not. There's no deeper story.

It's a pragmatic approach that similarly deflates/dissolves the issue of free-will and determinism. We can make predictions (she will drink tea rather than coffee) and give ordinary causal explanations without needing to posit metaphysical explanations.

By the way, I have been making the distinction between empirical and probabilistic determinism and predictability. I have a feeling those are not the right terms to use. Are they ok or are their others I should be using? — T Clark

Is that your billiard balls/coin flips distinction? That seems to be just an issue of precision. You can set up a robot to flip a coin to always land heads. Conversely if the billiard balls are small enough (or isolated enough) then probabilistic quantum effects will be observed.

In the OP and subsequent posts, I laid out specific meanings for "determinism" and "predictability" and the kinds of situations to which I think they apply. You seem to be using different definitions than I did. — T Clark

I think the example of the light switch/light bulb system captures the definitions you gave in your opening posts. That is, determinism (or non-determinism) relates to the system itself while predictability relates to an agent's knowledge (or information about) the system.

How would you summarize your definitions if you understand them to be different to that?

How is determinism different from predictability. — T Clark

To answer that question, I think it's useful to consider a simple system and how it would be represented.

Consider a light switch that is connected to a light bulb. The state of the bulb (lit or unlit) is determined by the state of the switch (on or off). With that specification, the state of the bulb is also predictable. That is, if we know the state of the switch then we can predict the state of the bulb with certainty.

In this scenario, the term "determined" relates to just the system itself whereas the term "predictable" relates to an agent's knowledge of the system.

Some observations:

1. The claim of determinism for the system depends on particular assumptions. For example, there must be power present, the circuit must not be broken or subject to interference, the bulb won't store power, etc. That is, we're considering the system in a formal (or idealized) sense.

2. The example system is a closed system - the output (bulb state) is fully specified by the input (switch state).

3. We could introduce a randomizing component into the circuit such that the bulb is randomly lit when the switch is turned on. If the randomizing element is an input to the system, then the system is both non-deterministic and unpredictable. If the randomizing element is internal to the system but its mechanics unknown, then the system would be deterministic but unpredictable.

4. At a more detailed level of representation, the system may have non-deterministic components. For example, there are molecular quantum events that do not affect the predictability of the high-level operation. Thus the system can be non-deterministic yet predictable.

What Aristotle has argued, consistently throughout Metaphysics, is that the form of the particular is necessarily temporally prior to material existence of that particular, as a cause of it. — Metaphysician Undercover

Going back to this. Is your claim that this temporally prior form is itself separate from particulars? If so, then why would that not be a Platonic form on your view?

My own view is that the unmoved mover should be understood in terms of Aristotle's hylomorphism and naturalism and not in Platonic terms. That would be consistent with his rejection of Plato's forms.
— Andrew M

Interesting to consider how that might work. — AJJ

So Aristotle gives a concrete example in Physics Book 8 where he describes a man who moves a stone with a stick.

Consider this in terms of a golfer hitting a golf ball with a golf stick. The golf stick is the moved mover of the golf ball (the efficient cause). In turn, the golfer's hand is the moved mover of the golf stick. But what causes the golfer to move his hand? Aristotle identifies a different kind of cause - a final cause. The golfer moves his hand because he desires to play golf. Thus he is the unmoved mover that causes the golf ball to move.

But note also that the golfer's hand moves, which is a part of his body. So he is the compound of a moved mover and an unmoved mover (in different causal senses). In this scenario, it is the "unmoved mover" explanation that finally grounds the golfer's activity. It is this intentional aspect of the golfer (his purposes, thoughts and desires) that explains the motions of the golfer, golf stick and golf ball throughout the game.

That is the kind of concrete and observable scenario that Aristotle generalizes from to explain all activity (or change) in the universe as by an unmoved mover in terms of final cause. In both the specific and universal contexts, the locus of causality (in terms of Aristotle's four causes) are the natural particulars.

I like the Aristotelian emphasis on the material, as opposed to the Platonic notion of the world being something we must ascend from; but I’m inclined also to think the world is an imitation of things higher than it - seems there’s enough ambiguity to hold to both approaches. — AJJ

A subtle but important point: Aristotle's hylomorphism is not merely material, nor merely ideal. Instead it combines both aspects in the natural particulars that we observe.

Aristotle was a student of Plato, he was not educated in modern naturalism. — Metaphysician Undercover

For Aristotle, knowledge comes from experience in the natural world.

Aristotle's immanent realism means his epistemology is based on the study of things that exist or happen in the world, and rises to knowledge of the universal, whereas for Plato epistemology begins with knowledge of universal Forms (or ideas) and descends to knowledge of particular imitations of these. — Aristotle - Wikipedia

What Aristotle has argued, consistently throughout Metaphysics, is that the form of the particular is necessarily temporally prior to material existence of that particular, as a cause of it. — Metaphysician Undercover

Perhaps you could specifically quote where you think Aristotle argues this. If you simply mean that there is potential for things in prior (actual) states of the universe, then that is not at issue. But neither does that imply dualism.

What he describes here is a problem with locating the unmoved mover as within the universe. He says that things closest to a mover move the quickest, but with circular motion the quickest is the circumference. This leads us toward the conclusion that the unmoved mover is not within the universe. — Metaphysician Undercover

Aristotle doesn't say or imply anything about the unmoved mover not being in the universe. You're ignoring his natural cosmology.

I think the question would have to be asked, then, why Aristotelian philosophy is not nominalist. Because nominalism denies that 'forms' or 'types' have any reality outside the things which instantiate them; — Wayfarer

No, it is Aristotle's immanent realism that denies that 'forms' and 'types' exist in separation from particulars (though they can be considered separately).

Whereas nominalism denies that 'forms' or 'types' have any reality outside the people that name them. Ockham wrote, "I maintain that a universal is not something real that exists in a subject ... but that it has a being only as a thought-object in the mind".

I’ve been confusing terms - I thought the active intellect was another way of describing the unmoved mover. — AJJ

While they are given independent accounts in Aristotle's writings, some commentators do consider them to be equivalent and that is one of the interpretive controversies.

So it seems to me on Aristotle’s view that universals must be ultimately grounded in the unmoved mover, rather, which is why I don’t fully understand the rejection of Plato’s Forms. — AJJ

Aristotle rejected Plato's theory of forms and replaced it with his own hylomorphic theory. But per Aristotle's description, the unmoved mover doesn't seem to be a hylomorphic or natural being. Which puts the unmoved mover in apparent tension with Aristotle's otherwise consistent hylomorphism and naturalism. So interpretation here is also controversial with different commentators providing a range of Platonic and naturalist accounts.

My own view is that the unmoved mover should be understood in terms of Aristotle's hylomorphism and naturalism and not in Platonic terms. That would be consistent with his rejection of Plato's forms.

Although it does still puzzle me why Aristotle would ground abstractions only in the world when the world is grounded in the active intellect - can you tell me where in particular Aquinas or others wrote about that? — AJJ

The world isn't grounded in the active intellect for either Aristotle or Aquinas. Both were realists about the world (which contained concrete particulars) and moderate (immanent) realists about universals. Aquinas says:

It is necessary to postulate a power, belonging to the intellect, to create actually thinkable objects by abstracting ideas from their material conditions. That is why we need to postulate an agent intellect. — Thomas Aquinas and the Early Franciscan School on the Agent Intellect

This SEP article on active intellect is also useful and highlights the nature of the controversies. Regarding interpretation, "The first and most consequential fault line, then, concerns whether De Anima iii 5 should be taken as characterizing the human mind or the divine mind." As indicated above, Aquinas argued for the "human mind" view.

"the things nearest the mover are those whose motion is quickest, and in this case it is the motion of the circumference that is the quickest: therefore the mover occupies the circumference." (Physics 8.10.267b.7-8)
— Andrew M

However, he also says it is 'clear that it is indivisible and is without parts and without magnitude' (which is the basic argument of the whole section); so rather difficult to imagine the sense in which the unmoved mover is 'located within the universe'; for without parts or magnitude, how can something be located? — Wayfarer

Just my quick thoughts here, but if the unmoved mover is identified with the universe itself then, from the universe's frame of reference, it would have no location. Location (like time) would have no meaning in that reference frame. However from each of our reference frames, the universe does have parts and magnitude.

I look at this as contradictory. An entity is by definition a particular. I find this to be a common problem with modern day philosophers, they define "dualism" in such a way as to make dualism impossible, then they frown on dualism as if no rational individual would ever accept it. — Metaphysician Undercover

The context here is Aristotle's hylomorphic particulars. Aristotle rejected the existence of anything separate from hylomorphic particulars - and specifically Platonic Forms.

I admit that the no-boundaries theory of the universe is similar to Aristotle's eternal circular motion, but it does not contain the final cause, which is an essential part of "unmoved mover", as the cause of the motion. This is why Aristotle is very clearly dualist, the cause of motion of material objects is a 'thinking'. — Metaphysician Undercover

The thinking is not a Platonic Form, it is the thoughts of the unmoved mover. If the unmoved mover is the universe itself then the universe is also the final cause of the changes that occur within it (in any observer's reference frame). Also scientific theories wouldn't normally reference a final cause as they are usually represented in a Humean framework rather than an Aristotelian framework - a separate philosophical issue to dualism. Sean Carroll briefly discusses the theory framework choice here:

The difference between the two conceptions is that the former [Aristotelian view] naturally associates things that happen with a deeper kind of reason why they do, while on the latter [Humean] view every “why” question is definitively answered by “the dynamical laws of nature and the initial conditions of the universe. — Why Is There Something, Rather Than Nothing? - Sean Carroll

The "universe" is not necessarily the precondition for particulars. We observe particulars, and we can conclude the reality of particulars, from empirical evidence, but we need a principle of unity to conclude that all the particulars are part of a whole, "the universe". — Metaphysician Undercover

A reference frame provides this (see the experiment I linked earlier). The universe is an inseparable and unchangeable unity (in the universal frame of reference). Whereas in our frame of reference, the universe is separable and changeable.

I read The Theological Origins of Modernity (Michael Allen Gillespie) a few years back. One of the underlying arguments of this book is precisely that modern culture has tended to equate the cosmos itself with the totality of existence, therefore, in some sense, the cosmos ('all there is', according to Carl Sagan's well-known aphorism) has displaced God. — Wayfarer

That may have been fine with Aristotle who had a natural theology and located his unmoved mover within the universe. As he wrote, "the things nearest the mover are those whose motion is quickest, and in this case it is the motion of the circumference that is the quickest: therefore the mover occupies the circumference." (Physics 8.10.267b.7-8)

(Although the remark about time being observer-dependent seems a re-statement of the claim made in the post about Andrei Linde above.) — Wayfarer

Yes, they are talking about the same thing.

Notice in the blog post above, it is said of the 'unmoved mover' that 'For something to be eternal, it is neither created nor destroyed, but always has and always will exist.' I wonder if there is anything corresponding to this, on a very high level, in current scientific discourse? Because it seems, if the big bang cosmology is true, that it doesn't apply to the Universe as a whole. — Wayfarer

The Wikipedia page for the Big Bang has a discussion including the emergent time option ("Certain quantum gravity treatments, such as the Wheeler–DeWitt equation, imply that time itself could be an emergent property.")

Also Sean Carroll canvasses various options and some of their philosophical implications in this paper (for the forthcoming Routledge Companion to the Philosophy of Physics).

Are Forms and forms thought to be incompatible? Can’t material objects be manifestations of Plato’s Forms, while also having form as an essential metaphysical component as conceived by Aristotle? I don’t know their metaphysics well, but at a glance it seems to me that both accounts must (if they are at all) be true; my considerations being that in material objects matter and form are inseparable, and the forms that matter takes must (since both accounts posit a divine intellect) have existed prior to - and so also be separate from - their instantiations. Maybe this is all obvious, but it’s not clear to me why you’d adopt one view but not the other. — AJJ

Yes they are thought to be incompatible since Aristotle explicitly rejected Plato's theory of forms [*]. The difference is that Platonic Forms are independent of (or separable from) particulars whereas, for Aristotle, form and matter are correlates that are not separable from particulars.

Consider a typical abstract object such as a number or triangle. For Aristotle, these abstract objects are ultimately grounded in concrete particulars, not in a Platonic realm. As Aristotle wrote, "The best way to conduct an investigation in every case is to take that which does not exist in separation and consider it separately; which is just what the arithmetician or the geometrician does." (Aristot. Met. 13.1078a) [italics mine]

--

[*] As you are probably aware, there is much disagreement over what that rejection entailed. Some Neo-Platonist and Christian thinkers (such as Aquinas) argue that Aristotle didn't really (or fully) reject separability, with the unmoved mover and active intellect put forward as examples of this.

What does "dualism" mean to you? — Metaphysician Undercover

Dualism assumes there are entities that have a reality independent of particulars. In this context it's the Platonic Forms (which Aristotle rejected).

This position, that the actuality of formal existence is prior to potentiality of material existence is reinforced by the logic that if there was ever a time when there was only potential without anything actually, there would always be potential without anything actual, because that potential could not actualize itself. However, what we observe is that there is actual existence. Therefore it is necessary that the actual is prior in time to the potential, in an absolute sense. — Metaphysician Undercover

Yes, but as an actual particular, not as an independent form. Adapted to a modern scientific context, the universe is that grounding existent and, in its reference frame, is the unmoved mover (with nothing external to it). Note the parallels with a modern scientific analysis:

It suggests that time is an emergent phenomenon that comes about because of the nature of entanglement. And it exists only for observers inside the universe. Any god-like observer outside sees a static, unchanging universe, just as the Wheeler-DeWitt equations predict. [bold mine] — Quantum Experiment Shows How Time ‘Emerges’ from Entanglement

So it's true, as you say that the geometer, as a physical object, did act to bring about the geometrical construction on paper, but the cause of that act was a final cause, intention. — Metaphysician Undercover

The final cause was the geometer himself, who acted intentionally. You seem to be reifying intention here - it is the particular that acts (in this case, an intelligent human being), not the form.

The One, being most universal is first, and imparts itself to the less and less universal, with the form of the individual being the last. What Aristotle demonstrates is that the form of the particular thing is necessarily prior in time to the material existence of that thing. — Metaphysician Undercover

The universe is as universal as it gets and it is the precondition for the (particular) subsystems for which change and time are applicable.

I do believe there was fruit before there was pears or apples. — Metaphysician Undercover

That is a Platonic form that Aristotle rejected. For Aristotle, fruit does not exist in separation from pears and apples, but it can be considered separately (i.e., in abstraction). We might see the potential for fruit in prior particulars, just as a scientist might see the potential for life in earlier states of the universe.

As I said, Aristotle clearly denied matter without form, but he did not deny form without matter. In fact, the principles of his Metaphysics necessitate it, as is evident in his cosmological argument. Understanding Aristotle's cosmological argument is very important to understanding his metaphysics, because it unlocks the door to understanding the consistency between Aristotle, Neo-Platonists, and Christian theology. — Metaphysician Undercover

I've addressed the cosmological argument above. Aristotle's rejection of Platonic forms just was his denial of form without matter.

I contend that the pre-modern mentality was very different in this respect, as it didn't conceive of the world as being essentially machine-like but as animated by intelligence. (After all, Aristotle's 'de anima' is translated as 'On the Soul'.) So the whole conception of the human's place in the universe was different, in ways that we generally don't understand, because of the incommensurability of these orientations; much more of an 'I-thou' relationship (Martin Buber's term) than 'I see it'. — Wayfarer

For a non-dualist take on the unmoved mover that is sympathetic to what you say above, you may find this essay interesting.

Quoted in Wikipedia entry on Active Intellect — Wayfarer

I was wondering when the discussion would bring in the unmoved movers or active intellect. There's nothing like an excursion into theology or philosophy of mind to clarify things! ;-)

So as you no doubt know, both the interpretation and perceived centrality of those passages are controversial. As Sachs says, it's "the source of a massive amount of commentary and of fierce disagreement".

My interpretive principle for Aristotle is his consistent application of hylomorphism as inseparable form and matter. That, I think, best captures Aristotle's thinking about the natural world and makes sense of his rejection of Platonic forms. Now as suggested by your quote perhaps Aristotle did not always consistently apply it, and naturally the judgement of that depends on the textual evidence.

So the other interesting question to me is whether that general hylomorphic model has application today, and whether it can be consistently applied in respect to modern science and metaphysics. In that sense Aristotle (as Plato before him) can potentially provide insight into the specific problems of our era.

The point is that Aristotle does not disallow the possibility of form without matter, as he does disallow matter without form. He does not say specifically "immaterial form", but he refers to Ideas, essences, Forms, and intelligible objects throughout his Metaphysics, and clearly determines that essence is substance in Bk.7. — Metaphysician Undercover

Yes he refers to all of those things. However I'm asking for specific quotes that would demonstrate your claim that they are separable from particulars. Without that, you're assuming dualism without basis in your reading of Aristotle.

I cannot see how this is relevant. The potential for a particular material actuality precedes that material actuality in time, this is clear. — Metaphysician Undercover

Thank you. It is relevant because you seemed to deny it in your last two posts.

However, to actualize that particular potential, rather than some other potential (because potentials consist of multitudes) requires an act of agency. It is this actuality, the act of agency, which is necessarily prior in time to the existence of any particular thing, which is being discussed here. The need to assume this form of "actuality" is what necessitates dualism. — Metaphysician Undercover

You regard the form as the agent whereas I regard the particular as the agent. The form of the geometer (somehow separate from the geometer?) didn't actualize the geometric construction, the geometer did.

"Substance" is substance, whether it is primary or secondary substance. — Metaphysician Undercover

A true but cryptic response. Do you think fruit would exist without particular fruit such as pears and apples?

Aristotle denies that matter can exist independent of form, but not that form can exist independent of matter. And, when you understand the earlier part of his Metaphysics, which I referred to earlier, you'll see that the form of a thing is necessarily prior (in time) to the material existence of that thing. This necessitates a dualism between the immaterial form and the material form. — Metaphysician Undercover

For Aristotle, form is the correlate of matter and they are not separable from particulars. You can only consider them in separation which is a different issue. For example, as quoted earlier, "The best way to conduct an investigation in every case is to take that which does not exist in separation and consider it separately; which is just what the arithmetician or the geometrician does." (Aristot. Met. 13.1078a)

If you disagree, can you provide a specific quote where Aristotle would distinguish and refer to "immaterial form" and "material form"?

He clearly argues that actuality is prior to potentiality temporally at the end of Ch 9, Bk 9, "so that the potency proceeds from an actuality". That's why potential cannot be eternal. I think you ought to read the entirety of Bk. 9, especially Ch. 8 where he explains in what sense actuality is prior to potentiality in time. 1050b, (5) "...one actuality always precedes another in time right back to the actuality of the eternal prime mover.". — Metaphysician Undercover

I'm well aware of the senses in which actuality is prior to potentiality but that is not what I was referring to. The temporal sense in which actuality is not prior to potentiality is discussed by Aristotle where he says, "... for the individual actuality is posterior in generation to its potentiality." (Aristot. Met. 9.1051a) [italics mine]

For Aristotle there are two senses of "substance" primary substance and secondary substance. One can be said to be material, the other formal. He provides the principles to deny that there can be material substance without form, but there are no principles to deny a substance which is form. without matter. This is why the Neo-Platonists and Christian theologians who posit independent Forms as substance, maintain consistency with Aristotle. — Metaphysician Undercover

Primary substance is particular such as Socrates or an apple. Secondary substance is formal, such as man or fruit. To suppose that man or fruit are separable from particulars comes from Plato, not Aristotle. This is what Aristotle's rejection of Platonic forms was about and it is why Platonism and hylomorphism are not consistent with each other. Though, of course, Aristotle is fine with "taking that which does not exist in separation and considering it separately" (Aristot. Met. 13.1078a) [italics mine].

Right, now we have here what you call "an intelligent act". This is an act with a purpose, its purpose is to demonstrate the angles. The cause of such an act, in Aristotelian terms is a final cause. In Aristotle's biology, the existence of such acts is accounted for by the soul. And this is why he is dualist. — Metaphysician Undercover

Dualism doesn't follow from Aristotle's examples. The soul is not separable from the body - it is always the particular that acts (and thus is the locus of causality, including final cause). That is standard hylomorphism.

But his demonstration goes deeper than this. Notice that he is arguing in this section, that actuality is prior to potentiality, in all senses of the word "prior". — Metaphysician Undercover

Logically, but not temporally. Which is what Aristotle says in the last sentence of the Chapter 9 quote.

Let's assume that the geometrical figures inhere in the sensible world, prior to being actualized by the human mind, as potentials. — Metaphysician Undercover

In Aristotle's examples the geometrical figures were not actualized by the human mind (which is a form), they were actualized by the human being (the actor). It's essential not to reify mind here. What is actual are the particulars.

According to Aristotle's cosmological argument, there must be something actual which is prior to these potentials. This is because if the potential was prior in time to the actual, it would not have the capacity to actualize itself, so there would always be only potential without any actuality. Something actual is needed to actualize a potential. And what we glean from observation is that there is something actual, therefore actuality is prior to potential. The Neo-Platonists, and Christian theologians take up this argument for Forms (actualities) which are prior to material existence (material existence having the nature of potential). — Metaphysician Undercover

We agree that something actual is needed to actualize a potential. However the Aristotelian position is that that thing must be substantial, not merely formal. That is what we observe.

Can you provide a reference in Aristotle's writings where he asserts this position (that these forms are actualized by the human mind)?
— Andrew M

I suppose the best reference here would be Metaphysics Bk.9 Ch.9. — Metaphysician Undercover

Thanks. The issue has motivated me to dig more into the literature on Aristotle's philosophy of mathematics. The relevant passage in the chapter you reference is where Aristotle discusses geometrical constructions:

Geometrical constructions, too, are discovered by an actualization, because it is by dividing that we discover them. If the division were already done, they would be obvious; but as it is the division is only there potentially. Why is the sum of the interior angles of a triangle equal to two right angles? Because the angles about one point <in a straight line> are equal to two right angles. If the line parallel to the side had been already drawn, the answer would have been obvious at sight. Why is the angle in a semicircle always a right angle? If three lines are equal, the two forming the base, and the one set upright from the middle of the base, the answer is obvious to one who knows the former proposition. Thus it is evident that the potential constructions are discovered by being actualized. The reason for this is that the actualization is an act of thinking. Thus potentiality comes from actuality (and therefore it is by constructive action that we acquire knowledge). <But this is true only in the abstract>, for the individual actuality is posterior in generation to its potentiality. — Aristot. Met. 9.1051a

So to take the first example ("Why is the sum of the interior angles of a triangle equal to two right angles?"), the parallel line is drawn by the geometer. The "act of thinking" does not mean that the construction is in the geometer's mind, it means that drawing the line is an intelligent act (by the geometer). Once drawn, the question about the angles can then easily be answered. Similarly for the second example.

What Aristotle is showing here is that mathematical (and thus universal or eternal) truths can be discovered by acting intelligently on sensible objects, in this case the geometrical drawing of a particular triangle and a particular line. The geometrical figures (as geometrical) are neither located in a separate Platonic realm nor in the mind, they inhere in sensible objects either as potentials (before construction) or actuals (after construction) and thus are a legitimate source of knowledge. A mathematician properly considers mathematical objects separately from sensible objects (i.e., in abstraction), since that is just what distinguishes mathematics from the physical sciences. As Aristotle later says, "The best way to conduct an investigation in every case is to take that which does not exist in separation and consider it separately; which is just what the arithmetician or the geometrician does." (Aristot. Met. 13.1078a)

What Aristotle denies is the eternality of these "forms". They are actualized by the human mind, and so if they existed prior to human beings, they could only exist as potential. Then he shows, with the cosmological argument that anything potential cannot be eternal. This creates a distinction between the forms of particular things, which may be eternal as the eternal circular motion is, and the forms which are activated by the human mind, which are not eternal because they are dependent on the human mind for their actuality.

This position is derived from the later Plato, Timaeus for example, — Metaphysician Undercover

Can you provide a reference in Aristotle's writings where he asserts this position (that these forms are actualized by the human mind)?

Also, perhaps I'm misunderstanding you, but you seem to be denying that particulars (say, ordinary objects like trees) have form prior to the existence of human beings. If so, I'm curious whether you also deny that particulars exist prior to the existence of human beings.

I’m sure your depiction of the contrast between them on the question exaggerates the difference, — Wayfarer

What's to exaggerate? Aristotle famously rejected Plato’s theory of forms and proposed his own theory in its place.

but I really need to hone in on some writing about it. I’m thinking ‘Aristotle and Other Platonists’ by Lloyd Gerson — Wayfarer

Given the criticisms and the absence of an explicit commitment to harmony, is not the reasonable default interpretation of these texts anti-Platonic? This concluding chapter explores one possible way of answering this question: namely, by suggesting that perhaps Aristotle is a Platonist malgré lui. I mean the possibility that Aristotle could not adhere to the doctrines that he incontestably adheres to were he not thereby committed to principles that are in harmony with Platonism. In short, I explore the claim that an authentic Aristotelian, if he be consistent, is inevitably embracing a philosophical position that is in harmony with Platonism. — Lloyd Gerson

Note that his conclusion is not that Aristotle didn't reject Platonism but that, in spite of that, Aristotle was a Platonist anyway. (Which he then argues for, unconvincingly in my view.)

Forms only manifest as particulars, but the forms are what grasped by the active intellect so as to enable us to determine what a thing is. — Wayfarer

Forms only manifest in particulars and are how we perceive those particulars. That's a difference that determines whether you see particulars as imperfect representations of ideal forms (per Plato), or instead as exhibiting form (per Aristotle).

For Aristotle we can't know the form of the particular because we know through universals. This leaves a gap of separation between the form of the particular, with all its accidents, and the form which a human being knows, the essence of the thing. Since "form" is the actuality of things, there is two distinct actualities and therefore dualism. One actuality is substantiated by the form of particular material things, and the other actuality is substantiated by the form of "the soul".. — Metaphysician Undercover

That's not my reading of Aristotle. It is always and only the particular that exists and acts. A form(alism) without matter is merely an abstraction and thus not able to act.

Thanks - I think I've got Kant's epistemology sorted out now! ;-)

Perhaps the philosophical denier of representationalism is a naive realist concerning both the existence of objects and the knowing of them. The "ordinary" naive realist, if she thought about the issue, might accept representationaism as to knowing objects, that our representations don't "capture" them exhaustively, but nonetheless do so veraciously; or something like that. — Janus

I think naive realism and representationalism are two sides of the same metaphysical coin here. Do our senses reveal the world as it is (as if our eyes were windows) or is there a veil between mind and the world (and thus an obstacle or limit to knowledge)?

A different approach is to say that we decide what we mean by "the world" in our use of language. So, pragmatically, what we point to - the objects of everyday experience - constitute the starting point for natural investigation and knowledge.

Differences in perspective. To another, the appearance is of a clown, and the judgement will be with respect to a clown and clown will be cognized. Even with knowledge beforehand of the person presenting the clown, if clown as disguised person is observed, induction is the only means to claim knowledge of the person, and we all know the inherent dangers of inductive reasoning. In effect I know it is me with absolute certainty; any one else has the certainty only of clown. — Mww

I agree that induction is not useful here. However hypothetico-deduction can be. For example, on the hypothesis that the clown is you, one prediction is that you and the clown won't be observed at the reunion at the same time. So it's a testable and explanatory hypothesis.

It would seem that a similar approach can be taken with things-in-themselves. For example, while we may not be able to observe non-Euclidean spacetime, we can construct a model that posits it and use it to make predictions about what we do observe.

I must admit to not being aware of one. Schema are pure a priori conceptions, but they can be reproduced as empirical objects. Noumena are not, so cannot. Our kind of rationality is the only one we have on which to base any philosophy of knowledge at all. But our kind of rationality does not have to be the only one there is. Another kind of rationality may very well incorporate noumena specific to its methodology, in fact, it must, otherwise it would be indistinguishable from human rationality, hence would not be another kind after all. We cannot deny noumena, but we also cannot claim anything with respect to what they might be. — Mww

OK, though I'm still not clear on what noumena specifically refers to. Are they ideas that are beyond human capability to understand (or even conceive of)? Just as things-in-themselves are beyond human capability to sense?

What would be examples of noumena?

Finally, as an aside.....one opinion cannot over-rule another, if the opinions reside in separate subjects. — Mww

Agreed. I appreciate that you and Janus are referencing the source material here and pointing out when interpretations differ.

But there are not two things - there’s simply ‘how things appear to us’ as distinct from ‘how they really are’. The whole point of making the distinction is to draw attention to something inherent about knowledge.

Incidentally in hylomorphic dualism, what is really known is the form, because the form is something like an archetype. — Wayfarer

You seem to be forgetting that Aristotle inverted Plato's ontology. For Aristotle, what is fundamental, and thus primarily known, is the particular. Hylomorphism is not a dualism, it is an abstraction over particulars. What is known about particulars (by way of experience) is isomorphic to how they (really) are.

That would be the blind spot — Wayfarer

Didn't we already go over that ? ;-)

PRECISELY! — Janus

I think our opinion has been overruled...

Thanks for your responsive comments.

The person's mind synthesizes the phenomenal object that subsequently appears to him.
— Andrew M

Yes, the mind synthesizes the phenomenal object, However, there is some controversy on the Kantian rendition of appearance. Some say it means what a thing looks like, others say it is mere presence, like, e.g., I made my appearance at the family reunion. I favor the latter, because to say what a thing looks like presupposes the very attributes conceptions are supposed to give it. This relates because “subsequently appears” is temporally misplaced; if there is an affect on sensibility, then the mind is aware of an appearance of something. This affect, or appearance, is also called sensation by materialists, and occurs antecedent, not subsequent, to any synthesis. — Mww

So on your view, would it be more accurate to say that the mind subsequently determines what first appears in the senses?

Also where you say 'if there is an affect on sensibility, then the mind is aware of an appearance of something' is that 'something' the thing-in-itself?

If so, does Earth also refer to the 'raw' thing-in-itself (that appears phenomenally) or only to the phenomena (as a separate thing)?

What I'm getting at here is whether the Earth is thought of as a presentation of things-in-themselves or a re-presentation of things-in-themselves. (Albeit a synthesized or 'cooked' presentation or representation.) As an analogy, you could present at the family reunion in a clown costume but it's still you, or you could send a robot replica as your representative, which is not you.

As space and time are pure intuitions, that is, not derivable from any object of experience but belonging to any object of experience in particular, so too are the categories pure conceptions, that is, having no object of their own, but belonging to all objects of thought in general. Re: Wayfarer’s triangle, the category of quantity makes the thought of lines possible, the category of quality makes the thought of flat possible, the category of relation makes the thought of arranging lines in a certain shape possible, henceforth conceived as a triangle. Lines, flatness, arrangements are all mental images, called schema. — Mww

Got it.

Noumena are NOT things-in-themselves of the world, they are objects-of-themselves of the mind. — Mww

So to clarify, what is the relationship between schema and noumena? Are abstractions like triangle and number schema or noumena or both?

All the above is relatively instantaneous, of course. In the case of Earth, which is nothing new, all the concepts pertinent to the phenomenon have been previously processed, so all that’s required is for judgement to give its blessing.....yup, that’s Earth all right.....we cognize logical consistency, and know we’re looking at, talking about, picturing.....whatever....a very specific object of common experience. — Mww

OK, so as I understand it the object goes through various internal processing stages after which the person judges that he's talking about the Earth.

The person's mind synthesizes the phenomenal object that subsequently appears to him. So, logically, phenomena are at least partly dependent on mind. However in accordance with the a priori categories of time and space applicable to phenomena, the Earth is judged to be a distinct and several-billion-year-old entity - temporally prior to and spatially external to the person.

Does that capture it?

I do not acknowledge noumena. They serve no purpose other than to make people go where Kant himself refused to go and suppose for themselves things he never meant. It’s fine to understand how they were developed, but to use them for anything cannot be done. — Mww

Is the purpose of noumena just to serve as a logical placeholder at the boundary of knowledge? That is, if anything were (or could be) known about noumena, then it wouldn't be noumena, it would be phenomena.

You can't really equate the domains since naturalists and dualists conceptualize the world differently
— Andrew M

But I’m not criticising dualism. I hold a kind of dualist view myself, as a kind of working hypothesis. — Wayfarer

Yes, I know. What I mean is that for the naturalist, the natural world is all there is. Thus 'the study of nature' excludes nothing. Whereas for the dualist, the natural world is one part of reality that excludes whatever the other dual part is (noumena, mind, Platonic forms, or whatever).

If, as a dualist, you assume the natural and dualist conceptions of the natural world are the same, then you will conclude that the naturalist must be missing something important - the other dual part. But that's not how the naturalist conceives of the world. That other dual part is already integrated in the naturalist's conception of the world in some other form (likely in ways the dualist doesn't easily recognize, since it is not incorporated dualistically).

That is the basic point, that is where the argument hinges. That is there the whole recursive loop happens. Seeing through that is the task of philosophy as distinct from science. — Wayfarer

OK, what would be the recursive loop and is it a problem?

Wouldn't that apply to other humans as well as elephants? How do I know other people exist? The same way I know elephants exist. If that's just part of what appears to me, then solipsism is the logical conclusion. If that's what Kant meant.

This isn't to say Kant intended solipsism, only to show that this sort of view leads there. Why would other people be the one exception? Aren't they part of the world being perceived, just like elephants?

For that matter, don't elephants perceive? — Marchesk

Yes, so you can substitute something non-sentient instead, say, a tree. As I understand Kant's view, the precondition of something appearing to a person as phenomena is that it is situated in time and space. So that precludes solipsism since other people and things appear phenomenally. But if there were no sentient creatures at all, then there would be no phenomena, including trees. Just noumena which seems to be a placeholder for what can't be referred to or described.

I equate 'the phenomenal domain' with 'the domain studied by the natural sciences', in other words, the realm of phenomena. — Wayfarer

You can't really equate the domains since naturalists and dualists conceptualize the world differently. For a naturalist, the natural world encompasses everything - for example, Aristotle's form and matter are immanent in the natural world.

But this is because the realist view doesn't grasp that everything we say about 'what exists' presumes an implicit order which already presumes an essentially human, or at least sentient, perspective. — Wayfarer

Yes, everything we say about 'what exists' presumes a human perspective. So that isn't a point of difference between Kant's system and naturalism or realism.

H. Sapiens' brain is the most complex entity known to science, and what it does, is generate a world. But when you ask, 'you mean, without the brain, the world would disappear?' the answer is, 'what world?' — Wayfarer

OK, so that seems a point of difference. For the realist, human beings (and their brains) are part of the world, not the generators of it. What exists (as opposed to what we say about what exists) does not depend on a human perspective.

Thanks for your comments.

“......The undetermined object of an empirical intuition is called phenomenon....”

While it is true that without humans there is no phenomenal domain, it does not follow from Kantian speculative epistemology that the Earth **only** exists within the phenomenal domain. The Earth is named in accordance with conceptions belonging to it, so is known to exist as a determined object. Still, it is phenomenon only insofar as the immediate temporality of the human cognitive system passes it by rote to judgement.
(Judgement merely for logical consistency a posteriori, because understanding already thinks the phenomenal object as representation contains the manifold of conceptions experience says it should have) — Mww

Using the Earth as the example, what is the undetermined object here? Simply the Earth's referent (without its characteristics)? Also, on Kant's view, where else would the Earth exist? The noumenal domain? In one's experience or judgment?

It seems to me the model here is of an unfurnished object that acquires form when it is perceived. Is that correct?

“....If the intuition must conform to the nature of the objects, I do not see how we can know anything of them a priori. If, on the other hand, the object conforms to the nature of our faculty of intuition, I can then easily conceive the possibility of such an a priori knowledge......( )......Before objects are given to me, that is, a priori, I must presuppose in myself laws of the understanding which are expressed in conceptions a priori. To these conceptions, then, all the objects of experience must necessarily conform....”

It is the how they necessarily conform that is the ground of the epistemological theory itself, and where all those confusing terms and their temporal locations are to be found. — Mww

So why would Kant be assuming we know anything of objects a priori? It seems he is inverting the 'conform' direction simply to reinforce that assumption.

Thanks for your useful comments.

My interpretation is as follows: to say that we have knowledge of only of phenomena is not to say we know nothing, as pragmatically speaking, the phenomenal domain exhibits all of the regularities and consistencies which natural science observes. So when I said 'not mere appearance', I'm saying that Kant doesn't regard the appearance of phenomena as a mere trifle or an optical illusion or something that can simply be dismissed. — Wayfarer

Yes, nonetheless the phenomenal domain is not the world of naturalism since the former is dependent on the perceiver (per Kant's "Copernican revolution"). That is, without human beings there is no phenomenal domain, and the Earth only exists within the phenomenal domain.

But the practical import for all of these discussions is that 'things only ever exist from a perspective'. That is, nothing has real 'self-existence' or exists in its own right. — Wayfarer

Whereas the natural view is that things are only ever known from a perspective.

In terms of the blind men and an elephant parable, naturalism permits different descriptions of the elephant from different perspectives. Sans the blind men there is no perspective, but there is still an elephant.

However it seems on Kant's view that without the blind men (or anyone else), neither is there an elephant.

↪Andrew M I may be mistaken, but I think this shows an inaccurate understanding of Kant.

The Kantian distinction is that the straight stick is itself "an appearance" and not what the stick is "in itself".
— Andrew M

This is not at all true - Berkeley addresses the same point, and Kant in much greater detail. What Kant means by 'phenomenon' or 'appearance' is not mere phenomenon or mere appearance. — Wayfarer

I'd be keen to get to the bottom of this. From the SEP entry on Kant’s Transcendental Idealism, 'Objects in space and time are said to be "appearances", and [Kant] argues that we know nothing of substance about the things in themselves of which they are appearances.'

That is, according to Kant, the straight stick is an appearance and the things in themselves that give rise to the appearance of the straight stick are unknowable.

If you don't think that's right, how would you (briefly) characterize Kant's phenomena/noumena distinction?

" “Abandonment of the goal of a first philosophy. [Naturalism] sees natural science as an inquiry into reality, fallible and corrigible but not answerable to any supra-scientific tribunal, and not in need of any justification beyond observation and the hypothetico-deductive method” (Quine 1981: 72).
...
Instead of starting with sense data and reconstructing a world of trees and persons, Quine assumes that ordinary objects exist." [A passage on Quine] — Wayfarer

I agree with Quine about ordinary objects (and the rejection of sense data and positivism), but would put the inquiry issue like this: While physics is the study of nature, metaphysics is the study of the study of nature (which is itself a part of nature). So a natural metaphysics is reflective in a way that operational physics is not.

But it's just that assumption which has been called into question by physics - that's why all of the controversy about the 'observer problem'. — Wayfarer

What has been called into question by physics is an implicit assumption about ordinary objects, termed counterfactual definiteness. No interpretation denies that trees and persons exist.

It's also called into question by philosophy. When we 'see the tree', what's actually going on? There's no 'light inside the skull'. The brain constructs the image on the basis of received sense-data combined with judgement; this is what's really happening. But when naturalism eschews 'first philosophy' it 'brackets out' all those considerations and says, more or less, 'let's start with what is "really there" '. And in doing that, the critical project of philosophy has been abandoned. Or, essentially, we're equating science with metaphysics. — Wayfarer

The phrase 'see the tree' is a language abstraction and implies nothing about the underlying natural processes. The role of science is to investigate the objects and processes involved. The role of philosophy is to sort out the conceptual problems that arise (such as 'light in skulls' and 'sense-data').

It's not so simple as that. It's about judgements of what is real, of the ground of the understanding. I know it's perplexing, baffling and an apparent outrage to common sense but I have good reason to argue it. (Actually, in this context, I've learned a lot from Buddhist philosophy of 'mind-only' and 'emptiness', which provide an interpretive framework within which these ideas make sense.) — Wayfarer

Equally, I know that positing the reality of ordinary objects is perplexing, baffling and an apparent outrage to philosophical sensibilities but I have good reason to argue it. ;-) Observation and reflection on the natural world provides an interpretive framework within which these ideas make sense.

The problem is that you’re answering a philosophical question about the nature of knowledge with a scientific question based on the knowledge of nature. That's why we're talking past one another. (I've now answered AndrewM below about a similar point.) — Wayfarer

The problem is that you're giving two contrary answers to the same question. :-) You seem to be saying that space and time existed in a scientific sense prior to humans, but not in a philosophical sense.

So how could he be both? Because the 'transcendental idealist' perspective is about the grounds of the possibility of knowledge itself. It is not about natural phenomena, but about the nature of our understanding, of how 'nature' is known to us (i.e. as phenomena) and how we must necessarily understand appearances in accordance with the apparatus of the understanding. This is the basis of his well-known Copernican revolution in philosophy, that 'things conform to thoughts, not thoughts to things'. — Wayfarer

So the Earth conforms to thoughts of the Earth? If so, does that imply that without humans there would be no Earth?

The human point-of-view is a relational one (i.e., between natural systems, of which a human is one) and does not depend on a Kantian phenomenal/noumenal distinction.
— Andrew M

That distinction doesn't require the blessing of naturalism. — Wayfarer

Understandably, since the Kantian distinction opposes a natural epistemology. The natural distinction is, for example, that there can be a straight stick that appears bent in water. The Kantian distinction is that the straight stick is itself "an appearance" and not what the stick is "in itself".