Perhaps they'll turn out to be useful, sometime. — Ciceronianus

Exactly. This is the point I made previously, glad we can agree.

I think the majority contends that the Equal Protection Clause provides that all applicants must be treated the same. — Ciceronianus

You clearly have a fundamental misunderstanding of the opinion that no amount of discussion will help you understand. Your quote above is NOT what the majority opinion is saying. Not all applicants must be treated the same because then there would be no basis on which to accept/reject any applicants. And before you claim to have meant "criteria", it is totally within the law to have different criteria for different applicants (such as the elderly and people from different geographical regions).

Now, though, it's necessary that in order for the race of an applicant to be considered, the applicant must establish that they have those qualities due to their race. — Ciceronianus

Yes. Race is necessarily a factor, as those having the qualities the majority thinks merit consideration will have them because they're black. — Ciceronianus

Exactly wrong. The applicant must establish that they have certain qualities based on their experience. Now, their experiences can absolutely be impacted by their racial/cultural identity, and they are free to elaborate on that, but qualities are not determinable by race, says the majority. Assuming someone has certain characteristics/qualities based on their race is the classical definition of racism, by the way. Your wording isn't clear on whether you believe this (though it is a declarative statement), but if you believe some people have certain qualities (non-biological but rather personal/social) BECAUSE of their race, I find that incredibly problematic.

Do you treat all people the same? Or do you acknowledge that some of them should be treated differently "based on their personal characteristics, many of which are directly derived from their racial/cultural experience of being black in a world of systemic racism?" — Ciceronianus

Couldn't have said it better myself. This is exactly the question to the majority is asking to Harvard/UNC, and they have found that the answer is that they DO treat people differently, not only because of their personal characteristics, but also because of their race in general (i.e. assuming that people of different races by definition have different qualities).

...they state that the Equal Protection Clause allows some of them to be treated differently due to "their racial/cultural experience of being black (for example) in a world of systemic racism." It would seem to me essential that one must be black to have the "racial/cultural experience of being black in a world of systemic racism." — Ciceronianus

Exactly (leaving aside the idea of someone who is trans-racial or racially fluid, which I don't have enough knowledge to speak about).

You are there in the end, the above quote is how it works, and the key idea you need to understand is that a causal chain can have many links. According to the Supreme Court, being black in and of itself does not CAUSE you to have certain qualities, but it CAN cause you to experience circumstances that (by means of your response to those circumstances) creates those certain qualities.

Well, try to understand I've never before been asked to render a legal opinion on what a court didn't say in deciding a case, or about a holding it didn't make. It's not something that's come up in my practice. I assumed you were trying to address the actual decision in question. — Ciceronianus

An actual decision is useful for more than just it's legal impact. Even concurring and dissenting opinions are valuable barometers for where the legal establishment may be on an issue, as has been evidenced many times in history via famous dissents like Dred Scott, Korematsu, and even Plessy v Ferguson. To dismiss those dissents (as well as concurring opinions), because they have little current use in the courtroom is to miss the point of the dissents/concurrences altogether. They are not written for the courtroom, they are written on and for the issue. Otherwise why write them, if they have no value?

According to the majority, those making the admission decision may consider the impacts of discrimination against the applicant because of race (e.g. because the applicant is black) in coming to a decision. — Ciceronianus

Correct.

But, the admission decision cannot be made because the applicant is black, despite the fact that there would have been no discrimination, the impacts of which may be considered, had the applicant not been black. — Ciceronianus

Do you treat all black people the same? Because all black people are black? Or do you treat them differently based on their personal characteristics, many of which are directly derived from their racial/cultural experiences of being black in a world of systemic racism?

Where does the black go? — Ciceronianus

This is a facetious question. It stays in the equation, it's just not the sum total at the end.

Applicant X should be admitted because of characteristics and abilities arising from discrimination against the applicant because the applicant is black (characteristics and abilities which presumably would not have arisen but for the racial discrimination), but that doesn't mean the fact the applicant is black figured in the decision to admit? It doesn't work, I'm afraid. — Ciceronianus

It DOES mean the fact that the applicant is black figured into the decision. What you summarized there is EXACTLY HOW it DOES work. It was FACTORED IN (via the experiences an individual who is black ACTUALLY faced), it was not DETERMINED solely by racial group.

If that doesn't make sense to you, I'm not sure we have anywhere further to go, because the majority opinion devotes many words to explain exactly how that works IN PRACTICE going forward (and how it does NOT work). If you can't see the nuance of that position, then you're not going to be willing to see any other point either.

I have no idea how such a determination may be made But the statement that a person must not be treated on the basis of race seems rather clear. — Ciceronianus

The part of the decision you cited lays out EXACTLY how that determination is made.

In other words, the student must be treated based on his or her experiences as an individual—not on the basis of race. — Majority Opinion

They use the passage you quoted to EXPLICITlY clarify that experiences stemming from race, whether they be racial injustices personally experienced (which could include systemic racism), racial identity as a means to empowerment, or otherwise are valid forms of acceptance metrics. Just that race in-and-of itself is not. A prospective student is free to explain how their racial identity forms their worldview, ethics, etc... but the selection committee must look at the individual's experiences, rather than their stated race to make the final decision. That much is clear from the passage you cited, so your confusion about determinations is puzzling.

Perhaps if you had read the very next sentence it would have been hammered home even further:

Many universities have for too long done just the opposite. And in doing so, they have concluded, wrongly, that the touchstone of an individual’s identity is not challenges bested, skills built, or lessons learned but the color of their skin. Our constitutional history does not tolerate that choice. — Majority Opinion

Racial inequities faced in life can be "challenges bested", overcoming systemic racism can be a skill, and racial/cultural/socioeconomic differences can lead to important lessons about diversity or the lack thereof, and all are EXPLICITLY valid according to this BINDING opinion.

What Justice Gorsuch concludes regarding Title VI, in this case, is no more binding on a court (and of no more importance to me) than is the ass of a rattus rattus. — Ciceronianus

Of course it's not binding, nowhere did I say it was. The fact that you immediately dismiss concurring (and I assume, dissenting) opinions even in terms of their usefulness and veracity is a sad state of affairs. Unless I've mistaken your affinity towards rats?

I look forward to the time when all the esteemed legal scholars in this thread actually engage with the written decision instead of tossing about the vague idea of affirmative action as desirable/non-desirable. The devil is always in the details.

Especially since the majority opinion did NOT rule out race as a factor in admissions, but rather qualified that experiences/character/life circumstances that have occurred BECAUSE of race are still allowable when occasioning the decision related to an individual's application. In other words, using one's experience with systemic racism as a touchstone related to one's fitness for application to university has been, and is still allowable (according to the majority).

Additionally, concurring opinion by Gorsuch makes it clear that the case in question ALSO violates Title VI of the Civil Rights Act.

Love to hear from the great legal minds here how Asian American university applicants' rights have not been violated under the language in Title VI.

The reality of causation “needs” no jargon for the exact same reasons I laid out for the cosmos.

But you have confirmed you have no interesting point to make. — apokrisis

Yes, but it’s quite a burden for me to be uninterestingly correct all the time, you know.

Ducking the issue again. — apokrisis

The issue of your claim that the cosmos needs a jargon? A moderate one at that? The same cosmos that existed for billions of years before any sentient mind learned enough Greek to call it a cosmos?

Yeah, nah. A little too anthropocentric for my taste.

There was a rhetorical purpose to claiming nature was ruled by mathematical laws. — apokrisis

What a funny statement, as if abstract notions and geometric ideas control the universe. Nature is. It is what is. It is not ruled by anything. Mathematics is a useful means of describing and communicating about nature.

Mathematical law describes reality in mechanical and exceptionless fashion. That directly contrasted with the organic and Aristotelean conception of nature that prevailed until Newton’s scientific revolution.

I’m unclear what point you really want to make in disputing this. — apokrisis

Disputing the previous paragraph? I haven’t done so. If you’re getting hung up on the words, then I think you’re getting my point exactly right.

You are ignoring the fact that talking in terms of either abstract laws or mentalistic purposes aren’t accidental choices. They are quite deliberate in their metaphysical commitments. — apokrisis

I said they were arbitrary, not accidental. Arbitrary choices can still be deliberate.

And even scientists might want to get down to the “truest” model even if it ain’t also the most pragmatic — apokrisis

The “truest” model (whatever that means) is the most pragmatic model.

pragmatic (in the everyday and unphilosophical sense of being the maximally simple, or most utilitarian, encoding of Nature. :razz: ) — apokrisis

That’s a pretty non-pragmatic definition of pragmatism.

But why are folk happy to call those same fundamental constraints of nature “laws”? — apokrisis

Because it's useful to do so.

Yet still, it seems just as problematic to abstract away the causes of being - paint them as unplaced laws - — apokrisis

The language is the abstraction in the first place. "painting" is by definition abstracting. Causes and effects were occurring long before there were people around to describe them. We use words to describe these causes and effects so we can communicate about them, and because they have pragmatic value.

The reality of causation - at the general physical level of the Cosmos - needs a jargon that steers between both extremes. — apokrisis

A jargon can be useful, but it "need" not be anything. Whether it moderates on an arbitrary principle is purely, well, arbitrary.

Some might go as far as to say that a purpose of trees is oxygen production from carbon dioxide. — jorndoe

To a weary traveler, the purpose of trees, or a particular tree, might be shade. To Siddhartha Guatama, a tree serves as the setting for the transformation into Buddhahood. It seems these purposes (and any others you or I or anyone can think up) are defined simultaneously. If teleology is a particular pattern or use of language, this is fine, but if anyone believes that teleology as an objective characteristic inherent to the substance (material or otherwise) of an object, that seems dubious to me. As I understand it, this is essentially the Aristotelian view, although I accept that you can read in a healthy degree of nuance into Aristotle's thoughts on the subject if you so choose.

Is there a faint residue of sufficient reason in such thinking — jorndoe

I think it's the other way around. The idea of the principle of sufficient reason is a residue of the way we think and speak about things. We find the concept of "purpose" useful, and therefore we continue to apply it to larger and larger contexts, eventually (mistakenly) trying to apply it universally. That universal application is what we call teleology, and it's a not necessarily incorrect, it's more a red herring as to what is really going on. We should focus on our propensity to ascribe purpose to phenomena, not on the phenomena and it's "inherent" purpose.

Purpose is a language game we play to try to make sense of the world. It's useful, and it's value extends only as far as it's usefulness.

Are you now agreeing with me that thermodynamics does not tell us what we ought do? — Banno

I am now and was then in agreement. However, that's not a point I was arguing.

I focus on the following premise:

The thought seems to be that we can rid ourselves of ethical considerations, since these will reduce to thermodynamics. — Banno

I disagree with the thought that a thermodynamically determined world precludes the relevancy of ethics.

From what has been said, a reply that is open to apokrisis is to agree that this is so, but to repeat that
'Ethics only comes into it as a backfill of decisions taken for other reasons - unfortunately perhaps.'
— apokrisis
...and hence while it might not tell us what we ought do, it will tell us what we in fact will do, and hence that ethics is rendered irrelevant. — Banno

Bold is mine. That's what doesn't follow.

You say:

All of this to say, it is not at all clear that we could replace ethical considerations with thermodynamic calculations. — Banno

I say: It doesn't matter, because we don't need to in the first place.

What is the topic here? 'cause I'm lost. — Banno

Clearly.

The thought seems to be that we can rid ourselves of ethical considerations, since these will reduce to thermodynamics. — Banno

...and hence while it might not tell us what we ought do, it will tell us what we in fact will do, and hence that ethics is rendered irrelevant. — Banno

To which I'll reply again:

Even if every action is fully deterministic, that doesn't mean ethics no longer has meaning — Voyeur

Yeah. I'm nonplussed. What makes you think it doesn't? — Banno

Who said I think it doesn't?

That'd be aesthetics, not ethics. — Banno

Distinction without a difference. But, to avoid a needlessly semantic discussion, use good or bad if you like, it changes nothing about the point I'm making.

So we would have the three steps of {teleomaty {teleonomy {teleology}}} to cover the physical, the biological, and themindful. Or in more everyday language, {propensity {function {purpose}}}. — apokrisis

I guess the issue would be with the idea of "intent" being the watchword for "purpose". But I'm content with the idea of decoupling purpose from any semantic baggage and using in a categorical and observational sense. Probably closer to the original Aristotelian intent in the first place! Although, now I'm back to intent and at perilous risk of going in circles!

Thank you for the link, I enjoyed it.

Remember the supposition is that the calculation will tell us what we will indeed do, regardless of what we ought do. — Banno

All of this to say, it is not at all clear that we could replace ethical considerations with thermodynamic calculations. — Banno

I don't think the question is about replacement, to me it seems that thermodynamics gives us further context and insight into understanding what ethics truly is. To the true nature of ethics. I could form an ethical judgement even about Laplace's demon, I could find it beautiful or ugly. But what it would mean to find something "beautiful" or "ugly" in the context of Laplace's demon, would change exactly what was referred to when I uttered those words.

Even if every action is fully deterministic, that doesn't mean ethics no longer has meaning, it would just change the meaning from what is typically assumed under the assumption of a non-deterministic framework. Of course, if the universe (and everything in it) is deterministic then this has likely always been true, and we simply haven't realized it. Every murder in the history of humanity has been inevitable under this model, but from a pragmatic perspective, we can still view murders as undesirable, and work to prevent them. It's just more of a futile gesture at that point... a futile gesture which we are destined to continue... and so forth along the lines of your argument. The same concept applies to the rising and falling of nations, or to individual votes, murder is just usually a clearer example when talking about traditional ethics because traditional ethics (pretty much across the board, but not universally) finds murder unpalatable.

This is where I tend to agree with apokrisis's pragmatism. That what happens need not be thought of as "oughts" at all, but merely as necessary effects of pragmatic, necessary truths. If the universe is deterministic, then perhaps those truths are ultimately thermodynamic after all, and if the universe is not (wholly) deterministic, then perhaps those truths are ultimately personal (and therefore ethics as we currently describe it re-enters the fray). Or perhaps it's somewhere in between. Either way, it seems to me that there's probably no way to know for sure at the present moment.

Well, no; that's a question, not a statement. — Banno

Sure. Doesn't change the point. What makes you think an ethical dimension applies to the possible unraveling of nations?

Life and mind arose as systems with purpose. — apokrisis

I think my main issue with this line of reasoning is that "purpose" is a construct of rational minds, whereas it's perfectly reasonable to imagine the universe without any rational minds, and therefore with no "purpose". Not that things wouldn't be happening, but that there would be no verbal or metaphysical baggage.

The wise long run behaviour would be to price in the cost of the environmental sink needed to dispose of the resulting waste. Plus the issue of what replaces the coal and oil as the supply peaks. — apokrisis

It seems to me that the nature of all life is to be a consumer. Certainly, some (if not all) life produces some byproducts that could perhaps be consumed again, but eventually, the entropy you're talking about will lead us to equilibrium where the energy of the universe is no longer in any consumable or usable form (at least that's one theory based on our current understandings). In the short term, we can monitor our effects on the environment, and perhaps maximize conservation of energy for later days, but I tend to agree with the Keynesian thesis: "In the long run we're all dead."

And the point is that good and bad are social constructs used to encode thermodynamic outcomes. — apokrisis

Even thermodynamic outcomes are probabilistic, which gives rise to the possibility of chaos. And indeed, in our journey toward higher entropy, the human race has experienced its fair share of chaos. Of course, we know that entropy rises in the long term, but it's important to remember the reason for this is an atomistic probability (a probability which allows for temporary decreases in entropy as well), and not a Hegelian Zeitgeist leading us by the hand.

On a side note, I wonder whether a multi-polar or uni-polar world is a higher entropy state of affairs? Could this be calculated?

I'm a pragmatist rather than an idealist so ethics becomes just another way of talking about an optimisation function. — apokrisis

I (mostly) find myself in that same camp, but interestingly:

Nature isn't about right and wrong. — apokrisis

I tend to agree.

It's about systems with the balances to achieve purposes. — apokrisis

I tend to disagree.

Anyway, whether America is unraveling or not, evolution is always chaotic. Natural or Political. Whether it's good... maybe one day a historian will tell us.

The United States is no longer a leader among nations. — Banno

"Is" statement

Is there something - anything - positive in this? — Banno

"Ought" statement

Seems the conversation jumped an awfully large chasm in just two lines. Not saying you aren't allowed, merely asking for the underpinnings of the thought.

It's a practical political question for many nations when the US and China are demanding you pick a side and yet you depend on a healthy economic/security relation with both. — apokrisis

A multi-polar world certainly seems to be an inevitability. Whether that state of affairs carries ethical consequences/connotations... that seems less clear to me.

Is there something - anything - positive in this? — Banno

Why assume an ethical dimension?

There are a handful of examples where armed US citizens clashed with the government (in the form of one armed agency or another) and always goes poorly with the former. It is a delusional fantasy to think that armed US citizens can stand against the US government. — Maw

"It is a delusional fantasy to think that COLONIAL citizens can stand against the BRITISH government."

How unpleasant this idea would have been if it were mainstream in the 1770s. Thank god the founding fathers weren't disposed to it.

Ironically, Socrates' unwillingness to part from (his concept of) rational action is one of the most unreasonable things about him. Who else would willingly die rather than express a little bit of selfish, less-than-perfect rationality? Even Jesus cried out on the cross and begged to be spared in Gethsemane. Socrates is a saint in the church of the rational. Showing total devotion to self-mastery and reason like Paul to God.

I think Paul understood that teachings such as Christ's Sermon on the Mont gave rules that sounded outlandish at the time. Impossible goals, and he tried to show how these teaching were goals to be striven for, even if un-achievable. — Cavacava

Where the Greeks strove for a moral duty to reason, Jesus (and later his Christian followers) strove for a moral duty to God. Perhaps both quests are ultimately impossible to achieve, but when a man undertakes moralizing (whether through reasoning or intuition) he implicitly assumes an "ought" and therefore I think both the followers of the Greeks and the religious (those things are not mutually exclusive, obviously) are noble precisely because they give him something to aim at. This is basically the concept that gives rise to Christian saints, as well as the nuanced Greek view of tragedy as a struggle against our sorry natures... one that we are all destined to lose.

What I was referring to is the anthropological connotations of religion when thought about in this way. After all, the Jews and later the Christians were hardly the first to claim a moral duty to God. Why are we so focused on systematizing (I'm avoiding the term "rationalizing" for clarity but it would fit as well) our moral beliefs and adapting lifestyles suited to them? Which came first, the idea that there exists a God who outlaws murder, or the implicit sense that murder is immoral? I suspect the latter came first, but that begs the question: Then why involve God at all?

The charioteer's choices are choice worthy if they correspond to reasons demands, they do not have a trace of Paul's existential dilemma, in my opinion, — Cavacava

I think Plato got the cause and effect wrong, which seems to be what you are pointing out. From that passage in Romans it does appear like Paul is intuitively feeling out the concept of emotive intuitiveness that is our current best theory (as far as I know, anyway) on the motivation of thought and action. However, I do think Plato's conclusion, as far as it is normative, does still offer some value (and this reveals me as a Platonist, I suppose). Namely that Reason OUGHT to dominate over emotion/passion/appetite/intuition. This is the idea I've been mulling over while reading "The Righteous Mind". The idea that Plato got the diagnosis slightly wrong, but still may have prescribed the right treatment. It's an interesting concept, and it's the basis on which I am examining this issue in the context of the "is/ought" problem.

Even more interesting to me, and relevant via your summoning of Paul to the conversation, is whether religious thought and belief was implicitly developed to combat this emotive/intuitive "gut feeling" and the actions that follow in order to maintain a society with a diverse population. In other words, when our intuitive reactions to others are divisive and threaten the social order, did religion pop-up to glue us back together?

Their concepts may not have been exactly congruent to ours, but I would disagree with the idea that Plato did not conceptualize the will.

https://en.wikipedia.org/wiki/Chariot_Allegory

This all rings true (a good example of intuitive emotion governing my purportedly rational response), especially as I am in the middle of "The Righteous Mind" by Jonathan Haidt, which is basically a guidebook to this theory. But there's something that rubs me the wrong way about the philosophical framework of this entire discussion. Specifically, I feel like the "is/ought" problem is being approached incautiously.

With regard to Plato, he clearly straddled both sides of the "is/ought" problem, but was unquestionably unafraid to make prescriptions, ultimately being more lauded (historically, at least) for his normative statements and theories. "Here is what Plato believed about Justice, about Piety, about Politics..." is a common refrain of easy study guides or professors. All of these subjects eventually made their way to normative conclusions, and even Platonic realism was partially in service of these Normative fundamental truths.

So when you and others make the claim that emotion IS the dominant and reason the submissive in their psychic relationship, I have no problem agreeing to it. It seems true both reasonably and intuitively, and the book I mentioned above does a great job at aggregating experimental results that suggest the same conclusion. But I do still fight back a bit on the OUGHT side of the divide, where I would put forth the premise (as I think Plato would) that while emotion IS the dominant force in MOST people, Reason OUGHT to be. And we can look no further than his most famous allegory to see a poetic description of this thought.

Are we puppets to emotion? I would say yes, at least at first. But like Plato (and his student Aristotle), I hold on to the idea that the reversal of that master-slave relationship is the goal of human life, and the journey from one state to the other is philosophy, and is a source of Eudaimonia. However, I have a natural aversion dogma where possible, and so I come at this from a skeptical point of view. This is not a rebuttal to what you have said, as it is a continuation based on the ideas you've caused me to confront.

It's interesting because I think it's often overlooked that the point of Zeno's paradoxes isn't to prove that motion is impossible, it's to reduce to absurdity the concept that reality is divisible rather than indivisible.

I've always gained more insight from looking for the hints of things he sort of got right or was on the right track about, than trying to defeat the paradox and move on.

These seem to be metaphysical questions, not questions of logic or language. — SophistiCat

True, but in order to progress to a logical analysis, I think metaphysically defining our subject is a worthy cause.

Thompson's Lamp, on the other hand, as well as a number of other such paradoxes, including the Bernardete paradox that you brought up later, are just logical puzzles. The key to their solution is that their premises are either inconsistent (Bernardete) or incomplete (Thompson). — SophistiCat

But in comparison, wouldn't Zeno's paradoxes just be a version of this? Zeno just happened to target physical phenomena as his subject, but isn't his reasoning and the scenario he cooked up just as much a logic puzzle as the other two paradoxes you and I mentioned?

Can't we use the same methods of investigation, discussion, and analysis for all three?

A supertask is logically impossible. — Metaphysician Undercover

If your statement is true, then the next question is whether motion is a supertask. And if it is, doesn't that mean motion is logically impossible?

Depends if you think the sequential distances or steps required to traverse a distance are countably or uncountable infinite. They both have seemingly identical properties, as far as I can tell? They just apply to different sets of numbers.

I hate to keep stealing my comments from Wikipedia, but there is another interesting version (at least I would call it a version) of Zeno's paradoxes in the form of Bernardete's Paradox of the Gods:

A man walks a mile from a point α. But there is an infinity of gods each of whom, unknown to the others, intends to obstruct him. One of them will raise a barrier to stop his further advance if he reaches the half-mile point, a second if he reaches the quarter-mile point, a third if he goes one-eighth of a mile, and so on ad infinitum. So he cannot even get started, because however short a distance he travels he will already have been stopped by a barrier. But in that case no barrier will rise, so that there is nothing to stop him setting off. He has been forced to stay where he is by the mere unfulfilled intentions of the gods. — J. A. Bernardete

This version takes it out of the physical realm and makes it a pure thought experiment. How would one deal with this version of the paradox?

So I would set aside the two questions that you formulated - is motion a supertask? and are supertasks (metaphysically?) possible? - as open questions that, prima facie at least, are not incoherent or trivial. Other things that you mention, such as Thompson's lamp, might actually be less problematic than you think, being ultimately language problems rather than problems of metaphysics.

But anyway, if you want to talk about the point, a good way to start would be to give a crisp statement of the alleged paradox. — SophistiCat

I agree that most of the time discussions on this topic tend to descend rather quickly and that’s what I was trying to point out, but you’re quite right. The actual questions raised by the paradox are rarely ever even addressed.

The language problem of Thomson’s lamp: Yes, this is exactly what I’m getting at, that the profundity of Zeno’s paradox (as well as Thomson’s) don’t lie in the realm of mathematics, but in logic/language. This is the point that I feel is often missed.

A form of the paradox that I like is this (from Wikipedia):

• Motion is a supertask, because the completion of motion over any set distance involves an infinite number of steps
• Supertasks are impossible
• Therefore, motion is impossible

From this, I think it's easy to see that the issues that can be taken with the paradox are issues of logic, not of mathematics and especially not of sums of series.

What does it mean for a motion to be "complete"? Is motion made up of "steps"? These are the core issues that the paradox is getting at.

And before someone brings up physical properties of space and the Planck length, this same argument can be applied to time as well. I find that it is not as contentious a statement to say that time is continuous when compared to space.

Space and time must be thought of in a different way as not being divisible. An object doesn't travel half-way. It moves from here to there in one indivisible motion. There is no half in a continuously flowing and changing space. — Rich

The is no paradox if one a treats time and space as indivisible - which is clearly the case. Only those trapped in the works of numbers would agree otherwise. Of course, the is motion and duration always flows, but for some their experiences are not as real as numbers. — Rich

This, incidentally, does not appear far off from what Zeno was arguing for in the first place. Would you consider yourself a Parmenidean? Maybe a Neo-Parmenidean?

Moving back toward the original question of this thread, I'm eager to introduce the notion of Supertasks to the conversation. A great summary with examples of Supertasks can be found here

I always get a little uppity when people try to dismiss Zeno's paradoxes with the fact that an infinite series can have a sum. It misses the point entirely. And the paradox can even be worded to INCLUDE the summation idea within itself. If I tell you I want to walk 10 feet and that I'm going to walk 5 feet first, and then 2.5 feet, and so on... Haven't I just implicitly stated that I believe an infinite series has a finite sum? Namely the 10 feet I talked about at the beginning? It's just lazy to think that the idea of an infinite series is actually a good response to Zeno's charge of the impossibility of motion.

Just stating that an infinite series can have a sum, as some have done in this thread is not enough to resolve the paradoxes of Zeno or the other examples on that wiki page, in fact Thomson's Lamp is a brilliant example of just how ineffective that argument is, at least in this case.

I think the question that ought to be asked, in light of Zeno's criticisms of the pervasive idea of a divisible world, is whether motion is a supertask, or not.

Is motion a supertask?

Then, if we can answer that question, we might move on to the possibility of supertasks themselves, about which there has been much disagreement.

Further, I'd like to point out that Zeno's Paradoxes can be tweaked to not only attack the continuity and coherence of space, but also time. As has been alluded to already in this thread, time and space are central to Zeno's line of dialectic, and dealing with time takes us away from the pesky and ultimately fruitless Planck length explanations that crop up just as regularly as the sum-of-series ones do.

An example: Suppose you wanted to microwave your frozen tv dinner. You set the timer for one minute (this is one of those fast cooking dinners that you love so much), and then you wait. But before you wait a full minute, you have to wait a half minute, and before a half a quarter, and so on all the way down... And in the end, of course, you end up not starting at all, because there is no smallest amount of time that you can actually wait. And then you go hungry.

I've seen it argued that Zeno's Paradoxes are an indication that space is not continuous, but I haven't seen the same said of time. Maybe I just missed it?

And finally, I think it might be worth examining two of the modern "successors" (I use the term loosely) to Zeno's paradoxes, in the Thomson's Lamp Paradox and the Ross-Littlewood Paradox, both of which can be found in the wiki link I provided.