Actually Zeno's paradoxes prove that the "continuum" is a faulty idea.

Actually Zeno's paradoxes prove that the "continuum" is a faulty idea. — Metaphysician Undercover

It shows there is a paradox in that every object is both finite and infinite at the same time, almost in the same respect. This shouldn't prevent us from seeing motion and change as real. It just shows us it is weird. A tree can go from being a single organism to being toilet paper. The process is a continuum. The result is something discrete.

Heidegger contradicts de Beistegui in a number of ways. — Xtrix

Trying to figure out why you think this. In any case if I knew you only wanted to read things that agreed with your preconceptions then I ought not to have posted anything. As you were.

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The process is a continuum. The result is something discrete. — Gregory

Right, that's exactly the point of Aristotle's demonstrations, the process, (what you call continuous), is incompatible with the result, (what you call discrete).

It shows there is a paradox in that every object is both finite and infinite at the same time, almost in the same respect. — Gregory

From the Aristotelian perspective, it's not that the object is both finite and infinite at the same time, but the object is both matter and form. The continuity is provided for by matter, while the form changes.

When where? — tim wood

You can look them up on line.

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If everything changes every infinitesimal of time then it's being does not remain the same. Think thesuas ship. An infinite process can lead up to something that doesn't change. Maybe that will be the end result of the universe

It's quite simple. Zeno applies the principles of continuity toward simple observable motions, and shows that the observable motions are impossible, if understood using the principles of continuity. Therefore we can conclude that the principles of continuity are faulty for the purpose of understanding observable motions.

No. There is obviously a division among motion or it couldn't be motion at all

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Am I the only one who finds it unintuitive that a line segment can be shrunk for all eternity and never disappear? Just asking

Am I the only one who finds it unintuitive that a line segment can be shrunk for all eternity and never disappear? Just asking — Gregory

If something shrinks more and more slowly, it can continue to shrink without ever vanishing. This is an informal description of something that can be made mathematical.

What about the forces of nature? Are those "physical"? Newton thought that notion was absurd. Quantum entanglement, curved spacetime. Einstein considered a lot of this "non-physical." Etc. Is language and mathematics physical? — Xtrix

Physical laws are as much physical as the objects they obey them for the simple reason that they're perceivable or observable.

Sounds more like empirical to me, but I take your meaning. — Xtrix

Science is empirical.

The word "real" is likewise honorific. If we define reality as anything "perceptible" or "physical" or "natural," etc., then we get an answer in one step: reality = the natural. But that only means we have to understand what physical and natural mean, and then to have some idea of what "material," "matter," and "body" mean (including the senses, which are part of the body), and so on. So we're back to the beginning and the topic of this thread. — Xtrix

I offered you a definition of physical as that which can be perceived through the senses (and instruments). The real for naturalism is just that, the physical. This was in response to your query about phusis.

Well, let's notice right off that you moved the bar from perceived to detected and measure, which are not at all the same — Coben

I see no difference between our senses and detector instruments except perhaps in the sense that the former shares a direct connection to the brain. That's why I mentioned detectability through means other than just our five senses as a criterion for being physical.

This is an important point to bear in mind because, for instance, electromagnetic waves that lie beyond the visible spectrum wouldn't have been considered real before their discovery for they weren't perceivable to the senses. X-rays, gamma rays, and radio are now believed to be real because they're detectable with instruments which then are perceived by the senses. This clearly shows what the criteria for being real is: our senses must, either directly or indirectly, perceive; only then can anything be real.

I brought this up because it raises the possibility that there are real things out there that we may not be able to detect with either our senses or instruments. However, as was the case with radio waves and X-rays, and gamma rays, they will be considered unreal until and unless they can be detected in some manner. The bottomline is that realness is predicated on detectability/perceptibility.

But in any case the laws themselves are certainly not observed. — Coben

How did Newton come up with the laws of motion or for that matter how do scientists formulate laws of nature? They gather observational data and then observe patterns in the data; these patterns observed are the laws, no?

That's very hard to prove and further, are you willing to put in the time to become an expert in things you have decided are not real? And certainly some people both from experience and innate talent have a much easier time. And then last, again, my point was just how common it is that when one person can perceive something this is due to expertise/experience rather than your generalization that this is usually hallucinations, etc. — Coben

Well, if one gives it some thought, the talented expert may perceive a pattern which others didn't; such a person is otherwise known as a genius. Nevertheless, any pattern perceived by a genius must be proven i.e. everyone must be able to comprehend it (given adequate knowledge). In other words, there can't be such a thing as privileged knowledge in the sense that it's impossible for all to know it.

Also, bringing up experts into this discussion doesn't help because sensory perception doesn't require expertise: it's not that we can train our senses to peform better and help us see things others can't, hear things others can't, feel things others can't, taste things others can't, or smell things others can't. Of course, there's such thing as a better sense of sight, hearing, smell, taste, etc. but whatever extra perception gained needs corroboration by some other means. I mean how does one know if one has a better sense of smell if we don't know what smell was picked up by your nose and not by others.

nothing. Nor did you respond to the idea of being agnostic — Coben

I believe we can remain agnostic about reality in the sense that there could be real things we haven't yet detected but not in the sense that some real things are impossible to detect. In the former case, the criterion for realness remains as perceptibility/detectability but in the latter, this criterion no longer applies and then everything becomes real and so, the question that follows is "what is not real?"

Just what do you imagine "principles of continuity to be"? — tim wood

Infinite divisibility is a principle of continuity.

f Achilleus stops at every point for any length of time, then he can't get where he's going. It's continuousness that gets him there. But that's obvious, so what do you mean? — tim wood

I see you haven't really read, or at least have not understood Zeno's paradoxes. Zeno did not say that Achilles "stops at every point". Achilles must simply run the distance between the points. Since it takes him a period of time to run the distance from where he is, to where the tortoise is at that time, the tortoise has proceeded to a further place during that period of time which it takes him to get there. Now Achilles must run to that place, and the tortoise moves along to a further place in that period of time, so Achilles must run to that place, ad infinitum.

The fault here is in the assumption that space and time are continuous and infinitely divisible. This produces the illusion that there is always a smaller space to be run, consequently a smaller amount of time required to run that space, allowing the tortoise to always stay ahead. It is basically a more complex version of the dichotomy paradox, which maybe we ought to address first because it's simpler, and therefore easier to get a clearer understanding of the problem. When space is considered to be continuous, and therefore infinitely divisible, one must move through an infinity of spaces before one can move through any space at all.

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Physical laws are as much physical as the objects they obey them for the simple reason that they're perceivable or observable. — TheMadFool

That's not what Galileo or Newton thought. But regardless, if those things are all "physical," then anything we can understand is physical. Not much of a definition.

Science is empirical. — TheMadFool

Partly, but not always. It's also theoretical. It involves logic, mathematics, etc.

I offered you a definition of physical as that which can be perceived through the senses (and instruments). — TheMadFool

I never asked you for a definition of "physical" and, as I've stated before, I'm really not interested. All you've done is offer a fairly commonplace idea of what physical is -- you've not advanced the conversation, which is about phusis. Giving me your own personal opinion about what you think "physical" means is useless. Quite apart from that, this definition itself is problematic, and only pushes us to now ask "what is perception and the senses?" If the senses are part of the body, and we have no idea what "body" means, then the notion of "physical" as "anything we can perceive with our senses" is itself a definition built on sand.

This definition also tacitly assumes a subject/object dichotomy as well, which I've written about elsewhere.

This conversation isn't supposed to be simple. It's not a matter of me inquiring about "what physical means" and then everyone offering their own "take" on it, based on their favorite readings. It's also not an exercise in "let's try to come up with a definition." This problem has been around for centuries, thought about by far better minds than ours, and persists even today. To think we're going to settle it by throwing around a definition is pure hubris.

That being said, I'd like to return to the actual guiding question:

So the question "What is 'nature'?" ends up leading to a more fundamental question: "What is the 'physical'?" and that ultimately resides in the etymology of φῠ́σῐς and, finally, in the origins of Western thought: Greek thought. — Xtrix

This perhaps was vague, as I didn't emphasis the notion of "phusis" enough. But since I've now clarified what I meant several times, I don't feel this is a reasonable excuse anymore. Others on this thread have understood me correctly.

So if you have insights or analysis about the Greek notion of "phusis," which has shaped every concept of "nature" or "physical" to this very day, including yours, then please do share. Like I said, I'm particularly struck by Heidegger on this one but am open to others I may not have been aware of.

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Really? Where? What, exactly, do you mean? — tim wood

As the apple that fell on Newton's head
All things, towards the center of gravity, head

That's not what Galileo or Newton thought. But regardless, if those things are all "physical," then anything we can understand is physical. Not much of a definition. — Xtrix

Observable.

Partly, but not always. It's also theoretical. It involves logic, mathematics, etc. — Xtrix

Focus on the essential. Logic & math are also found elsewhere but the empirical is an exclusively scientific feature.

I only offered my personal views on the matter. I am simple; ergo my notion of the physical is also simple. I was hoping that if the notion of the physical is not as simple as my formulation of it, then some account of why that is would come up in the discussion between us.

Perhaps there is more to the idea of the physical than meets my eye but what could it be? What could possibly be added onto the definition of physical, that I provided, that would make it more accurate in re the way we use the word, "physical"?

You say you're not interested in definitions but I was under the impression that philosophizing began with definitions? Also, if you didn't care for the definition, why bring up etymology of "phusis"?

It's highly likely that I misunderstand you.

Aristotle was wrong to say a segment is not infinitely divided. Parts are real. The finite merges with the infinite in objects probably by some non-euclidean extra dimension.

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Here's the fault. You apparently imagine that Achilleus gets where he is going because, you suppose, space is not infinitely divisible and continuous, whatever these mean - as if the divisibility or continuity of space had any relevance. Suppose it isn't and suppose it's relevant. — tim wood

Of course the divisibility of space is relevant, it's stipulated by Zeno in his presentation. If there were no divisions there would be no presentation of the problem. The problem is presented as a problem of spatial divisions in relation to temporal divisions, the distance in space covered in a specified period of time. So the problem is a problem involved with dividing space and time into increments. It would be rather ridiculous to say that the divisibility of space is not relevant.

Suppose it isn't and suppose it's relevant. You would acknowledge, I trust, that even being just finitely divisible there are still a lot of divisions, so many that it would take Achilleus a very long time to reach his destination. — tim wood

This is what is irrelevant. If it takes Achilles a "very long time" to win the race, he still wins the race. The point of Zeno's presentation is that under the assumption that we can keep dividing space and time to shorter and shorter increments, infinitely, Achilles can never win the race.

Further, the tortoise covers the same distance without difficulty, which under your argument he should have at least as much difficulty doing as Achilleus. How do you account for the tortoise? — tim wood

Again, this is irrelevant. The degree of "difficulty" is not a factor in Zeno's presentation. What is presented is that it is impossible for Achilles to catch up to the tortoise, not that it is difficult for him to do that.

2) notwithstanding how divisible the way is or is not, we do routinely get where we're going. . — tim wood

Exactly, that's why representing space and time as infinitely divisible is a faulty representation. As Zeno demonstrated, if space and time actually were infinitely divisible it would be impossible to do what is routinely done.

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That is, if at every point of division Achilleus paused for the same increment of time. — tim wood

There is no pause in Achilles' running. That's not part of the scenario. You are just adding things in, making things up, which constitutes a bad interpretation, a faulty reading of the example.

The question was/is, how do you account for the tortoise? And that's just one of many. Given the tortoise has a head-start of any increment at all, how does Achilleus even get off the starting line? What is the distance to the first point that the tortoise got to? And so forth. — tim wood

The length of the tortoise's head start is irrelevant. The result is the same. In the time it takes Achilles to reach the point where the tortoise started from, the tortoise has moved further ahead. So, the tortoise still has a head start, and so on, ad infinitum.

It might help if you made clear just what your point is. — tim wood

I stated very clearly what my point is:

Actually Zeno's paradoxes prove that the "continuum" is a faulty idea. — Metaphysician Undercover

You could not understand the point and requested an explanation. Now I've provided that. If you still do not understand, study Zeno's examples more closely, eventually you ought to apprehend what the examples demonstrate.

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Pay attention to the language! — tim wood

Zeno was Greek, and a long time ago. I don't even understand modern Greek. If you want someone to explain it in Zeno's language you'll have to find someone else, sorry about that.