What do you mean stipulated? That Achilles cannot overtake is a non-sequitur. It simply doesn't follow from there being a way to divide the journey into infinite segments. — noAxioms

It's not a non-sequitur, the conclusion follows logically from the way that Achilles' movement is described. From the description there is always further distance for Achilles to move before he overtakes the tortoise. Therefore he cannot overtake the tortoise. The issue is not that the argument is invalid, it is that the argument is unsound. The description of motion employed provides false premises.

Time not being allowed to pass was never a specification in the OP. — noAxioms

In the OP, it is not the case that time is not allowed to pass, but the premises imply that a minute cannot pass for Icarus, who always has to take more steps before a minute can pass. Just like in Zeno's paradox, the premises which describe how Icarus moves down the stairs are faulty.

So, in the OP, the false premise is the description of acceleration. Acceleration from rest is described as continuous and open ended (infinite). But this is false, acceleration does not happen like this in reality. Imagine if the OP was expressed in the following way. Someone states that the universe is infinite in size. Then the person states that a rocket accelerates from being at rest on earth at a rate of acceleration which will take it to the edge of the universe before a minute passes. Then the person concludes that after a minute passes the rocket is at the edge of the universe. Do you see the incoherency? That's what's going on in the OP. The premises are arranged so that there cannot be an end to the staircase, just like there cannot be an end to pi. Then it concludes, that after a minute has passed, the end has been reached.

So the OP makes a non-sequitur by concluding that the end is reached. Zeno on the other hand, concludes that Achilles cannot overtake the tortoise, which is the valid conclusion. And the absurd conclusion reveals the falsity of the premises.

The dichotomy thing was better illustrated by something that actually seems to be a paradox.
You are at location x < 0. The goal is to traverse the space between x=0 and x=1.
Thing is, a magic barrier appears at x=1/2 if you are at x <= 1/2, but x > 1/4.
A second barrier appears at x=1/4 if you are at x <= 1/4, but x > 1/8.
And so on. Each barrier appears only if you're past the prior one.
Furthermore, for fun, the last barrier is red. The prior one blue, then green, then red again. Three colors in rotation, all the way up the line.

Per the dichotomy thing (and Keystone's stairs), there can be no first barrier. So you walk up to x=0 and are stopped, despite there not being anything there to stop you. I mean, if there's a barrier, you'd see it and know its color, which is like suggesting a remainder if you divide infinity by three.

So paradoxically, you are prevented from advancing despite a total lack of a first barrier. You can see the goal. But you can't move. — noAxioms

I don't think that this is representative of the OP at all. You have changed the divisibility of time in the OP to a divisibility of space in your interpretation. Then, instead of dealing with the problem of acceleration, which the OP is concerned with, you have to employ "magic barriers" to make sense of the steps. There are no such magic barriers employed by the OP, only steps, and each step is made in half the time of the prior step. So clearly, the OP deals with the issue of infinite acceleration.

I don't think the intention was for physics to be a problem. — flannel jesus

If a person does not take into account what is physically possible in this type of thought experiment, then one can make up false premises however one wants, and create the illusion of a "mathematical problem" when no such problem actually exists. The real problem is that the premises are false (physically impossible), and by employing the false premises the illusion of a mathematical problem is created.

Do you truly believe that Achilles is unable to surpass the tortoise? — keystone

By what is stipulated, yes, Achilles cannot surpass the tortoise. But, the stipulations are not a true representation and that is why there is a problem. The issue is with the way that motion is described. We employ a conception of time and space as a continuity which is infinitely divisible. However, if motion actually consists of discrete changes like a "quantum jump" for example, then the representation of a continuous existence, is false.

Do you think that Icarus's deeds influence the passage of time? — keystone

No, I do not think that Icarus's deeds influence the real passing of time. However, the passing of time is a subject in your example, and it is determined by the premises of the example. So. according to the premises of the example, half as much time is covered each time Icarus makes a step, as compared to the previous step, and Icarus can keep on stepping forever. Therefore the passage of time is defined in relations to Icarus's deeds in the example. That is what is stipulated in the example, That the passage of time is relative to Icarus's steps. Whether it is a truthful representation of the passage of time is irrelevant at this point.

It looks like a simple question, but it isn't. I wouldn't want to reply without looking up his argument for a start. One reply might start from the argument here, that solitary thinking (which may or may not be what he is talking about) doesn't produce the best ideas on its own. The answer from that stand-point would be, no. But that might mean rejecting his argument about "contemplation". That is thinkable. I'm not a fan of his hierarchical argument for the Supreme Good. — Ludwig V

For what it's worth, I believe you'll find it in Bk 6 of Nichomachean Ethics. A lot of any such argument is a sort of stipulation of intuitive principles, so of course the premises are debatable. I think the general idea is that contemplation produces the most universal, principles of theory, and these are required to ground practical principles, and practical principles are required for moral actions. Therefore contemplation produces the highest principles because these are a requirement for all the other virtues. So contemplation is the highest virtue. Then, he moves to show how contemplation is consistent with "happiness" at the end of Bk 10.

After a minute, yes. Do you contend otherwise, that the sum of 60/2**n is not 60? — noAxioms

The specifications do not allow for a minute to pass, that's the problem. It's just like Zeno's Achilles and the tortoise paradox. What is specified by Zeno, disallows the possibility of Achilles passing the tortoise. Here, what is specified in the op by keystone, disallows the possibility of a minute passing.

So it's like you're saying, "after Achilles passes the tortoise...", when Achilles cannot pass the tortoise, because of what is specified, he must pass an infinite number of spaces first. Here, you are saying "after a minute..." when a minute cannot pass because of what is specified, Icarus must pass an infinite number of steps fist.

So it's just like the Achilles and the tortoise paradox, with a different conclusion. Here, instead of concluding that a minute cannot pass, as Zeno concluded that Achilles cannot pass the tortoise, keystone changes things up to say that after a minute has passed the infinite number of steps has been reached. But @keystone has made a invalid conclusion, and should have stuck to Zeno's formulation, to say that a minute cannot pass for Icarus because he always has another step to make first, and that step will be made in a shorter time than the last.

So her argument is that traditional philosophy privileges one kind of human experience, typified by Descartes' solitary thinker (and, perhaps Rodin's statue, which also suggests the thinking is a solitary occupation) or Virginia Woolf’s desire for a room of her own. — Ludwig V

So, philosophy, as the ideas which are produced from the solitary thinker, is a representation of that kind of human being, the solitary thinker. Now, Aristotle shows how contemplation is the highest virtue. So can we conclude that philosophy provides us with the very best ideas?

Despite the staircase being endless, he reached the bottom of it in just a minute. — keystone

But also, there is a slight of hand that occurs when we are encouraged to imagine Icarus's position immediately after he's finished traversing the infinitely long staircase in the original direction. If he would have traversed the staircase in Zeno like fashion, as specified, although he would have stepped on all the steps in a finite amount of time, there would be no definite position along the staircase that he was at immediately before he had arrived at his destination. — Pierre-Normand

Yes, there is a "slight of hand" involved. The real solution is that the only "finite time" in the description is the starting time, and the formula for figuring the increments. And, according to the prescribed formula for figuring the increments, there can be no finish time. It's analogous to finding the end of pi, you just keep going. Despite the defined, and finite starting point, Icarus is currently covering an infinite number of steps in an infinitely short period of time, and by adhering strictly to the description we must conclude that the bottom will never be reached. Bye bye Icarus, enjoy the "black hole's core".

He reaches the bottom of something with no bottom. It taking a minute is fine, but there being a bottom is contradictory. Hence I think resolution. Just as there is no first step to take back up, there is no last step to reach, even if it is all reached in a minute. — noAxioms

How does that work? He's traveling by steps. Each step takes a discernible amount of time which is a different time from the prior step. You say he reaches the bottom, yet there is not "last step". Clearly he doesn't do a bunch of last steps at the same time, so ambiguity is not the problem. How do you think it is possible that he got finished with all the steps, in the described order, yet there was no last step?

Peter Wohleben, a career forester has a very well written, bestselling book called "The Hidden life of Trees: What they feel, How they communicate". In it he talks as if trees act with intention, and he describes how trees communicate with each other through electrical impulses that travel through mycelium which grow around their roots. The electrical impulses of trees have now been studied scientifically.

To communicate through the network, trees send chemical, hormonal and slow-pulsing electrical signals, which scientists are just beginning to decipher. Edward Farmer at the University of Lausanne in Switzerland has been studying the electrical pulses, and he has identified a voltage-based signaling system that appears strikingly similar to animal nervous systems (although he does not suggest that plants have neurons or brains). Alarm and distress appear to be the main topics of tree conversation, although Wohlleben wonders if that’s all they talk about. “What do trees say when there is no danger and they feel content? This I would love to know.” Monica Gagliano at the University of Western Australia has gathered evidence that some plants may also emit and detect sounds, and in particular, a crackling noise in the roots at a frequency of 220 hertz, inaudible to humans. — Smithonian

https://www.smithsonianmag.com/science-nature/the-whispering-trees-180968084/

Wohleben now has a book called "The Inner Life of Animals: Love, Grief, and Compassion: Surprising Observations of a Hidden World". If it's as good as the tree one, it's well worth the read.

You're missing the point. The act, which is called "interpretation", "to interpret", requires a relationship of representation of some sort. This is commonly understood as the relationship between sign and what is signified by the sign. It could also be understood as information and what the information says. To "interpret" is to bring out the meaning which is apprehended as being inherent within this relationship between sign and signified. So any act of "interpretation" requires these two aspects, with this relationship. For simplicity we could say these two are signs and what is signified, representation, and what is represented, or, the information and what the information says, or means.

So if the body/mind "interprets what is given to it", then what is given to it is the signs, information, or representation. But we still must consider the separation between the representation given to the body/mind and what is represented by that representation, or, the separation between the information given, and what the information says, signs and what is signified.

In the act of interpretation, "what is represented", or, "what the information says", is something created by the mind of the interpreter. The interpreter looks at the representation or information, and produces (creates) what is thought to be the meaning of it. "What is represented", "what the information says", "what is signified by the signs", is a creation of the interpreting mind.

Therefore, if "the bodymind interprets what is given to it precognitively", as you say, and what is given to it is a representation, sign, or information (as implied by the concept "interpret"), then what is represented by that information which is given to the mind precognitively, is something created by the mind in this act of interpretation. And so, if "what is given to it precognitively" is determined to be a representation of "the world", or information about "the world", then the world as what is determined as being represented, through the act of interpretation, is something created by the mind which interprets the representation, signs, or information.

People generally prefer to recognize difference over similarity. It feeds the ego and cultivates the superiority complex derived form the person's denial, or refusal to accept oneself as a very small part of a very large whole. Brute or savage, same difference.

The way I see it the world is always already interpreted, so we are not going to agree about this. — Janus

How do you make that consistent with what you said earlier:

It is true that the way we perceive the world is conditioned by the ways in which our sentient bodies and brains are constituted. The suggestion that the mind creates the world, rather than merely interprets it seems absurd and wrong. — Janus

If, "already interpreted" is a prerequisite of there being such a thing as "the world", and minds do the job of interpreting, how would you dismiss the proposition that the mind also creates the world, being prior in time to the world? Since a mind is already necessarily prior to the world to perform that interpretation which is already done in order for there to be such a thing as the world, it seems very likely, rather than absurd, that a mind also creates the world.

Our interpetations are constrained by the nature of the world including ourselves, so it's not right to say that we create the world. — Janus

If the world is always already interpreted, then an interpretation is prior in time to the world. Why would you think that the interpretation which is prior in time to the existence of the world, would be constrained by the world? As is the case with cause and effect, the posterior is constrained by the prior, not vise versa.

No, representing the world to ourselves just is interpreting it. — Janus

To "interpret" is to bring out, or explain the meaning of. To "represent" is to stand for, signify, or correspond to. In no sense are the two the same thing. As I explained, one can interpret a representation, but a representation is not an interpretation. This is because representation is meaning without the requirement of understanding, whereas interpretation requires understanding.

So, in relation to your prior statement, we can only interpret meaning, which we find in the representation of the world. We never actually interpret the supposed independent world, only the representation of it. Therefore the world which we interpret is just an artificial representation, a creation. And when we analyze the representation process, we find that the representation is always a representation of a further representation, in what appears to imply an infinite regress. This is why skepticism cannot be ruled out.

This is going too far. It is true that the way we perceive the world is conditioned by the ways in which our sentient bodies and brains are constituted. The suggestion that the mind creates the world, rather than merely interprets it seems absurd and wrong. — Janus

The primary problem with this statement is your use of "interprets". What is present to the mind, is just a representation which is created by the mind. The thing represented is supposed to be "the independent world". But the relationship between a representation and the thing represented cannot be called an "interpretation". An "interpretation" would be an explanation of the representation, which may attempt to describe that relation between the representation and the thing represented. But we cannot truthfully say that the relation between the conscious representation and the supposed independent world is anything like an interpretation.

Furthermore, if we proceed to a deeper level in our analysis, and attempt a true interpretation of that relation between the representation and the thing represented, we find a secondary problem. If we look at what is actually represented by the conscious mind, when it creates its representation which is supposed to be a representation of the independent world, we see that what is represented is just the information which the subconscious part of the mind, along with the sense organs and neurological system, provide to it. Now we have a distinction between the conscious part of the mind which creates what we know as the representation, and subconscious part (the neurological system), which creates the raw material which is being represented by the conscious representation.

Therefore it is really correct, and not at all absurd or wrong, to say that the mind creates the world, even though this may seem extremely counter intuitive to you. The conscious mind creates a representation of "the independent world", but what is actually represented here is just something created by the subconscious part of the mind. The analysis I provided above shows that the conscious mind creates something which is a representation of what is supposed to be "the independent world". However, what that representation really represents is the information provided to it by the subconscious part of the mind, and this part of the mind produces that information through the various acts of sensation. So what is really represented by the conscious mind's representation, which is claimed to be "the independent world", is just something created by the subconscious part of the mind.

Ok, let me break down more clearly what I do and do not mean. To your credit, value is always assigned but, to my credit, it is not always extrinsic value. Intrinsic value is value assigned to a thing because, and to the degree that, it innately insists (or demands) on being valued. Extrinsic value is value a thing has been assigned relative to how well it fulfills a (subjective) purpose.

Intrinsic value, unlike extrinsic value, is objective because, although we assign it, it is being assigned because the thing actually (mind-independently) motivates people to value it for its own sake and not for the sake of something else: a person is motivated, even if they overcome it, to value a thing with intrinsic value despite what they believe or desire to value it at. It is external motivation (for the subject) which they can not think or desire away.

Another way to put it, is that intrinsic value is value a thing has (1) for its own sake and (2) is attributable to the thing (which exists mind-independently) from its natural ability to motivate people of #1. — Bob Ross

I still do not see how this description of "intrinsic value" makes any sense. You seem to be saying that there are some things in the world, which demand of people, that the people want them, and they want them simply for the sake of having the thing, itself, and not for anything else. But doesn't this really just say something about people in general, that people exist in such a way that there are specific types of things which they will want, simply for the sake of having that thing.

Notice, that I say "specific types of things" that people want, but you portray particular things as having this intrinsic value, rather than types. If it is a type of thing which is valued in this way, then the value is not really intrinsic to the things themselves, but it is attributable to the type.

So take food for example, as such a type. Food appears to be valued for its own sake. This type of thing is inherently good. But what is the case, is that we make a category of things judged as good to eat, we name this category "food", and then we judge which things ought and ought not be placed in this category. So "good" is a defining feature of the category, and its definition is based on what is needed by the human being, it is not based on what is intrinsic to any particular thing.


We might say that nutrition is a good which is intrinsic to particular things, but it is only classed as "nutrition:, or "good", based on how it is received by human beings. It appears like the good is intrinsic to the thing, but it is really only "good" in its relation to humans. These chemical compounds are ones needed by humans. Isn't this very similar to pleasure and pain? These two are categories, one of good feelings, the other bad feelings. They are types of feelings, the good type and the bad type. Then particular instances of feelings need to be judged as to whether they fit one category or the other. So they are really only good or bad as a result of their relation to the conscious mind which does the judging.

I would simply want to speak about what is correctly valued as opposed to what is incorrectly valued; or what is rightly done for its own sake as opposed to what is wrongly done for its own sake; or what is the highest good/end as opposed to what appears to be the highest good/end.

* This last sentence seems to represent Aristotle's thought. Plato, Augustine, Aquinas, and others go beyond Aristotle in this, but Aristotle's position is careful and easily defensible. He does not commit himself to goodness simpliciter in any substantial sense. — Leontiskos

Yes, I think Aristotle was the first to distinguish between the apparent good, and the real good. Aquinas followed him on this distinction, and I believe Augustine did too, to a large degree. Plato was more vague on his notion of "the good".
.

I don't agree with the use of random here. Stochastic phenomena are just simply not precise (this is the word I was looking for) as an analysis. Commonly, (and I say erroneously) it is the precision upon which we judge whether something is random, or in the case of Heisenberg, uncertain. But to further judge a phenomena as undetermined is really troubling. — L'éléphant

I agree with this. The appearance of randomness is created by the system which analyzes, it is not a feature of the thing being analyzed. That the analyzing system does not apprehend the patterns being searched for and produces the conclusion of "random", is an indication that the system is not properly formulated for the application it is put to.

You have a very strange way of reading 180 Proof. Did bert1 say that "capacity" = "structure and function"? That's an odd interpretation, to assume that a capacity is a structure or function.

Aristotle says that eudaimonia is the highest end because of its nature, not because subjects happen to value it. But Aristotle and Aquinas immediately address the most obvious objection, namely that different people are made happy by different things (↪Leontiskos).

Here is how Aquinas puts the quandary:

So, then, as to the aspect of last end, all agree in desiring the last end: since all desire the fulfilment of their perfection, and it is precisely this fulfilment in which the last end consists, as stated above. But as to the thing in which this aspect is realized, all men are not agreed as to their last end: since some desire riches as their consummate good; some, pleasure; others, something else. Thus to every taste the sweet is pleasant but to some, the sweetness of wine is most pleasant, to others, the sweetness of honey, or of something similar.
— Thomas Aquinas — Leontiskos

Yes, this is a problem. If "last end" is defined as happiness, then we need a separate description of happiness or else the two words just become representative of each other. Then "happiness" means "last end", and "last end" means "happiness", and all we have is a vicious circle.

So if we look at the broader context, to get an understanding of exactly what happiness is, we see that it is something which is produced in a variety of different ways for the various different people. This appearance of a multitude of differences prevents that mode of inquiry from proceeding, and we are forced to look back at the more general, to find a description with a more universal application, instead of referring directly to all the specific differences.

Notice that Aquinas mentions "the fulfilment of their perfection". Developed from Aristotelian principles, the goal of "perfection" becomes the last end for Aquinas. Every existing thing, by the nature of its very own form, has a perfection which is proper to it, and it alone. So that is what could bring a person true happiness, the perfection of one's very own form, the unique form which is proper to oneself, and this becomes the last end, the goal of each individual.

So this defines "happiness" in "perfection", and leads us toward the need to understand this concept, "perfection" which is revealed as a sort of ideal form.

But math itself does not refer. — fishfry

Math is a field of study, it's not a symbol, sign, or even a group of such, so it's not used to refer to anything. But that's irrelevant. So this discussion is useless from the start

In the evolution of thought, people are going to decide math is wrong because it doesn't actually refer to anything? I thought that was a feature. — fishfry

In practise the math always refers to something. In theory it is designed to be applicable to a very wide range of circumstances. When the theory is not being used to refer to anything, it sits idle. So it only "doesn't actually refer to anything" if it never gets used, in reality it refers an endless number of things.

From what I can see, the Lounge is now the best part of this site. — fishfry

It is a pretty cool place to hang out, lots of activity down there. And they call it The Lounge. Now that's a misnomer.

Law of identity, that each thing is identical with itself, isn't actually math, but general philosophy. So I guess the law of identity is simply a=a or 1=1. Yet math it's actually crucial to compare mathematical objects to other (or all other) mathematical objects. Hence defining a set "ssu" by saying "ssu" = "ssu" doesn't say much if anything. Hence the usual equations c=a+b. — ssu

This is the crucial point, which I'd like to bring to your attention. The law of identity is an ontological principle which deals which "objects" as we meet them in our daily lives, all the different objects which we sense around us, and it forms a defining principle of what it means to be an object. It is meant to recognize the reality of these objects, in the face of skepticism, and offer guidance as to the type of existence which they have. It is probably the most universal of general principles, applying to all the different types of objects that we might possibly encounter.

On the other hand, supposed "mathematical objects" are distinctly different, and the law of identity does not apply. Now we might simply consider that the so-called mathematical objects are not even objects, therefore they don't have any identity as such, and they are really just thoughts and ideas. That seems like a reasonable approach. However, some people want to compose a special type of "identity", specifically designed for these thoughts and ideas, and through reference to this special type of identity they argue that these thoughts and ideas actually are a special type of object, mathematical objects.

However, it ought to be clear to you, that this is just smoke and mirrors sophistry. The special type of identity is formulated for the special purpose of creating the illusion that these thoughts and ideas are a type of object. But it is actually impossible that these ideas are a type of object because the law of identity applies to all types of objects which we might possibly encounter, and this supposed special type of object requires a distinct form of identity which is incompatible with the law of identity.

It's like comparing what in Physics is work and what in economics / sociology is work. The definitions are totally different. — ssu

I don't think that's true true, "work" in physics is consistent with "work" in economics/sociology, physics is simply a broader sense, and "work" in sociology is narrowed down to work is done by human beings.

In the case of "identity" in mathematics, it is inconsistent with, (in violation of), "identity" in the law of identity.

Suppose I owe a creditor a certain amount of money, and ask them, "I have record of my balance as being 582 dollars plus 37 dollars. Do you have the same number?" They say, "Yes, your balance is 619 dollars and 0 cents." It would be ridiculous for me to say, "No! 582 plus 37 is not the same number as 619.00!" — TonesInDeepFreeze

Obviously, you do not understand the law of identity. By the law of identity, the symbols printed here, 582, are distinctly different from the symbols printed over here, 582. Although they appear very similar there is a different position, context, etc., so it is very clear that this is not two instances of one and the same thing, 582. By the law of identity two separate occurrences of the printed symbols, are not the same thing, they are two similar things. Under the conditions of the law of identity we cannot say that 582 printed here is the same thing as, or has the same identity as, 582 printed here.

Therefore I recommend that any wise person would completely disregard the following statement, as coming from the mind of someone who does not know what they are talking about.

The law of identity is a philosophical principle.

It is adopted in mathematics. — TonesInDeepFreeze

Your thesis is that someday, Internet archeologists are going to discover this thread and go, "My God, math is wrong!" — fishfry

It's actually an ongoing process, the evolution of thought. Look at Russel's paradox for example.

Even if the discussion has moved on, I'll just point out this, what identity in math is and why math does deal with identity:

In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B (which might contain some variables) produce the same value for all values of the variables within a certain range of validity.[1] In other words, A = B is an identity if A and B define the same functions, and an identity is an equality between functions that are differently defined. — ssu

All right, you just confirmed what I thought. "Identity" in mathematics is equality. That clearly violates the law of identity. The law of identity allows that identity is a relation between a thing and itself, so there is only one thing involved. Equality on the other hand allows that two distinct things may be equal to each other. So unless you can provide this distinction between equality and identity, or else show that to be equal necessarily means to be one and the same thing, in set theory, then you ought to accept this violation. And, as I mentioned already, we know that the latter cannot be done, because set theory allows that two sets with the same elements in different orders are equal. Therefore I think we ought to just conclude that "identity" in mathematics is a violation of the law of identity. Agree?

You just described your own posting style. — fishfry

That's very observant of you fishfry. Generally speaking, one's language use is a reflection of the conventions and habits which the society has immersed that person in. I like to seek, determine, and then exaggerate within my own usage, the various ambiguities, misleading implications, false representations, and overall misgivings of deceptive habits and conventions which permeate our communications, thereby laying them bare, exposed for the world to see, so that perhaps, at some point in time, the general population will start to realize that something needs to be done about this situation. Wayfarer knows me as the obfuscator.

Bob, in my own moral theory, I believe everything has intrinsic value by the fact of its existence. — Philosophim

This is a fair proposal. It bases value in existence, allowing for "intrinsic value" by the very fact that a thing's existence is intrinsic to it. The problem now would be how to scale different values. By what principles would you say that one type of existence is higher or lower than another type of existence?

My analysis doesn't determine what has intrinsic value based off of what is done for its own sake: — Bob Ross

Since value is relative, in the way I described, your discussion of "intrinsic value" doesn't make any sense. It's an oxymoron. Things like pain and pleasure do not have value, they would be better described as "invaluable", meaning beyond valuation, or impossible to value.

Do you see that "value" implies the ability to scale the worth of a thing relative to the worth of other things? The idea that things have "intrinsic value" would negate the idea that the thing's value is determined by the scale of worth. So this, "intrinsic value" cannot be "value" as we know it.

You are trying to overload the word with metaphysical baggage that it simply does not have in math. — fishfry

What I've argued is that this use of "same", is not consistent with "same" as defined by the law of identity. And if this sense of "same" is claimed to be constitutive of "identity", as Tones argues, then this is a violation of the law of identity. If this is what you want to call "metaphysical baggage", that's ok with me. There are many words with similar forms of "metaphysical baggage". The use of a specific word in one field may contradict its use in another field, and it only becomes a problem if people start to believe that the two uses are consistent with one another.

They are NOT implying any kind of metaphysical baggage for the word "same." If pressed, they'd retreat to the formal syntax. — fishfry

You may want to take this up with Tones, and his notion of "identity theory", which obviously is a kind of metaphysical baggage.

Make sense? You are using "same" with metaphysical meaning. Set theorists use "same" as a casual shorthand for the condition expressed by the axiom of extensionality. It's a synonym by definition. The set theorist's "same" is a casual synonym; your "same" is some kind of ontological commitment. So all this is just confusion about two different meanings of the same word. — fishfry

That completely makes sense. However, not every mathematician is as reasonable as you are. If you look at what TonesoffTheDeepEnd is writing here, you'll see great effort to support some kind of formal identity theory. That is not a "casual shorthand for the condition expressed by the axiom of extensionality".

Also, meta: This thread, "Infinity," is active, and I keep getting mentions for it and replying. But this thread does not show up in my front-page feed! Anyone seeing this or know what's going on? — fishfry

What has happened is that there was a new policy initiated which was to relegate a whole lot of these rambling, bickering, blah. blah, blah, type of threads to The Lounge. And threads in The Lounge don't show on the front page. You'll find The Lounge in the list of Categories on the left side of the front page.

What do you think identity in mathematics / set theory is? — ssu

I don't think mathematics/set theory deals with identity at all. I think that identity is an ontological principle defined by the law of identity. Mathematics deals with equality, which is distinct from identity. Some people on this forum have argued against this, claiming that there is an identity within set theory. But then they only seem to be able to argue that "equal" means "the same", when clearly this is false.

So I think then the question for you, Metaphysician Undercover, is how is the identity different between two sets that have the same elements? — ssu

Having the same elements does not mean being the same as. Having a different order for example would make two sets with the same elements not "the same" by the law of identity which indicates that a thing is the same as itself only. So, even identifying them as "two sets" indicates that they have a different identity.

Because you say "to read the axiom of extensionality as indicating identity rather than as indicating equality is a misinterpretation", it seems that you think this is different. A lay person would think that a set defined by it's elements. — ssu

Yes, identity is very different from equal. By the law of identity, we only call it "the same" if it is one and the same thing. The computer I typed on this morning is the same computer as the one I type on now. Two equal things are not necessarily the same. There were other computers at the store which are equal to mine but each one of them is different, i.e. not the same computer as the one I brought home. I think a lay person would agree with that.

And please just look how identity is defined in mathematics, and you'll notice what fishfry is talking about. — ssu

If you can find that definition for me, I'll take a look. Then we can discuss whether "identity" in mathematics is consistent with the law of identity.

I'm pretty sure I never said that, but if I did, please supply a reference to my quote. — fishfry

My apologies, for misrepresenting what we argued about. I thought you argued that the axiom of extensionality indicated identity.

Goodness is identical to ‘having value’... — Bob Ross

The problem with this perspective can be found through reference to Aristotle, as the others have indicated. "Value" is relative, and it is determined in relation to a further end. So if something has value, it is apprehended as the means to an end. You go to work for the sake of earning money, for the sake of buying things, for the sake of this or that want, or need, etc., etc.. Aristotle noticed that this cannot go on as an infinite regress so he said that there must be an ultimate end. Therefore he proposed happiness as that ultimate end, which is desired only for the sake of itself.

To explain the problem now, the relative values, as means to ends, are validated in relation to the ends which they are needed for. Without the end which a thing is given value for, as the means to that end, the thing on its own cannot be said to have any value. Its value exists only in relation to the end which it is useful for. The ultimate end, proposed as happiness, has no such thing which it is useful for, or else it would not be the ultimate end. Therefore it cannot be validated as a value. If it has nothing which it is useful toward, it cannot have any value. So if goodness is defined in reference to the end, instead of the means, it must be defined by something other than "value", because value is what defines the means.

...nobody really knows what entropy really is so he will have the advantage in winning any arguments that might occur... — Wayfarer

This provides a good representation of this thread. Use a term with sufficient ambiguity, "information" in this case, so that the unintelligible is adequately hidden within what is proposed as intelligible, and it will appear like you are saying something intelligent. The majority of people are fooled by appearances.

They are bad, and when you pull up the floorboards, they aren't even sensible. — AmadeusD

Are you implying that one has to "pull up the floorboards" to access the plumbing? Can't we just go into the basement?

But for what it's worth, the symbol string "same" has no meaning in ZF. — fishfry

"Same" has a meaning in the law of identity. So when you say that the axiom of extensionality is a statement of "identity", you are employing the concept of "same", where it does not belong. "Same" is implied by "identity". That's why I argued that to interpret the axiom of extensionality in this way, as a statement of identity, is a faulty interpretation.

You're adding things that aren't in the game. — fishfry

Actually, it is you who is adding things that aren't in the game, with your faulty interpretation. You are adding "identity", when the law of extensionality is really a definition of "equal". As I've been telling you, equality and identity are not the same concept. This is because "identity" implies "the same" whereas "equal" does not. So, we can have two different things which are equal, but two different things cannot have the same identity.

Therefore it is incorrect to interpret the axiom of extensionality, which is clearly an expression of equality, as an expression of identity. To interpret as a statement of identity is to add something which is not in the game, sameness, when the statement really concerns equality instead, which does not imply "same".

"Subject" is a complicated word. I believe that the meaning of "subject" in the sense of referring to a person, is derived from the ruler-subject relation in which "the subject" is under the dominion of the ruler. Since the activities of "the subject" here are subject to the will of the ruler, this does not provide a good base for understanding the human person as a conscious, free willing agent.

So "conscious subject" is full of hidden implications, the principle one being the physicalist idea that the person's actions, and perceptual apprehension of the world in general, are simply a response, or reaction to the world, as the person is subjected to one's environment. That is the determinist perspective, which commonly inheres within the notion of "subject". This is the alternative to representing the person and the person's perceptual apparatus as acting agent.

Their thoughts, unlike yours and mine, had powers enough to keep them gazing into the pool of solitude.

I would say, it's not the power of one's own thoughts which is the subject here, but the power of the divinity which the contemplative mind comes into contact with. Since the divinity is a real "other" for that mind, to portray this as solitude is a false representation.

@fishfry
From that wiki page:

"or in words:

Given any set A and any set B, if for every set X, X is a member of A if and only if X is a member of B, then A is equal to B."

I see the phrase "A is equal to B", but where does it indicate that A is the same as B?

Ha, ha, very funny.

So I'll go back to a point I made earlier, that even if she is wrong about what Descartes said, she may not be wrong about how the hegemony of the solitary white male has mislead philosophy. — Banno

I take it that no one wants to address the issue of the philosopher's (whether the philosopher is a solitary white man or not) relationship with the divine. It appears to me like the issue is not the hegemony of any particular human being, but that of the divinity which some appear to establish a relationship with.

To exist is one thing, and Berkeley gives me no reason for supposing that existence of anything depends on being perceived or judged to exist. I can make some sense of the idea that anything that exists is capable of being perceived - especially if indirect perception is allowed. — Ludwig V

To "exist" is not well defined, and we tend to use it in whatever way we find suitable for the occasion.

Berkeley is no doubt relying on his argument against abstract objects. It supplies a way of accommodating abstract objects in his system, but is not obviously effective in the absence of his axiom. But his introduction of the notion of "notions" undermines his slogan, since he accepts the existence of my own mind and other minds, and God, even though they are not (directly) perceived. It is clear that he accepts that they are not (directly) perceived, because he introduces notions to get around the problem that my ideas do not themselves include the idea of myself. It's the same objection that was raised against the cogito. — Ludwig V

I agree, it is likely that a thorough analysis would reveal that minds don't actually "exist" if we adhere to Berkeley's principles. That is the problem I referred to earlier, which inclines me to think that we need to bring matter in, through the back door. He provides no principles to provide a separation between one mind and another, or a human mind from God's mind. If we want to conceive of separate minds we need something (like matter) to separate them. Having distinct and separate ideas, in itself, does not suffice because something needs to separate the ideas, one from another.

One of Berkeley's principles is "esse" is "percipi aut percipere", which, on the face of it and in fact, is false. He seems to treat this as a axiom, so I don't know why he believed it. — Ludwig V

I don't understand why you would say this. How can you conclude that the principle is false? To be, or as you state it, "esse", is to be something, and that means to have been judged as having a whatness, or "what it is". This, "what it is", is a judgement based on perception. You cannot dissociate the whatness from the judgement, to give a thing an independent whatness, or "esse", because the whatness. "what it is", is a product of the judgement.

The point was the reality of our communion with the divine. It shows that Midgley's representation ("Philosophers have generally talked for instance as though it were obvious that one consciousness went to one body, as though each person were a closed system") is a strawman. Philosophers, in general, do not represent an individual's consciousness as a closed system.

But the true way to understand that the individual consciousness is not a closed system, is through one's internal communion with the divine (like Socrates' daimon), not to apprehend the connection as an external relationship with other consciousnesses. The external relations, with the misgivings of lies, deception, disappointments, and the general failures of communication with others, only reinforces the feeling of isolation. Yet the internal relation with the divine remains the most true and honest, allowing for one to really "break free" from isolation.

Nature of the Higher Realm: Plato describes a transcendent realm that is "colourless, utterly formless, intangible" and accessible only to true knowledge (epistēmē). This description emphasizes the abstract and non-physical nature of the One beyond being and non-being. In this metaphysical domain, the only faculty capable of perceiving this is reason (nous). Plato often characterises reason as the pilot or charioteer of the soul, guiding it towards true knowledge. This underscores the idea that reason, rather than sensory perception, is what allows the soul to apprehend the true nature of reality. — Wayfarer

The logic of "being and non-being", represents the discrete nature of the reality of "now". At each moment as time passes, there is a true representation of what is and what is not at that precise moment. Since this is a static form, a true "what is" at each precise moment in time, it transcends the sensory realm of what we know as the physical world. Sensory perception gives us a projection of continuous activity, rather than discrete moments of "what is". It is only reason which can lead us beyond the illusion of temporal continuity which our material bodies present our conscious minds with, through the unreliable, and deceptive, sense organs.

This is the way out of Plato's cave. If you study Augustine, you'll see that he takes up this position very strongly. The importance of "the free will", is the strength of will power. The free will allows us to separate ourselves from the temporal world of sensory diversions, to focus on the eternal principles, "being and non-being", and the true nature of reality.