Very interesting. — chiknsld

Yes it is, isn't it? But the need for a schema like this is only really understood when one recognizes and accepts the reality of free will.

This does not follow from any hard-deterministic physics. Quite the opposite in fact, by definition. — noAxioms

In any physics, a force is required to change a state. I'm very surprised that you would try to deny this.

Perhaps you should give an example where the forces are not a function of the state at a given moment. — noAxioms

From Wikipedia: "In physics, a force is an influence that can change the motion of an object." So, in physics, a "force" is what what would change the state which exists at "a given moment". Therefore it is clearly not "a function of the state at a given moment", because that would mean that the change has occurred to the state before the force was applied. You are attempting a misrepresentation.

he problem is with the nature of philosophy not with my statement describing the incompatible nature of supernatural assumptions. — Nickolasgaspar

No the problem is with the opinion expressed by your statement. Clearly when the assumption of the supernatural is necessitated by a combination of the evidence, the definition of "natural", and logic, then philosophers ought to assume the supernatural. Your opinion is that philosophy should stop short of assuming the supernatural, even if the supernatural is necessitated by the logic. That's why your opinion is faulty.

We either have evidence for a natural mechanism or have zero evidence for a natural mechanism. This is the true dichotomy. — Nickolasgaspar

You left out evidence for something which has no natural mechanism. Take free will for example. We have evidence of free will, and there is no natural mechanism to explain it.

In order for the supernatural to be part the discussion, you will first need to demonstrating the existence of the supernatural. — Nickolasgaspar

This is not true. All that is required is evidence of something which is not natural. This effectively demonstrates the necessity for the supernatural to be part of the discussion.

Logic dictates that you need to have evidence for your claim( the supernatural). The lack of evidence for an other claim doesn't automatically render yours the answer. — Nickolasgaspar

As I said, evidence that there is something which is not natural, is evidence of the supernatural.

What occurs to me on reading it, is the question of what faculty or property unifies a single memory in such a way that it can be deposited across a number of different systems (it is referred to as an ‘engram’). What makes it whole? I don’t discern any comment or speculation in the article about that point. But, philosophically, this is where I think there is evidence for something like vitalism: that there is a faculty or attribute of living systems which orchestrates a huge number of diverse, individual cellular interactions into a unified whole, which operates on a number of levels, including memory. — Wayfarer

Consider that there are separated points in space, non-dimensional points which have real existence. Between the points is "space" as we know it through our techniques of geometry and measurement. The non-dimensional points are very real though, having some sort of internal structure which is completely foreign to us because it is non-spatial, and we understand physical things only through their spatial representations. Within these points is the immaterial reality which is very intuitive to us. And the activity in here (whatever it could be), accounts for the observed oddities of our universe, oddities which appear to us when the universe is represented by spatial models; like spatial expansion, dark energy etc.. The non-dimensional points though, might be related to each other, through their internal activity, and these relations cannot be represented as spatial relations.

Seeing things in this way opens up a whole "internal universe" which is completely different from the external spatial universe that we are aware of through sensation.

Now, the problem in accessing and understanding the internal universe is the failings of our geometrically based conceptions, which were constructed chiefly for utility in the external, spatial universe. The principal problem today, is the relativistic concept of space-time, which portrays time as a fourth dimension of space. This forms our conception of time around our conception of space, making time a property of spatial activity, instead of making spatial activity a property of the passing of time. The true logical conclusion is that the passing of time is required for spatial activity, not that time is the product of spatial activity. So if we invert the existing conception, to give proper logical priority to time, making the passing of time the logical necessity for the existence of spatial activity, then we allow for non-spatial activity at the base of, or the cause of spatial activity. Then the activity within the non-dimensional points, described above, becomes intelligible to us, as non-spatial activity. And time is properly positioned as the zeroth dimension rather then the fourth.

OK, you seem to be interpreting it as a statement of determinism. Under a completely deterministic interpretation of QM (such as Bohmian mechanics), the future action any robot, human or squirrel is completely determined by the state at a given time. Unless you can falsify such an interpretation, your statement above is a mere assertion, not any kind of evidence that a human can in any way do something other than what is utterly determined. — noAxioms

This is easily falsified, as you request. A "state at a given time" cannot by itself determine any future activity. This is because a state is static, without activity, and any future activity of the thing in this state is dependent on what forces are applied to it. Therefore it is clearly false to say that the future action of a thing is "completely determined" by its present state, because it is also dependent on whatever forces are applied to it.

All philosophical explanations should stop before entering any supernatural assumption. — Nickolasgaspar

This is clearly a biased statement.. Whenever evidence and logic indicate the reality of that which is beyond the natural, then the appropriate conclusion is the supernatural. To deny the reality of what the evidence and logic lead you toward, because it's contrary to what you already believe, is simple prejudice.

The rash is back. So I'm bumping this thread. There are good philosophical and social reasons to remove certain threads.

The list in the OP would today read:

Adam Eve and the unjust punishment
Divine Hiddenness
Multiple Messiah Theory
Explanations of Christian Hell?
Understanding the Christian Trinity
The Possibility of Infinite Punishment in Hell
Are there any scientific grounds for god?
The eternal soul (Vitalism): was Darwin wrong?
An Argument Against Theological Fatalism
Jesus and Greek Philosophy

Again, these threads should be removed if they
...take scripture or revelation as a starting point for discussion; theology, not philosophy.
— Banno — Banno

Banno utters nonsense again! Philosophy will take any commonly held belief as a starting point for discussion or inquiry. That's very evident in Plato's dialogues, and Plato is arguably the definitive philosopher. The subjects mentioned here involve deep philosophical questions. Banno seems to want to limit "philosophy" to "what interests Banno", and that's a very selfish attitude, especially since Banno's interests are very shallow.

So in stage 1, you examine the options and rightly conclude that quitting smoking would be in your best interest, and in stage 2, the immediate-gratification-monkey (a waitbutwhy term) totally ignores the output of stage 1 and reaches for the ciggy. Still not an example of free will or the lack of it, and not anything that cannot occur with a deterministic robot, a supposedly not free-willed thing.

So my point is: what distinguishes a supposedly free willed human (or squirrel if you want) from something else that isn't free willed? — noAxioms

Look at the example. At the end of stage 2 the person might reach for the ciggy or not reach for the ciggy. Therefore the person's will is free. If the person was a deterministic robot there would be only one way which the person could go after stage 2.

Thanks for bringing that to my notice. Stage 2 covers that phase of the choice-making process. Looks like it didn't quite satisfy your high standards of accuracy and truth. I've been accused of wooly thinking. So there. — Agent Smith

The problem is that there is a division between decision and whatever it is which motivates, or initiates action (will). So for instance, you decide what you are going to do, but you do it later, or you don't do it at all. The decision does not necessitate action. That's why we need to assume a separation between what we call "will" as the initiator of action, and the decision making.

How could you choose what one likes and dislikes? These are, as far as I can tell, formed way before one is even conscious about them. I, for example, didn't opt for heterosexuality, but, from what I can gather, I have. The same goes for homo/bisexuals. This proves my point to my satisfaction. — Agent Smith

When you pay proper respect to the separation described above, whether or not you choose your likes and dislikes is irrelevant. Your likes and dislikes may have influence over your decision making, but your will, which initiates your actions, is not necessarily determined by your decisions. So whether or not you have control over your likes and dislikes is irrelevant to whether your will is free, because your will is not determined by your decisions.

In stage 2, all the choices have been processed and the one that we like is selected. It's in this stage, our preferences come into play, preferences we had no hand in determining i.e. we're not free now. — Agent Smith

You've left out stage 3, and that is what you actually end up doing. And stage 3 might be contrary to what you decided in stage 2, like if you decided not to smoke anymore, and you actually light up a cigarette. That stage 3 is not necessarily forced by something subconscious, nor is it necessarily forced by the conscious decision, is evidence that the will is free.

Why is there existence at all? This is truly absurd. This is the absurdity of existence. There is no reason that existence should exist. There should just be nothing. Nothing existing for all of eternity. Nothing on top of nothing on top of nothing...on top of nothing. And there should never be existence after that. — chiknsld

Actually what you propose is what's absurd. To conceive of the possibility of nothing requires negating the appearance of all that is. This becomes completely absurd, and the possibility of nothing becomes a true impossibility. So pondering the possible reality of nothing is just like pondering the reality of any absurd impossibility, like a square circle, or anything like that. It's just another useless exercise in futility. The proposition of absolute nothing is the most preponderate absurdity, being truly inconsistent with absolutely everything.

Our intuition is that it defies all logic. — chiknsld

This, unless you have access to some very strange intuition, is also the opposite to reality. Intuition surely presents us with the idea that existence is highly intelligible. That is what motivates us in our attempts to understand it. If our intuition was that existence defies logic, we would not be at all inclined to apply logic toward understanding it.

part from the question of whether causes and first principles exist outside of the individual beings they bring into existence, they can be distinguished from each other during the inquiry into their nature. What, after all, is an inquiry into causes if one cannot make that distinction?

The soul is the cause and first principle of the living body. But these are so spoken in many ways, and similarly the soul is cause in the three ways distinguished; for the soul is cause as being that from which the movement is itself derived, as that for the sake of which it occurs, and as the essence of bodies which are ensouled.
— De Anima, 415b8, translated by D.W. Hamlyn

But the intellect, as a potential (from the passage I quoted), is posterior to the material body, dependent on it, just like every other power that the soul has.
— Metaphysician Undercover

The potentiality of the intellect in III.4 is not described as a dependency upon the "material body" but as a condition that allows it to think "all things": — Paine

Do you apprehend a difference between the soul, as "the cause and first principle of the living body", and the intellect, as "a condition which allows it to think 'all things'"? The latter is posterior to the former, as the former is the cause of being of the latter.

Also, the potentiality of the intellect is definitely described as dependent on the material body. That's the point of the reference to imagination. Thinking requires imagination, which requires the bodily senses. That's how Aristotle describes all the powers of the soul, the higher are dependent on the lower, and they are all features of the various living bodies. We can conclude that the powers, or potencies, of the soul are materially based, because in his physics, matter provides the potential for change. They are potential, therefore they are materially based.

He demonstrates that the powers exist as potential, by explaining that any of the powers is not active all the time, it must be actualized. So the power resides in the potential (we can conclude matter). Aquinas looked at this with respect to the nature of "habit", and found that the habit, even though it is a specific way of acting, resides in the potential, material aspect, not in the act itself, the formal aspect.

I am still no closer to understanding your interpretation and you report the same consternation about mine. — Paine

I have to admit, I do not see the point you are trying to argue. There appears to be no consistency to what you say. You assert an "active intellect" which "exists separately", but then you readily admit to the obvious, that Aristotle describes the intellect as a potential, in all of its facets. When attempting to support the idea of a separate "active intellect", you refer back to "the soul", as if there's no separation between the soul and the intellect. But you need to respect the fact that the intellect is a product of the soul, just like all the other powers of the soul, which are all features of the material body. In describing the intellect, you cannot refer directly to the soul, because one is just a property of the other.

They are not separated in the generated individual, but Aristotle distinguishes between the soul as form and the individual repeatedly as the bulk of my quotes demonstrate. De Anima begins with the distinction: — Paine

The soul, as the form of the individual, is not a being which is separate from the matter, nor is it an intellect. The soul is a type of actuality which is necessarily prior to the material body, as the cause of it. A cause must be an actuality. That's what I tried to explain to you before, but you seem to want to describe the soul as some sort of intellect which persists after the material body. The intellect, as a power of the soul is a potency, or potential, though. And we have no principles to support the idea of a cause persisting after its effects.

The intellect is a property of what you call a combined (material) being. There is no principle to support an "active intellect" which "exists separately". The idea of a "separate form" is supported by the necessity of a cause (the soul in this case) preceding its effect (material body). The soul must be separate because it necessarily exists when there is no material body, prior to it, because of the temporal nature of "cause"; it is prior to the material body. As necessarily actual, Aristotle assigns "the soul" to the category of "form" But the intellect, as a potential (from the passage I quoted), is posterior to the material body, dependent on it, just like every other power that the soul has. Each and every one of the soul's potencies is dependent on, therefore not separable, from the body. In the case of the intellect, this is demonstrated by the example, the intellect is dependent on the imagination. The idea of a separate active intellect is a notion which is left unjustified.

True measurement, to me, simply means the correct value of (say) the length of a line. So, a square has a diagonal whose true measurement is 2–√2. — Agent Smith

Then how were you distinguishing between the true value of a measurement, and a measurement which is close to the true value?

Suppose there's a line. Do you think the line has a measurement without being measured? How could it?

Except for the forms and matter which make such beings possible. — Paine

But form and matter are not separate beings. Form and matter are principles of Aristotle's physics, which are applied toward understanding being, such that we can say that a being necessarily consists of both. Primary substance is individuals, and individuals consist of both form and matter.

And I'm saying we don't have an option. Infinity and infinitesimals are the best available tools we have to study curves. Maybe some day we'll discover something better. Until that happens, we're stuck with what we have. — Agent Smith

I have a slightly different opinion. I think we will not discover something better until we reject what we have. As I said, necessity is the mother of invention. Everyday I pick up my hammer and bang some nails. I think this tool's just fine, it serves the purpose well. I will never replace it unless I am dissatisfied with it. And until someone shows me, look it's got this problem and that problem, I'll continue to think it's just fine.

What is a true measurement to you? — Agent Smith

I don't know, that was your words. You were talking about being close to the true measurement. If you talk about "true measurement in that way, then there is no such thing. But I think any measurement is a true measurement, how could it not be a true measurement, yet still be a measurement? The issue is the measuring technique.

In Aristotle all beings are generated.

I'm fully aware of hylomorphism, as is evident in my last post. All things are "combined beings". So I don't understand your usage, as if "combined beings" refers to a special class of beings.

What I am saying is that the reason why perfection is impossible is that the tool (mathematics) is fundamentally flawed.

Imagine if the true value of a measurement is 4.5879... units. I can get very, very close to that value and that should be more than enough. Note mathematicians are fully aware of this rather embarrassing state of affairs. Irrational numbers were called incommensurables. — Agent Smith

It's not an issue of there being a "true value of a measurement" and we can get very very close to that, it's a matter of there being no true value, because the way of measuring is fundamentally flawed. So you have no justification to your claim that you "can get very very close" to the true value. If you could show the true value, to show how close you are to it, you wouldn't accept the "very very close" value, you'd accept the true value instead.

What you're not grasping, is that when measurement is impossible, which is what "incommensurable" implies, then there is no true measurement, and no such thing as close to the true measurement. What is evident is that the measuring tool is inadequate for the job. Need to get a better tool, properly designed for the job

So, something that is not perfect is deeply flawed? — jgill

Mathematics consists of ideals. An ideal which is not perfect is deeply flawed.

You're a perfectionist and so the mathematics of infinity and infinitesimals won't make any sense to you. — Agent Smith

That's exactly the problem. I thought mathematics was supposed to provide us with precision, perfection in our understanding. Then I was disillusioned, realizing that it's all a facade, and deep misunderstanding lies behind.

This does not reflect Aristotle's thinking. Only some combined beings are capable of thought. The capacity is directly related to the condition of the body. This is made clear in the passage preceding the one I quoted: — Paine

That's exactly the point I am making. The capacity to think is directly related to the material body. Therefore it is a mistake to represent that capacity (the intellect), as something which can exist independently of the material body.

The intellect seems to be born in us as a kind of substance and not to be destroyed. — ibid, 408b 18, emphasis mine

When the word "seems" is used, one must be aware that this is an idea which is being expressed as something to be doubted. It appears you are not distinguishing between the use of "intellect" at the beginning of the passage, and "soul" at the end of the passage. The two are very distinct in Aristotle, and statements about one cannot be used as a conclusion about the other.

Here again, it is important to follow distinctions Aristotle makes between the soul as a principle that animates all life from the experience of combined beings. Aristotle states at the beginning of the book that only combined beings can be affected: — Paine

I don't understand your use of "combined beings". It doesn't appear Aristotelian to me. Is this supposed to be like the Plato's notion of body and soul? If so, it is mistaken to represent Aristotle in this way, because he breaks down this ancient notion. For Aristotle, each individual thing, alive or inanimate, consists of matter and form, the living being has a special type of form, "soul".

Therefore the distinction you make "only combined beings can be affected", appears completely unsupported. Notice in your quote he talks about specific affections which are peculiar to the soul. He does not make the more general statement that affection is something unique to the soul. Of course in his physics he talks about all material substance as capable of change, matter being the potential for change.

Book 3, chapter 4 follows the discussion of imagination in chapter 3 and begins the argument of how the intellect can be seen as a potential in relation to what makes it actual. The last paragraph of chapter 4 says: — Paine

There is a very real problem with saying that the intellect "is actually nothing before it thinks". You ought to be able to see this clearly. Before it thinks, the intellect must have the capacity to think. And this is a very specific capacity, it's not the capacity to be warm or cold, the capacity of self-nourishment, the capacity to move, or anything like that, it is the specified capacity, to think. Therefore the thing which has the capacity to think, the intellect, must very clearly be something actual, prior to thinking, in order to have this specific capacity. So when we say that the intellect is "actually nothing" before it thinks, this must be qualified by a very specific set of possibilities,. It is actually nothing, in relation to that specific set of possibilities.

The following chapters demonstrate how admitting in 431a8 that the 'soul never thinks without an image" is not admitting that the intellect is a "form of imagination" as described at the beginning of the book. — Paine

I don't see what you're alluding to.

Now, you're joking, right? :smile: — Agent Smith

Of course I'm not joking. Let's assume that two straight lines is "close" to being a single curved line, two being "close" to one. The curved line is a single line, the two straight lines is two distinct lines. Now you seem to think that the more straight lines you put together, 3, 4, 5, 6, the closer you get to being a single line, such that as you approach an infinity of straight lines, it becomes one curved line. Can't you see that you're going the wrong way? Instead of getting closer and closer, you're getting further and further. Producing a larger and larger multiplicity does not somehow produce the conclusion that the multiplicity is getting closer and closer to being a single entity.

Show us then a different method of measuring the length of a curve if not using infinitesimally small straight lines. I bet you can't and so infinitesimals and infinity it is. Nevertheless we'll wait, with baited breath, for you to discover a new way of tackling curves. — Agent Smith

I use something flexible like a string, bend it around in the curve to be measured, then I lay it out straight and measure it as one long length. The single curved line is effectively converted to a single straight line, then measured as such, in that way. You have to be careful though because the "inside" measurement is always distinctly shorter than the "outside" measurement, and this is a problem which cannot be avoided. So the inside of the string will complete the circle in a shorter length than the outside of the string.

This thing you refer to, "using infinitesimally small straight lines", is not itself an act of measurement, because as I told you, an infinitesimal length cannot be measured, and therefore cannot be used as a unit of measurement.

Yes, curious isn't it? A problem is that this is an existence theorem. — jgill

The question then, is there a way to determine whether it is true or not? For example, if you stir a coffee, is there a way to determine that there is a molecule or something like that, which remains in the same place after stirring as it was prior? Or is this just a principle which is useful for some purposes, but is not really true? I guess it depends on what is meant by "continuous function" and whether it is true to think of things in terms like this.

Thus thought and contemplation decay because something else within is destroyed, while thought itself is unaffected, — De Anima, 408b 18, translated Ackrill

This idea, I cannot accept. The idea that when a person becomes old, and mentally incapacitated, suffering dementia or something like that, the person is still fully capable of "thought", and it's just something else that decays, I believe is completely refuted by evidence. We'd have to really distort the meaning of "thought" to support such a position.

What happens in Aquinas' principles, from what I remember, is that the human intellect is fully united with the material body, and is dependent on the body. Because of this dependency the human intellect is left deficient, and incapable of properly grasping the independent Forms, God and the angels. So Aquinas says that the soul of man is incapable of completely knowing God, so long as it is united with the body. It is implied therefore that the soul can completely know God after being freed from the body.

However, we can see a problem arising from this, in relation to knowledge and the intellect. The human intellect necessarily has a body, and "knowledge" is a property attributed to the human intellect, as is "thought" above. So if we disunite the soul from the body, then whatever union the soul is allowed to have with the independent Forms at that time, it is improper to refer to that union with those terms. "knowledge" and "intellect". It would not be a case of the soul "knowing" the independent forms because "knowing" is what the human intellect does, and the human intellect is dependent on a body. "Knowledge" being something which is fundamentally flawed, as fallible.

These observations move me to ask for you to provide textual references for the following statement: — Paine

I believe I produced this in the other thread. Read thoroughly \De Anima Bk 3 Ch 4.

"The thinking part of the soul must therefore be, while impassable, capable of receiving the form of an object; that is, must be potentially identical in character with its object without being the object." 429a 15. "Therefore...mind...can have no nature of its own, other than that of having a certain capacity." 429a 18-23.
Then:
"Once the mind has become each set of its possible objects, as a man of science has, when this phrase is used of a man who is actually a man of science, (this happens when he is now able to exercise the power on his own initiative), its condition is still one of potentiality, but in a different sense from the one which preceded the acquisition of knowledge by learning or discovery; the mind too is then able to think itself." 429b 5-10

The mind is shown to be fundamentally potential, therefore we can conclude that we're barking up the wrong tree if we think that we can proceed toward demonstrating that the mind could be an independent actuality.

There's a number of complex and difficult issues right here in this chapter. First, the mind being impassable, yet capable of receiving forms. This I believe is what allowed Aquinas to say that the passive intellect is some type of potential which is not matter. I believe that in reality we ought to reject this qualification "impassable", and allow the simple solution, that the material aspect of the human mind is what receives forms.

Another issue, which is much more difficult, and complex, not having been well explored, that I know of, is the way that different potencies relate to each other. Obliquely, we can see the foundation for a sort of hierarchy of potencies or capacities here, and this is consistent with Aristotle's powers of the soul, where the posterior potential is dependent on the prior potential. The mind must first receive forms, learn, and in this sense it has the capacity to become something. Prior to this, it is not any particular thing, but the potential to be many things (matter?). After learning, when the person has knowledge, the mind is described as the potential to act in numerous different possible ways ("able to exercise the power on his own initiative"). The capacity attributed to the posterior potential is dependent on the actualization of the prior potential.

So the potential to learn exists in a certain relation with the potential to act, which is a temporal relation. Learning is prior to acting. And what we can see, is that even though the actualization of a potential, (the capacity to learn is actualized), this actualized potential remains a potential still, in relation to the posterior thing, which is acting. So even though the base potential has been actualized (learning), it remains a potential in relation to the next actualization (acting).

They are, as I tried to impress upon you, estimations (not exactly a curve, but close). — Agent Smith

And as I tried to impress on you, a curve is not even close to a multitude of straight lines.

I'm sure you're aware of this but how different is a curve from a straight line between two points that are infinitesimally close to each other? Try drawing a chord between two points on a circle. As the two points come closer, the chord and the arc subtended by these two points approach each other. Extrapolate that unto infinity and you'll get an idea of what mathematicians are trying to convey here. — Agent Smith

I think I know what mathematicians are trying to convey, I've been told that numerous times. I simply believe that it's fundamentally incorrect. "Infinitesimally close to each other" is not a standard of measurement which has any rigorous meaning. I mean it's not a distance which is measured.

If you want to split hairs then all mathematics that depend on infinity and infinitesimals need to be scrapped. We would be much handicapped if we were to do that. — Agent Smith

Now you're getting the idea. Yes, I agree, that anyone who scrapped that stuff would be greatly handicapped at this time of scrapping the stuff. But necessity is the mother of invention, and what would develop out of the scrapping, making a fresh start, knowing what we know now, would be a great improvement.

Something similar to that has been tried: https://en.wikipedia.org/wiki/L._E._J._Brouwer — jas0n

That looks interesting.

Mathematicians in analysis or topology mostly know Brouwer for his famous Fixed Point theorem . — jgill

Of the following, I can see intuitively why #2 would be true, but I haven't a clue as to why #1 and #3 are.

1. Take two sheets of graph paper of equal size with coordinate systems on them, lay one flat on the table and crumple up (without ripping or tearing) the other one and place it, in any fashion, on top of the first so that the crumpled paper does not reach outside the flat one. There will then be at least one point of the crumpled sheet that lies directly above its corresponding point (i.e. the point with the same coordinates) of the flat sheet. This is a consequence of the n = 2 case of Brouwer's theorem applied to the continuous map that assigns to the coordinates of every point of the crumpled sheet the coordinates of the point of the flat sheet immediately beneath it.
2. Take an ordinary map of a country, and suppose that that map is laid out on a table inside that country. There will always be a "You are Here" point on the map which represents that same point in the country.
3. In three dimensions a consequence of the Brouwer fixed-point theorem is that, no matter how much you stir a cocktail in a glass (or think about milk shake), when the liquid has come to rest, some point in the liquid will end up in exactly the same place in the glass as before you took any action, assuming that the final position of each point is a continuous function of its original position, that the liquid after stirring is contained within the space originally taken up by it, and that the glass (and stirred surface shape) maintain a convex volume. Ordering a cocktail shaken, not stirred defeats the convexity condition ("shaking" being defined as a dynamic series of non-convex inertial containment states in the vacant headspace under a lid). In that case, the theorem would not apply, and thus all points of the liquid disposition are potentially displaced from the original state.[citation needed]'/quote] — Wikipedia

All I can say is you're not incorrect, but as I pointed out, infinity allows approximations that turn out to be useful when dealing with feminine geometric objects (curves). — Agent Smith

The issue is that this type of approximation produces the illusion that we understand what a curve is, when we really do not. There's a fundamental incommensurability between two dimensions of space, which makes things like pi and the square root of two irrational ratios. What it indicates is that we lack a proper understanding of space.

The fact that we are in the habit of reducing straight lines at angles to each other to curved lines through the application of infinity, Is evidence that we simply ignore this deep misunderstanding, and proceed as if we think that we understand. I would argue that the "damage control" which you claim, is basically non-existent, because those employing the principles actually believe themselves to have an adequate understand, when infinity proves useful, therefore wouldn't even seek damage control. The problem is prevalent all through modern physics, with vectors and spins, etc..

Yep! Thanks for letting me know. Metaphysician Undercover will find this tid bit right up his alley. — Agent Smith

Actually "infinite-sided polygon", to me, can only be interpreted as an incoherent object.

If I tell you that a tower of infinities actually exists in something like a Platonic realm, what does that mean for you and me? — jas0n

Only coherent intelligible objects could ever exist in the Platonic realm. Incoherencies are banned by the Ruler of the realm.

The issue is not in the system of symbols but in the relationship of that system to the rest of the world. — jas0n

Actually the issue is not as simple you say. In reality, incoherency is allowed to exist within the system, as the example of "infinite-sided polygon", demonstrates. What happens is that there are problems in the relationship between the system and the world, as you say. But since the problems are associated with the very fundamental aspects of the system, no amount of tweaking the system can overcome the problems. So the only way that the system becomes applicable to the world, is to allow inconsistency into the system, to overrule the problems with the foundational axioms.

The simple reality is that the entire system is flawed, right from the very foundations, so any attempts to make it more applicable will require inconsistency within it. And that's what we see, inconsistency is rampant within the system. The only true fix is to replace the entire system from bottom up, with principles derived from a better understanding of space and time. And that's how this discussion is related to mysticism. We need to turn to mysticism to find that better understanding.

Your eyes, for sure, will find it really difficult to tell them apart, even your sensitive finger tips will fail in this task. — Agent Smith

The senses deceive us, that's why we have logic.

I believe it's this very issue that you raise that makes infinity so attractive/appealing to mathematicians; You wouldn't be able to tell the difference between an ∞∞-sided polygon and an actual circle. Invoking Leibniz's 2nd law of identity (the identity of indiscernibles), I'd say it's all good; for all intents and purposes, won't you agree? — Agent Smith

I'd disagree, this is not a correct application of the identity of indiscernibles. An infinite sided polygon is an incoherent object. It could not have any identity.

We can reject infinity for many reasons, but look at all the good it's doing! — Agent Smith

Until we reject it, we'll never figure out how much bad it is doing. How much bad does it take to negate how much good?

A 96-sided polygon isn't a circle but is merely circle-like, that's all. — Agent Smith

It all depends on how you define "circle-like". Clearly it is not at all "circle-like" when we compare a curved line to straight lines at angles to each other. If the defining thing is practical purpose, then it is circle-like, because it serves the purpose in practice.

But since the representation, which serves the purpose, is really nowhere near like the thing it is meant to represent, we can see a deep problem, if truth is supposed to be correspondence. Our theories which work in practice, and are confirmed and validated by the fact that they do work, (experimentation), might still be far from the truth.

That's exactly what it means, it's basic calculus. — Pantagruel

The problem though is that a curved line is fundamentally different from a straight line, because the curved line, no matter how short the segment, will always require two dimension, and the straight line will always be on one dimension. So there will always be angles between the sides, no matter how many there are. If basic calculus denies this difference between the straight line and the curved line, it must be mistaken.

Well, I won't say you're wrong. There must've been a very good reason why the Greeks were so reluctant to incorporate infinity into their math. Even Archimedes & Eudoxus, two people who were among the first to employ the method of exhaustion simply stopped/limited their calculations at/to an arbitrarily large but finite number (Archimedes used, if memory serves, a 96-sided polygon to approximate a circle when calculating ππ). — Agent Smith

Things like this have proven to be very useful, just like the calculus that Pantagruel refers to, it's very useful. I would call these useful lies.

What, may I ask, are the specific issues you have with ∞∞? Is it the paradoxes (Cantor's mind probably couldn't parse them and ergo, his brain crashed) or something else? — Agent Smith

What if I said that the issues I have with infinity are infinite? Look at the issue in my reply to Pantagruel for example. The concept of infinity is used to blur the fundamental difference between the straight line and the curved line. The two are incompatible, but employing infinity makes it seem like they are not incompatible. There are countless examples of similar instances where infinity is used to blur the incompatibility between two fundamentally incompatible things, like discrete and continuous for another example. It's just a basic error carried out for convenience sake, like representing a circle as a 96 sided polygon.

Why? Do the math. Lemme show you: — Agent Smith

I do not accept any mathematics which employs infinity. Infinity is not applicable to real world situations Such mathematics may be very useful in many situations, but the infinity monkey example demonstrates how adhering to principles which are not actually applicable to real world situations, will eventually give us absurd conclusions.

I don't think there is a justified reason to think this. — Yohan

That's what I've been saying, the conclusion is based in faulty mathematics which employs infinity as a number.

So you're saying that if there is an infinite number of monkeys typing, it's very likely that one might sit down and type some Shakespeare right off the bat. Well, I see the point but I don't buy it. I guess the example not only shows how ridiculous infinite time is, it shows how ridiculous an infinity of anything is.
What if your die had an infinite number of sides, do you think it would be circular?

You have convinced me of one thing: what you say should be rejected because it is inconsistent. But according to you, you are in good company: — Fooloso4

The problem is that you have clearly not followed what I said, so you have simply convinced yourself through some sort of bias or prejudice. I clearly said that the whole of what the person said is not to be rejected, only specific propositions, which are judged to be inconsistent with truth, are to be rejected.

If I have given you two contradicting propositions, by what principle other than ad hominem, do you reject them both?

I see your point, only vaguely though. — Agent Smith

What does it mean to see a point "vaguely"? Does this mean that the point only has a vague existence, or does it mean that your mind only has a vague grasp of it? Or both, or neither? If the point itself is in your mind, then I would conclude both.

But your claim is not that you don't understand but that what you are reading is inconsistent. — Fooloso4

Yes, that's because I've gone through the further stage I've describe, reference to secondary sources. This justifies my claim. What I could not understand in my primary readings, it turns out that I could not understand it because of inconsistencies.

In that case you are no longer talking about one's judgment that they cannot understand but that one understands well enough to reject it. It may still be the case that a person still does not understand. — Fooloso4

Again, this is the secondary stage, which is justified by secondary sources.

It means that the judgment was wrong. — Fooloso4

No, that's clearly false. The possibility that one's judgement is wrong does not mean that the judgement is wrong. If the only way to justify a judgement was to exclude all possibility of mistake, then judgement would be unjustifiable.

More inconsistency. — Fooloso4

I don't think so, there's simply a clear lack of effort to understand, on your part, and a refusal to recognize the part between (reference to secondary sources), which separates statement A from statement B. Furthermore, you are comparing a statement about the whole, (not rejecting what has been read), with a statement about a part (rejecting a proposition). The first applies to an inability to understand what has been read, and the second to an understanding developed through further analysis.

For example, suppose there's a logical argument which consists of two premises which appear to be acceptable, and a conclusion. The conclusion however, appears to be wrong for some reason, outlandish, absurd, or totally inconsistent with observation. This is how Aristotle described sophistry, as using logic to produce an absurd conclusion. Take Zeno's paradoxes for an example of such sophistry.

Now, we ought not simply reject the whole thing, just because we do not like the conclusion. But, we cannot accept it because the conclusion is clearly wrong. So, we need to analyze the premises individually, along with the logical process applied, to see what the problem is. These are the puzzles of philosophy which I referred to earlier.

What Aristotle noticed, is that strict adherence to the law of excluded middle as a logical principle, by sophists, could produce absurd conclusions. He demonstrated that the reason for this is that "becoming" is of a completely different category from the logical category of "being and not being". Plato revealed this issue in numerous dialogues. So if an act of becoming, a movement for example, is described in a premise as states of being and not being, there is really an incompatibility between the thing being described, and the description. Therefore we ought to reject such premises as false. So for example, in relation to Zeno's paradoxes, if a movement (an act of becoming), is described as being at point A at one time, and being at point B at a later time (states of being), we ought to reject those premises as false. The movement is what happens between point A and point B, and it is categorical different from being at point A and being at point B, as "becoming" is categorically different from "being and not being". The law of excluded middle would incline us to believe that it must be either being or not being, thereby denying the possibility of becoming.

The question is: what significance and conclusion do you draw from the conclusion that some dialogues are placed in the early period, some in the middle, and some in the late period? — Fooloso4

When there is an inconsistency in a philosopher's material, between what is stated at an earlier time, and what is stated at a later time, we can accept that the later is more representative of what the philosopher believed as the truth. And when the philosopher has much material like Plato, we can usually find within the middle part, the arguments by which the earlier statements are refuted, and which ultimately support the later statements.

In the case of Bk Lambda, of Aristotle's "Metaphysics", which Paine refers to, this book has been placed at the end of "Metaphysics", which is supposed to be after his "Physics". So we get the illusion that this book expresses Aristotle's final decisions, his most developed thought. However, in reality we find the ideas and arguments expressed in Aristotle's other books, which actually refute these proposals of Lambda. Therefore we ought to conclude that this book should really be placed at the beginning of Aristotle's work, as the beliefs of a young Aristotle, which he later refuted, or the more likely conclusion, as I explained to Paine, that it is not really Aristotle's writing.

I still feel, time isn't really a factor in re the infinite monkey theorem. Why, as you yourself so graciously pointed out only one monkey would be needed for this rather boring task, it has all of eternity to try out all character combinations. — Agent Smith

The point being that the monkey needs all of eternity (infinite time). Assign any particular amount of time to the monkey and it is highly probable that it would not complete the task in that time. Give the monkey infinite time, and it is impossible that it will not complete the task. As I said above, this just shows how ridiculous the concept of infinite time is.

Is it possible that one is wrong? — Fooloso4

I don't see how this would be possible. How could a person be wrong, in one's judgement that they cannot understand something. This would mean that the person really understands something which they think they do not.

That one's own mode of interpretation in this case misses or misunderstands something? If so then rejecting what is read as inconsistent is itself inconsistent. — Fooloso4

It's not a matter of rejecting what is read, it's a matter of recognizing inconsistencies within what is read, which makes it impossible to understand it. So the interpreter never claims to understand what is written, because this is impossible, as it is interpreted as inconsistent and therefore impossible to understand. Therefore the initial assumption which the reader makes is that the material is misunderstood.

You are misrepresenting it as a claim of understanding. But this cannot be the case, because the person interprets the material as inconsistent, which renders understanding as impossible. This is why we move to secondary sources. So for instance, when Plato is interpreted as inconsistent with respect to the theory of participation, one might move on to Neo-Platonists and Aristotle, to aid in the process of trying to understand Plato.

The point being that it is not a matter of claiming to understand the material, then rejecting it because it is understood as inconsistent, it is a matter of recognizing that you cannot understand the material, so you move to secondary sources for assistance. Then, when the secondary sources offer conflicting interpretations, you have grounds for a judgement of ambiguity or inconsistency. The primary source then needs to be revisited, with a new attempt to understand, before that judgement is made. Nothing can be rejected simply on the basis of inconsistency, because one or the other of the two inconsistent parts may be acceptable.

Is the judgment of the individual subject always consistent with the truth? If it is not then it is inconsistent to say in this case that we really ought to reject the proposition. — Fooloso4

I really don't see that you have a point here. When a person judges a proposition as inconsistent with truth, this is grounds for the person to reject it, forcing the ought by implication, false therefore reject. The fact that the person might make a mistake, does not negate the judgement, nor the ought implied by the judgement. If the person is worried about mistake, and is skeptical, then the judgement is suspended. If the person is not skeptical, then the judgment is made, and the ought is implied, and whether or not the person is wrong in that judgement is irrelevant because the ought is forced by the judgement, not by anything else.

There is a clear inconsistency here. A contradiction. First you say there are distinct periods then you don't think there are distinct periods. Are you saying that there are distinct periods but you don't think there are?

What you say contains several inconsistencies. It should be rejected. — Fooloso4

I really can't grasp what you are saying. "His thoughts are divided into distinct periods", indicates an artificial act of division, so that the divisions produce distinct periods, which have become conventional. Think about the way that the day is divided into morning and afternoon. So, I told you that I don't believe that there are real distinct periods, I believe there is just a progression, which has been divided into distinct periods for pragmatic purposes, convenience. Likewise, I think that the passing of time is just a progression which has been divided into distinct periods, for convenience.

If you look into Lamarck's "Zoological Philosophy" you'll find a description of orgasm as a fundamental aspect of living.

Any task requires time. Even with an infinite number of monkeys it is not guaranteed that one of them would type any particular thing at first try. This is because many of them would type the very same thing. in the first few moments. So time is the essential feature. We might even consider that one monkey would type all of Shakespeare in an infinite amount of time.

But still we'd have to consider what constitutes all of Shakespeare. Would typing one text at one time, then another text at a much later time qualify? If so, then would typing the first letter at one time, then the second letter at another time, and the third letter at a later time, etc., qualify? What happens with all the intervening letters?

The infinite monkey theorem, as a rendition of the principle of plenitude, is really a demonstration that the idea of infinite time is ridiculous.

Consider Lamark's use of "orgasm" as the fundamental, and defining feature of life.

Lamarck claimed that gelatinous matter could receive the “vital orgasm,” a sort of agitation of molecules opposed to universal attraction. “Uncontainable” fluids, caloric and electricity, could provoke this “vital orgasm.” Later, the containable fluids, gases, and liquids, especially water, crossed this matter and deposited particles. This process was the beginning of nutrition. Lamarck considered that this steep of transformation corresponded to the structure of the... — https://link.springer.com/referenceworkentry/10.1007/978-3-642-11274-4_859

The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type any given text, such as the complete works of William Shakespeare. In fact, the monkey would almost surely type every possible finite text an infinite number of times. However, the probability that monkeys filling the entire observable universe would type a single complete work, such as Shakespeare's Hamlet, is so tiny that the chance of it occurring during a period of time hundreds of thousands of orders of magnitude longer than the age of the universe is extremely low (but technically not zero). The theorem can be generalized to state that any sequence of events which has a non-zero probability of happening, at least as long as it has not occurred, will almost certainly eventually occur. — Wikipedia

Infinite monkey theorem: — Agent Smith

You know the infinite monkey theorem is a feature of an infinite amount of time.