What is Leibniz's Law? - Gentleman Thinker

Perhaps one of the most important and widely used axioms in philosophy. What is it? What does it mean and how does it work?

[lineikatabs]

this channel is mind numbingly underrated.

[chemistryguy]

Really good stuff.  You have become my go-to for all metaphysical matters.  I think this channel is going places.

[DwalinDroden]

This is why most mathematicians deal with things which are "equivalent" rather than equal. It allows for there to be variations in properties without breaking the equivalence. I would say that 2/4 and 6/12 are equivalent, but they are not technically equal, since they have different numerators. Then when we decide to make equality, we use equivalence classes, the sets of things which are equivalent. Thus, the rational number 2/4 represents the class of all pairs (n, 2n) and in that sense, the class of 2/4 = the class of 6/12. Often times these things act more as an annoyance and so are suppressed, but it makes an important allowance, that some properties may be different without breaking identity. Me now and me ten minutes ago will have different ages (at enough detail) and so can not be equal, but we might be equivalent.

[Exiled_Rouge]

These were some of my favorite content videos on this channel. Great stuff.

[nimruil]

First time viewer here. I'm in love!

[abc_cba]

Except for the background music, this is the best explained video on Leibnitz . Cheers from India !

[amfar]

Mr./Miss/Mrs. Хрупа Хрупов 4 years ago, complained that this channel is underrated. It's still underrated. Why? This is surely one of the outstanding channels I have encountered.

[polinachka]

this is the best philosophy channel in the actual world

[Havre_Chithra]

Sweet! This video has given me some good ideas for my paper on David Lewis. Thanks!

[Sam_on_YouTube]

In one of the lesser known twists in quantum mechanics, the concept of numerical identity actually breaks down. It turns out, surprisingly, that it is an emergent property that stems from the statistical unlikelihood of of quantum properties exhibiting in large systems. But there is no such thing as "that electron" as opposed to any other one. We treat electrons as numerically distinct when they are sufficiently isolated that we can ignore their true nature, of being all just exitations in a field. But if we describe the field precisely enough, we cannot treat them as though they were seperate entities. And if they are entangled (I'm using the lay definition of that term, not the quantum definition) then they cannot be treated as though numerical identity exists. Indeed, even macroscopic objects, if we could be precise enough, would exhibit this behavious, but it is far more practical with macroscopic objects to use the approximation of numerical identity. It is an approximation that, for everyday experiences) will never lead you astray.

[maxwoods]

I love your channel! Thank you for getting me into philosophy.

[Weltgeist]

Excellent video, Abigail! Good to know you're still a great philosopher, even if you're not "identical" to the posh disembodied voice here 😉

[imiikhan]

Watching and learning from him in 2021. Cheerio old chap!

[fikkitchen]

Blimey! How dare have I stumbled upon this channel just now?

[ornleifs]

Love the posh accent - it's the only way to speak English old bean.

[akshayrathore]

God damn Leibniz, philosophy again! go back to your calculus homework.

[jaecynthiakendrick]

If you haven't done so already, I would like to see a video explaining logical symbols and how to read them.

[swolby]

It's interesting how like with 0.999... being treated as basically 1, we say our past self is numerically identical to our current self; both are infinitesimally close to the more known identity and so we just call them numerically identical.

[amfar]

And of course, many thanks from Iran.

[frederik]

You should do your regular videos in the same voice!