The Law of Identity

[@Dinhjason]

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

[@InventiveHarvest]

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.

[@KaneB]

Taking identity to be relative to contexts, where these are defined partly by our interests, seems like an interesting way to develop the relative identity view. I suppose you could still capture the standard idea of identity because "Venus is identical to itself" or "Venus is identical to Venus" will presumably come out true regardless of context. At least one could make an argument for that.

[@InventiveHarvest]

@@KaneB well, I am saying that in certain contexts, Venus is not identical to itself. For example, in this video, whether Verity believes it to be a planet or not is relevant. So in the context of discussing identity itself, Venus and the morning star are not identical. Take the example of a younger self. In many conversations, one is the same thing as their younger self, and in other conversations they are not identical. I say "i have always liked chocolate" then I am my younger self in that context. I say, "I am old and feeble" then I am not my younger self.

[@nicolasjay8850]

this is a fascinating line of thinking and in a lot of ways, what i think buddhism essentially tries to get at. the notion that any thing can be identified mistakenly or not so as another thing depending on the context of its mentioning. there’s a lot of parallel there with post-modern thought that actively recognizes the subjectivity in determining what parameters are used to distinguish any one given thing from any thing else

[@rogerwitte]

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.

[@KaneB]

The standard account regarding the letter 'a' would be that they are the same type, but different tokens. The first 'a' and the second 'a' are not one and the same thing; they just instantiate the same letter or the same form. The issue though is what does it mean for x and y to be the same token. On a more coarse-grained way of carving up the world, I'm not sure why we shouldn't take one as literally the same as the other. By analogy, if I cross my eyes and look at the cup in front of me, I will see a double image. It's one and the same cup, presented to me twice. We could hold a similar view of objects in general: it is not that two things instantiate the same form; there is merely the same form, doubly (or triply etc) perceived.

[@luyombojonathan6688]

Amazing channel !!! Love this in depth discussions

[@AnarchoAmericium]

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.

[@lbjvg]

Another way to critique identity: begin with the premise that there is no stable self. X cannot be identical to itself if the self does not exist. Also, another point: identity works well in logic and math as a premise to derive other properties but does not carry over as well into the real world where it seems useless.

[@RalphBrooker-gn9iv]

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)?

[@charlieyoutube5792]

Got popcorn🍿, exited to watch

[@prismaticsignal5607]

👌 "Omnis determinatio est negatio."

[@attackdog6824]

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

[@Voivode.of.Hirsir]

It didn't

[@das.gegenmittel]

@@Voivode.of.Hirsir😂😂😂😂

[@KaneB]

Good luck!

[@obcursus]

thumbnails go crazy

[@KaneB]

It's from the artwork "Sundai, Edo" by Hokusai

[@gmdlunar3461]

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

[@italogiardina8183]

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.

[@horsymandias-ur]

Where can I read more?

[@italogiardina8183]

@@horsymandias-ur library

[@horsymandias-ur]

@@italogiardina8183 Thanks

[@martinbennett2228]

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.

[@KaneB]

"One cannot step into the same river once."

[@martinbennett2228]

@@KaneB 👍

[@cavestoryking8761]

It's worth noting that he also says that we can indeed step into the same rivers: "We step and do not step into the same rivers; we are and are not." Fragment 49a I believe that Heraclitus was not a dialetheist and is merely being poetic here, and believes that we can step into the same rivers twice in one sense but not in another sense. But it is easy to see how one might interpret him in a dialetheic fashion.

[@horsymandias-ur]

Aristotle notes that Cratylus, a student of Heraclitus (and, if I’m not mistaken, another one of Plato’s teachers), criticized Heraclitus for suggesting that one can step into the same river twice (when one does not step into the same river at all)

[@whycantiremainanonymous8091]

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

[@writerightmathnation9481]

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

[@mcurtisallen]

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.

[@mcurtisallen]

Obviously one would have to accept the existence of abstracta to count this as a genuine example, but I think we get into similar issues with identity when we think about the relation of an object to time and the problem of individuation (of non-abstracta) in general. It seems to me there is no way of specifying a concrete particular such that one could make strict identity claims about it.

[@KaneB]

@@mcurtisallen I'm not sure you would need to believe that abstracta exist in order for this example to work. It seems like it would be sufficient for such abstracta to be possible or conceivable. If it's possible for there to be an object that is not identical with itself, then identity isn't be a necessary property. Similarly, Leibniz's law is supposed to be logically necessary, not merely an empirical generalization.

[@BaruchBender-r5o]

ахуенная тема брат, хорошо раскрыл, базовый контент, спасибо

[@alejandroperea98]

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.

[@ekki1993]

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".

[@BreezeTalk]

thank you so much

[@ostihpem]

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).

[@luisvasquez5015]

Model theory can produce counter examples to the way you formulated the axiom. Consider two structures with different sets of properties. Then you can have different objects that within one structure are the same (according to your axiom) and another one whhere they are different

[@ostihpem]

@@luisvasquez5015 I demand P to be an _arbitrary_ predicate and only if P(x) P(y) are a tautology (for arbitrary/all cases) then I‘d consider x identical to y. In your example, P(x) P(y) would not be true in one structure and so it would not be a tautology.

[@СергейМакеев-ж2н]

There's a similar definition sometimes used in type theory: "x is identical to y" just means that if you give me any (arbitrary) binary predicate P and a proof that, for any z, P(z,z), then I will give you back a proof that P(x,y)

[@TheLuckySpades]

​@@luisvasquez5015in model theory since we are not binding outselves to the theory the models model we can use the properties that make different models different For example if we are modeling Peano Arithmetic, then comparing the Von Neunann construction of the naturals and the naturals embedded in the reals (constructed via Dedekind cuts) I can use the cardinality of the element 0 in each to show they are different (since 0={} int the former and is a countable equivalence class in the latter), even if the models are isomorphic and both model Peano arithmetic

[@das.gegenmittel]

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

[@rath60]

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.

[@Laotzu.Goldbug]

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?

[@KaneB]

Suppose that X has F at t1 but does not have F at t2. Now let's say we claim that identity is not preserved through changes in properties. In that case, the standard view would be that there simply is no X at both t1 and t2; the first sentence of this comment describes the situation incorrectly. Rather, there is one object, X, at t1, then a new object, Y, at t2. X is identical to itself and Y is identical to itself. This is why Lewis thinks there is no debate about identity. We can debate whether an object can persist through changes in its properties. Regardless of whether we affirm or deny this, it will still be the case that the object is identical to itself.

[@cavestoryking8761]

No mention of Schrödinger logics, smh 😔

[@Focke42]

afaik identitiy can be derived from countability of categories

[@KaneB]

The standard view would be that countability presupposes identity -- it requires the self-identity of the things being counted, where each thing is identical to itself and distinct from other things.

[@Focke42]

@@KaneB mh that sounds true. Not the distinct part, but that each thing has to be self-identical. i mean nothing stops you from counting subcats, so counting tibbles and tib as two entities.

[@lupamartins8830]

Uro, Ryu, kashimo.

[@DarthCalculus]

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

[@KaneB]

It would usually be taken as a relation between Verity and Venus. It's not an intrinsic property of Venus (that is, it's not a property that Venus has in virtue of the way that Venus considered just in itself is), but it's a property all the same, in the sense that philosophers use "property". Similarly, Venus might have the property of being located 120 million km from Verity, and Verity would have the same property with respect to Venus. This isn't an intrinsic property of either Venus or Verity, but a relation between them. In any case, it doesn't make any difference whether we use the word "property". The issue can be reframed in terms of "properties and relations" or whatever else. If we say that Verity relates to Venus differently to how she relates to the Morning Star, but also that Venus is identical to the Morning Star, this would refute the traditional account of identity.

[@davib.franco7857]

Where can I find the thumbnail?

[@KaneB]

"Sundai, Edo" by Hokusai

[@luisvasquez5015]

As always, it was all a linguistical confusion

[@MochiB4mbi]

🎉

[@das.gegenmittel]

Thy

[@usameyalciner]

Sikko dan gelenler şukulasın

[@captainstrangiato961]

🔴

[@KaneB]

🔴

[@justus4684]

=

[@jandorian645]

.

[@Fiscacondaniel]

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.

[@KaneB]

That's not really the kind of identity we're talking about here...

[@Tocinos]

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