It's paradoxical

[UnseenParticipant]

I ran into a video on Friday last which rekindled my interest in the foundations of mathematics and Bertrand Russell. It’s a lecture given by an unusually talented young professor of philosophy, Jeffrey Kaplan, who makes set theory fascinating, exposes the paradox, and then goes on to argue that all attempts by mathematicians to solve the problem fail and, not only that, but that the paradox pervades all of language and thought as well.

Not too long after Russell, Goedel came along and between the two of them, mathematics is dead. Long live mathematics! (Well, not really, but we now know that mathematics has its limitations.)

There is a common way of expressing the paradox in language and it goes like this:

In a village where there is a barber who shaves all of the men who do not shave themselves, who shaves the barber?

Well, if he doesn’t shave himself then he shaves himself. See the problem?

If every philosophy class had a teacher as exciting, enthusiastic, and talented as Kaplan, no student would say “Philosophy is boring.” He also demonstrates for all of those who say “Philosophy is dead,” that philosophy is far from dead.

I don’t know if anyone wants to comment on this video (or dispute it), but I’m presenting it in the hope you’ll find it as interesting as I did. And, heck, if nothing else, he does an astounding job of teaching set theory in just a few minutes.

• This topic was modified 1 year, 2 months ago by  Unseen.

[_Robert_Participant]

He just shows that yes, math is a language and has the same paradigms as any logical system and therefore the problem doesn’t really exist. Treating math like it’s composed of matter or energy always gets you in trouble. You can take half a distance for forever and a day in math but damn it would be hard to walk if it was real.

[UnseenParticipant]

I also find it interesting that Kaplan appears to have great facility writing backwards. Someone in the comments stated that a mirror imaging digital effect is involved. I don’t see that that actually explains what’s going on. And it’s far from impossible he’s simply taught himself to do it.

[jakelafortParticipant]

I talk backwards. Never tried writing but seems easy enough.

[UnseenParticipant]

_Robert_ wrote:

He just shows that yes, math is a language and has the same paradigms as any logical system and therefore the problem doesn’t really exist. Treating math like it’s composed of matter or energy always gets you in trouble. You can take half a distance for forever and a day in math but damn it would be hard to walk if it was real.

The problem may not exist in any practical way. But Russell’s Paradox, along with Goedel’s Proof that there will always be unprovable formulations, does put an end to the enterprise of creating any system of mathematics (or linguistics) that is 100% complete and self-consistent. This doesn’t keep us from designing toasters or interplanetary spacecraft, of course, but to a philosopher of mathematics, it’s a disaster./

[—Participant]

I got a little distracted when he changed a painting from colour to black and white to make it look older when logically it makes it look more contemporary than it probably really was.

Then I got distracted wondering whether he was left-handed and writing backwards, or if he was right-handed and the video was mirrored (my bet is on the latter).

Then I got distracted thinking about video versus text and how I wished this presentation were in text so I could just search for the content I wanted instead of guessing how far ahead to skip wondering if I missed something actually important.

Then I got distracted by remembering what it was like to be in school, struggling with slow explanations that belaboured things* that were seemingly obvious leading my brain to go off on countless tangents until I’d checked out of the lecture.

The paradox is less paradoxical if you don’t start with the assumption that all things that can exist in language can exist in nature. It may seem ironic or paradoxical when you accept that language is derived from and descriptive of nature, but it really isn’t.

The real take away from this video is that I get easily distracted.

*N.B. I’m not faulting him his presentation style. It just doesn’t mesh with me, personally, for various reasons. Doesn’t mean there is anything wrong with it.

[_Robert_Participant]

Back in the early internet days many atheists rejoiced in the infinite number of paradoxical dilemmas the single word “omnipotent” brings with it. So, the Lord can create a rock so heavy that even he can’t even lift it, aye? “Omniscient” is another human construct that creates paradigms and begs… So, why did the Lord even bother?

 

[—Participant]

The rock paradox can be resolved either semantically or logically. That said, if taken as intended, yeah, it is the same issue of something that is definitionally self-contradicting.

When it comes to languages like English, however, it’s probably best to be cautious about using certain terms in an absolute sense. For instance, if we define ‘freewill’ in contrast to coercion, it’s both a useful term and one that is easily defined. But if we get absolutist with the ‘free’ portion of the word, then it becomes paradoxical. Without causality, we can’t exercise will, and with causality, that will can’t be free. It becomes self-contradicting.

[UnseenParticipant]

Autumn wrote:

Then I got distracted wondering whether he was left-handed and writing backwards, or if he was right-handed and the video was mirrored (my bet is on the latter).

He’s writing facing the camera, so if the image was mirrored in post, that means he was indeed writing backwards.

Or am I misunderstanding you?

Someone in the comments pointed out that they think his shirt buttons up backwards and that this argues for mirroring, though that isn’t conclusive. Elsewhere in the world they do put buttons and buttonholes the other way around from how we in the West do it. When I bought a made-in-China jacket recently I had to get used too a front zipper with the puller on the “wrong” side.

 

[UnseenParticipant]

Autumn wrote:

But if we get absolutist with the ‘free’ portion of the word, then it becomes paradoxical. Without causality, we can’t exercise will, and with causality, that will can’t be free. It becomes self-contradicting.

I think “free will” fails at the moment of definition. I mean, define “will” as used in “free will.”

We all know what “free” means. While there are various uses of the word (with separate meanings for each), they all have a core meaning in common:  without coercion or encumbrance.

But “will.” It’s not so easy with that one, especially when paired with “free.”

And of course free will is tied in with perhaps the greatest mystery of all. We know more about the cosmos than we know about what consciousness is. Lately, it’s being argued that reality itself, as we know it, is a hallucination created by our consciousness.

For example, there is no color outside consciousness. Our mind presents us a world with color by interpreting a portion of the electromagnetic spectrum as red, or blue. But is an apple actually red, a banana yellow, or a ginger cat orange? No. If a tree falls in the forest and nothing hears it, does it make a sound? No. Sound is another hallucination.

Just for a moment consider: What might our consciousness not be telling us? Is there a reality out there we know nothing about?

Well, that’s pretty far from Kaplan or Russell, but you started it. LOL

[—Participant]

Unseen wrote:

He’s writing facing the camera, so if the image was mirrored in post, that means he was indeed writing backwards.

Because he is facing us and writing on glass, the writing would either be forward from our perspective and backward from his, or backward from our perspective and forward from his. Because it is forward from our perspective, that means as-shown, it is backward on his side of the glass. However, if the image was flipped horizontally at some point, then that relationship reverses on the actual physical set at the time of filming: he’s writing forward, and we’re seeing it backward (only later corrected so it reads properly again).

It doesn’t matter much apart from the fact that if he wrote all of that backward from his perspective, he’s developed an odd skill quite well (or perhaps just has an aptitude for it).

[UnseenParticipant]

Autumn wrote:

Unseen wrote:

He’s writing facing the camera, so if the image was mirrored in post, that means he was indeed writing backwards.

Because he is facing us and writing on glass, the writing would either be forward from our perspective and backward from his, or backward from our perspective and forward from his. Because it is forward from our perspective, that means as-shown, it is backward on his side of the glass. However, if the image was flipped horizontally at some point, then that relationship reverses on the actual physical set at the time of filming: he’s writing forward, and we’re seeing it backward (only later corrected so it reads properly again). It doesn’t matter much apart from the fact that if he wrote all of that backward from his perspective, he’s developed an odd skill quite well (or perhaps just has an aptitude for it).

If he’s developed an odd skill, he wouldn’t be the first. Idiot savants can do far more amazing things. For me, that’s the explanation that makes the most sense.

• This reply was modified 1 year, 2 months ago by  Unseen.

[UnseenParticipant]

Unseen wrote:

Autumn wrote:

Unseen wrote:

He’s writing facing the camera, so if the image was mirrored in post, that means he was indeed writing backwards.

Because he is facing us and writing on glass, the writing would either be forward from our perspective and backward from his, or backward from our perspective and forward from his. Because it is forward from our perspective, that means as-shown, it is backward on his side of the glass. However, if the image was flipped horizontally at some point, then that relationship reverses on the actual physical set at the time of filming: he’s writing forward, and we’re seeing it backward (only later corrected so it reads properly again). It doesn’t matter much apart from the fact that if he wrote all of that backward from his perspective, he’s developed an odd skill quite well (or perhaps just has an aptitude for it).

If he’s developed an odd skill, he wouldn’t be the first. Idiot savants can do far more amazing things. For me, that’s the explanation that makes the most sense.

I’ve come around to your point of view for two reasons. One is based on evidence and the other is more direct than that.

As far as evidence goes, I noted in the paradox video that he appears to be wearing a wedding ring, but that it appears to be on the wrong hand, the right hand, but that in another video where he’s delivering a live lecture in front of a class, his ring is on the correct hand, the left hand, where one traditionally wears a wedding ring. This argues for your mirroring explanation.

The more direct evidence is…

[PopeBeanieModerator]

Trivia: In a typical online video session, you’re not seeing the same image of yourself that others are seeing. That’s because you’re shown your mirror image, the kind of image you’re more familiar with, and you would likely feel disoriented if shown your own image from the natural point of view of other people.

At your next video meeting, hold up something with writing on it and see. To some, this is obvious, but it’s easy for many to not notice this.

[Author]

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