If he can't create something that is so heavy he can't lift it - if that is impossible for him - he isn't omnipotent. That's the paradox.

Hegel's paradox: "the only thing we learn from history is that we learn nothing from history"

Dichotomy Paradox

To get from point A to point B, you must first travel half the way. To travel half the way, you must travel one fourth of the way, then one eighth, then one sixteenth, and so on. You must complete an infinite number of actions, so the motion cannot be completed.

Exactly this

hm ya you're probably right :(

This isn't even a real paradox. If you deny the mission, you haven't "completed" the mission as you never accepted the mission in the first place.

I can count the number of "real" paradoxes in this thread with the fingers on one hand.

Russell's Paradox (which actually is a paradox) is interesting to consider. As described to me in a lecture a while ago:
Ask yourself the question, is there any set which contains all sets?

AFSOC that there is.
Construct a set R = { x | x ∉ x } , that is, a set for which every element does not contain itself.
What are the members of this set like?
ℕ ∈ R, as every element of ℕ is simply a natural number, and not ℕ itself.

But what about R; is R in R? R contains all sets which do not contain themselves.
This implies that if R contains itself, then R cannot contain itself. Furthermore, if R does not contain itself, then R must contain itself.
Our result: "R contains itself" is logically equivalent to "R does not contain itself," as each implies the other. However, this result is clearly contradictory, so R cannot exist.

Thus, there cannot be a universal set as it cannot contain this R.

Back to studying for my math exam tomorrow.

well if ur just gonna treat taking infinite abstract measurements of a real world action as the action having infinite elements then i complete an infinite number of actions every time i take a shit, or walk to the fridge, or move my finger half an inch

i mean come on thats like saying numbers dont exist because they can be divided into smaller numbers and therefore can never be counted (thats not how fucking abstract measurements work)

at least use the achilles tortoise version so it at least sounds like a real paradox, goddamn

That plus the fact that you can't really move in a smaller increment than a Planck Length, so it isn't even an infinitely small length.

Planck length is more about the point at which physics isn't properly described by classical mechanics, and is described by quantum theories.

But yes fatswimdude, as you have eloquently noted, this individual has not successfully proven that it is impossible to move any distance (in stark contrast to all my intuitions about basic mechanics...).
A more cerebral response might consider how we can divide time. If we have an infinite number of moments, can we not complete an infinite number of actions?

You're arguing it from a scientific and not a philosophic point of view.

You think these Greeks knew what a fucking Planck Length was. In fact even from a mathematical point of view the paradox doesn't really hold as it would be what is considered a series and would converge meaning it isn't infinite.

But in reality if you think about it you do in fact meet an infinite number of half-way points while walking a distance, but since you cannot ever reach infinity then movement is in of itself a paradox that cannot be completed.

The point of philosophy is to examine the nature of our world and if it makes you sense and here you are bringing quantum physics into it smh. Just have some fun and think about it.

"Zeno's paradoxes are simply mathematical problems, for which modern calculus provides a mathematical solution"

Sorry, I forgot that you guys are obviously smarter than some of the greatest minds in philosophy.

You don't just make things up in philosophy, it has to be supported by logical thought, in this case validity and soundness aren't both being reached. The statement basically says:

if all movement is infinite stages, then movement is impossible
movement is infinite stages
therefore, movement is impossible - by modus ponens

The conclusion is provably valid because the premise reaches that logically. We can prove the premise isn't true, so that makes the conclusion not sound.

if all movement is infinite stages, then movement is impossible -- given premise
movement is not impossible -- observable premise, so this is a universal truth
therefore, movement is not infinite stages - by modus tollens

This conclusion is both valid and sound, unless the premise given from the first logic test isn't true, in which case it isn't a sound conclusion (referring to the first statement) anyway since both premises need to be true, so it doesn't matter.
In case anyone's wondering, this logic is provable, you can find a proof if you google 'modus ponens proof' and 'modus tollens proof' probably.

I guess it's all pretty irrelevant if the philosophical exercise is just that perception doesn't always equal fact

a better way to explain getawhale's bootstrap paradox (the time machine) without having to worry about someone seeing himself is to think of a hapless time traveler that wants to see beethoven, but upon going back in time he realizes that beethoven never existed. in a distressed rush he grabs beethoven sheet music from his time machine and copies it down, effectively writing all of beethoven's music himself (signing it as beethoven). the time traveler has saved history, but where did the music come from in the first place?

No where did I state that philosophy just makes shit up, I'm just saying that looking at philisophical problems and arguing them from a mathematical or scientific standpoint does not always lead to good philosphy.

In addition, just to continue the discussion of the dichotomy paradox, technically the smallest maximum unit of length currently is a Planck Length. Currently there is real way to even truly measure it as our instrumentation does not have the resolution required.

Meaning, a Planck Length is currently the smallest order of measurement that we can theoretically derive. So as our knowledge of physics increases there certainly could be a smaller unit of measurement found hence the paradox could even scientifically continue.

What I was describing was a causal loop or predestination paradox. Perhaps I didn't pick the best example.. the Wikipedia page has better ones. Another is going back in time to give Shakespeare a copy of his life's works. Which he then copies out and releases. So where did the work come from originally?

No idea how plaid shirts relate to that, sorry Ploxo

have you guys watched predestination?

The solution is that the unstoppable force would pass through the immovable object, where both of their conditions are met. There's also a minute science video about this somewhere.

Unbelievable movie and highly recommended.

Even though a lot of reviews said the twists were predictable, I didn't find that at all - I just tried my best to buckle in and enjoy things as they happened, without theorizing or speculating as to what might happen. Loved it. Fits great with this thread too.

I'm not a physicist and have only taken a couple physics courses, but I'll share what I understand of the matter:

Whether or not there IS a smaller unit of length than a planck, and more importantly, whether there is a SMALLEST unit of length is a really tough and complicated question, to which I don't believe we have any definitive answer. The same is true for time, and measurements of time.
Within general relativity, space and time are assumed to be continuous, i.e. there is no smallest unit of measurement of space or time. However, various quantum effects make this problematic when things get really small, and the more classical theories don't describe things remotely accurately (hence efforts to develop quantum theories that will hopefully describe things accurately). The dividing line is considered to be the planck length and the planck time.
However, the point at which length and time stop having meaning in general relativity is not necessarily the smallest possible or even smallest measurable length and time, and doesn't suggest anything about these two values or their existence -- this is simply the limit of general relativity.

I think this is probably exactly what you mean, but the semantics of your post weren't 100% true to my understanding of the current theories, so here is a slightly more detailed explanation for anyone curious on the topic :)

I hate this one a lot because the examples showed us situations where the combined statistics were more accurate to the goal of the study, as well as situations where the combined statistics were less accurate to the goal of the study. The gender bias one was where breaking it down made it clear that there was no gender bias, while the batting averages were more accurate if you looked at them on the whole rather than per year.

It's a true pain in the ass because being aware of the paradox makes it harder to accept anything at face value.

My take on the "stone so heavy even God can't lift it" thing: If you're working under the assumption of an omnipotent being and a stone so heavy even that being couldn't lift it existing at the same time, you've already thrown the Law of Excluded Middle out the window. Then God would just create the stone and still lift it.

If you take omnipotence as omnipotence within the laws of logic, you're done as well, because then such a stone wouldn't exist, and the question would be equivalent to "Could God create an arglbarglashnldsf?".

yo what would happen if Pinocchio said "my nose grows now" ??????????????

Wouldn't it just stop growing the same moment it's going to grow, and effectively not grow at all, since it's only false for an immeasurable amount of time?

this is just delaying the problem, since he stated that his nose will grow and in your suggestion it won't grow at all which gives a contradiction.

Yes, but then it will just be an endless cycle of a state of no growth, at least that's how I see it.

heh

It would penetrate it

Personally, the Banach-Tarski Paradox really twists my head

im better than the best