The Law of Identity 

Explaining the contradictions of properties are not the same as contradictions of perception and beliefs was just brilliant.

First of all, this video is fire. As a dialethist, I do not have a problem with the morning star having the properties of being believed to be a planet and being not believed to be a planet by verity. But also, much of the problem of self identity can be resolved to limiting properties needed to just properties relevant to the domain of discourse - instead of requiring all properties of a thing to be the same. If we are in a discussion where whether or not verity believes an object to be a planet is relevant, then Venus is not identical to the morning star in that domain of discourse. If we are instead interested in astrophysics of heavenly bodies, then Verity's beliefs are irrelevant and Venus is identical to the morning star. Limiting to just relevant properties is also how two things that are not the same thing can also be identical. I have two copies of the wizard of Oz book. I acquired one before the other, but I could not tell you which was the one I got first. One is on the right side of the shelf and the other on the left. But if they fell off, I would only have a 50/50 chance of putting them back on the same sides. They are for all intents and purposes, identical. As such, if the only property of interest for and inquiry was the property of color, then in that inquiry the car would be identical with the sky. So to define "identity" in terms of relevant variables, we could say that items are identical iff they have perfect multicolinearity.

Here's a counterexample to the law of identity I learned some time ago. Consider the term 'premwhite' which is defined as "white when used in the premise of a syllogism, falsity otherwise." Then "Snow is premwhite, therefore snow is white," is a true statement. However "Snow is premwhite, therefore snow is premwhite," is false.

Amazing channel !!! Love this in depth discussions

Just written my first undergrad essay on this topic- let’s hope it went well.

Got popcorn🍿, exited to watch

The idea of identity seems quite straightforward until you examine it closely. For example consider the letter 'a' in your channel ident above and the letter 'a' in the video title. Are they identical. They are both the letter 'a' so yes. However they are in different places in a sentence and I think one is smaller than the other so no. Surprisingly, this is a current hot topic in foundations of mathematics due to 'computer proof assistants'. The recent Univalent foundation, homotopy type theory, is one solution which says 'isomorphism is isomorphic to equality'. I am now of the view that deciding what kind of identity acts like a 'focus' on our mathematical universe - a tighter setting reveals more details of nearby structures like the natural numbers but a looser setting allows distant infinities (like large cardinal axioms) to become visible.

Really enjoying your exposition of so many core philosophical issues. Is Leibniz the first modern (post-Descartes) philosopher to move cleanly away from psychologist logic (eg. Hume, Kant, Mill)?

👌 "Omnis determinatio est negatio."

The 'numerical person' can virtually consume a multitude of qualitative identities, anchoring biological individualism in tangible markers like iris recognition or fingerprints. Yet even this is transient, suggesting future identity validation through neural network brain scans. Authentic identity becomes a commodity, linked to capital identity and the extraction of elemental identities in various economic sectors, like gold, electrons, data, or even rice grain counts.

thank you so much

thumbnails go crazy

When Heraclitus wrote to the effect that one cannot step into the same river twice, perhaps he should have noted that there was no same river to step into. I would suggest that all identities are abstract or Platonic ideas, so the identity lies in the characterisation of the idea. Depending on how the Thames is characterised (as an idea) Cirencester, Oxford and Maidenhead could both be considered to be and not to be on the same river.

I have a problem with the morning star having the properties of being believed to be a planet and being not believed to be a planet by verity.

What about infinitesimals (which have been revived in constructive versions of analysis, like smooth infinitesimal analysis, and by other forms of non-standard analysis)? The differential dx/dy seems to pick out an individual, but not one that has the property of identity and is also not nothing... If you find this example interesting, I take it from Gilles Deleuze's reading of Leibniz in _Difference and Repetition_ . There Deleuze argues that difference is prior to identity, and that 'identity' is some kind of relative identity in the sense the video brought up about Geach. For the regular notion, of identity, I think Wittgenstein and Lewis are saying the same thing in different ways, but I prefer Wittgenstein's construal.

Great video. Been waiting for something like this from you. I think the main problem lies in the "application" to the real world. By assuming the application is straightforward you're assuming Plato's world of ideas. You're assuming that there's a chair to identify directly to itself instead of a blurry set of particles and patterns that we would identify as "that chair".

Wittgenstein is so in its own fly jar - super funny.

Im currently eating mcdonalds and watching a video on logic, i really do feel like a redditor sometimes...

It seems strange to me to call absolute identity “numerical”, since the concept doesn’t originate in arithmetic.

16:05 in a way then does this not seem to imply that, in the deepest and truest sense, something can only really be identical to itself if it's properties and being are fundamentally immutable? The only true identity is the identification of the completely unchangeable with itself. in a way then only the universe actually has an identity and everything else is merely constituent or contingent?

ахуенная тема брат, хорошо раскрыл, базовый контент, спасибо

Where can I find the thumbnail?

🎉

Sorry I can't comment in detail on this video. I'm just not myself today...

Definition of Identity: x is identical to y iff P(x) P(y) is a tautology and P is an arbitrary predicate. Then x and y are just two names for one thing. Identity to Non-Contradiction seems to be what half-full is to half empty. The mentioned problem of presupposing identity here is a general one with all undefineable presuppositions: do we really understand them or are we using them like the dude in the chinese room? Because then you could derive from it our complete irrationality (and of course we could be always wrong anyway, just because we are forced to presuppose it doesnt mean it must be true what we presuppose).

afaik identitiy can be derived from countability of categories

Um... Isn't identity naturally a relation? A relation between a thing and itself. In plain language we typically don't go through the trouble to avoid using is, or other identity relations, but you can. Identity relates each thing "a" with another thing "a". Identity relates each thing a with a thing b if and only if it relates b with a. And so on for transitivity. Which does not prevent the creation of an undefinable it only kicks the bucket down another rung. Now relation becomes undefined. Mathematics tried to end the line at sets. Famously that didn't go very well.

No mention of Schrödinger logics, smh 😔

Thy

Uro, Ryu, kashimo.

As always, it was all a linguistical confusion

I wouldn't say a belief about X is a property of X. "Verity believes that Venus is a planet" is a property of Verity, not Venus

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if identity is undefinable then you can identify as trans, but trans cannot be born trans, since identity is undefinable, and therefore at each interval in time the elements of the set are different.