Leibniz Buys One Car Too Many

TheMadFool

I encourage you to look up Leibniz's take on Identity and Indiscernibility for more information. In this thread I would like to present my view on what has me stumped for the past year or so viz. the matter of identity of indiscernibles.

Let's start of with definitions:

1. Indiscernibility of Identicals: If X is identical to Y then, they share all attributes in the sense what is true of X is also true of Y. Charles Lutwidge Dodgson is identical to Lewis Carroll

2. Identity of Indiscernibles: If what is true of X is also true of Y then, X and Y are identical

My issue is with 2. Identity of indiscernibles if no more from the fact that in the case of 1. Indiscernibility of identicals is, in a mathematical sense, about the number 1. In the example I gave, between Lewis Carroll and Charles Lutwidge Dodgson there's only ONE object and this squares with the notion of identity as being about criteria that sets something apart from everything else. The bottom line is that when I talk of identity, I'm interested in isolating something from the rest of the universe - the only numerical value permissible is ONE.

However, when we consider 2. Identity of indiscernibles we have to contend with cars. Yes, cars. Cars have models - there can be thousands upon thousands of cars of a particular model. If two or more cars of a given model are shown to a person, not at the same time but one after another then, this person wouldn't be able to tell one apart from the other. In other words, cars of a particular model are indiscernibles but what's to be noted, this is the crucial fact, is that if one were to get mathematical about it, cars of the same model is/are clearly not about the number ONE. There are more than "one" cars of the same model and they're all indiscernible.

Ergo, it follows that if 1. indiscernibility of identicals is, mathematically speaking, about the number ONE, 2. identity of indiscernibles has to be false because it quite clearly isn't necessarily, again in a mathematical sense, about the number ONE.

What gives?

tim wood

2. Identity of Indiscernibles: If what is true of X is also true of Y then, X and Y are identical — TheMadFool

Perhaps with respect to what is true. I have two legs, you have two legs; that does not make me you, nor the same as you, except in that regard.

It seems to matter what the source of the information is. If the car, then all cars are different. And it may be that some are not obviously different (easily discernable) from some others, but of course they are at a sufficiently close level of examination.

If on the other hand the source of information is the discernment, clearly that can be deceived, even half-a-dozen times before breakfast. Nor does side-slip between words like identical and same, and identity and discernable help.

TheMadFool

Perhaps with respect to what is true. I have two legs, you have two legs; that does not make me you, nor the same as you, except in that regard. — tim wood

It doesn't work like that. All that's true of X must also be true of Y and only then is 2. the identity of indiscernibles applies.

The rest of what you wrote is gobbledygook. Sorry.

tim wood

All that's true of X must also be true of Y and only then is 2. the identity of indiscernibles applies.
The rest of what you wrote is gobbledygook. Sorry. — TheMadFool

Don't be, yours the blunt edge speaking to the caborundum stone. I understand, and this will hurt me more than you.

The idea is that if you rely on yourself - what you discern of observe, then you're subject to error. How, for example, would you know that all that's true for X is true for Y? If, on the other hand, you rely on the objects themselves, then more likely you will not be in error. Two "identical" cars are by no means at all in-themselves identical, and suitable inspection makes that quite clear.

Pfhorrest

↪TheMadFool

The different cars are discernible in that there are properties of them that they do not have in common: for example, one is here while another is there. If even those positional properties were made the same, then you would have truly only one car, because otherwise you would be in the strange situation of saying that right here in front of us right now at the same time are two (or more) indiscernible cars coexisting at the exact same place and time, even though of course in that situation it would to all appearances seem to be only one car.

Ciceronianus

Cars have models - there can be thousands upon thousands of cars of a particular model. — TheMadFool

Leibniz recommends the new BMW Monad, especially the Ultimate Monad, its most luxurious, but fundamentally simple, trim. It has a navigation system by which you can tell the location of all other Monads.

TheMadFool

Don't be, yours the blunt edge speaking to the caborundum stone. I understand, and this will hurt me more than you.

The idea is that if you rely on yourself - what you discern of observe, then you're subject to error. How, for example, would you know that all that's true for X is true for Y? If, on the other hand, you rely on the objects themselves, then more likely you will not be in error. Two "identical" cars are by no means at all in-themselves identical, and suitable inspection makes that quite clear. — tim wood

:up:

You're missing the point. It's not the practical impossibility of two objects possessing the exact same attributes that's the issue. What needs to be understood is there's no logical contradiction, ergo its possible, that there exists at least two objects in the universe with the exact same attributes such that they're indiscernible. My case builds on this possibility.

The different cars are discernible in that there are properties of them that they do not have in common: for example, one is here while another is there. If even those positional properties were made the same, then you would have truly only one car, because otherwise you would be in the strange situation of saying that right here in front of us right now at the same time are two (or more) indiscernible cars coexisting at the exact same place and time, even though of course in that situation it would to all appearances seem to be only one car. — Pfhorrest

You have a point. Spatial properties would make the cars of the same model discernible.

However, consider the following situation. You're seated in a viewing area and two events occur.

In the first event Lewis Carroll is brought before you, then ushered out and then brought back in. You wouldn't be able to discern any difference between Lewis Carroll's first appearance and his second appearance.

In the second event, a car of some model is brought before, taken away, and a second, "different", car of the same model is presented before to you. In this case too you wouldn't be able to discern any difference between the first car and the second car. For all intents and purposes, you would think the first car is the same car as the second one.

In other words, if I remove spatial properties from the equation, identity of indiscernibles is false. A special case scenario of course but definitely one in which Leibniz's law of identity of indiscernibles fails.

Also, what about ideas/concepts that lack spatial properties. Is it possible that two different ideas are indiscernible?

Pfhorrest

In other words, if I remove spatial properties from the equation, identity of indiscernibles is false — TheMadFool

So if you don’t count some properties, then two objects with all the same properties (besides the ones you’re ignoring) can’t be told apart. That’s not surprising.

The indiscernibility in question though is of a type that accounts for all properties.

If you look at a red car of a certain model and then a blue car of the same model, but both of them through black and white video screens, you won’t be able to discern them either.

TheMadFool

So if you don’t count some properties, then two objects with all the same properties (besides the ones you’re ignoring) can’t be told apart. That’s not surprising.

The indiscernibility in question though is of a type that accounts for all properties.

If you look at a red car of a certain model and then a blue car of the same model, but both of them through black and white video screens, you won’t be able to discern them either. — Pfhorrest

Yes, it's not a complete refutation of Leibniz's identity of indiscernibles. As I said, it's a special case. @tim wood said something along those lines in his first post.

At this point, Einstein's relativity seems appropriate. It's not that spatial property alone matters in discernibility, it's actually space-time. Your position stems from the belief that one object can't be in two different places at the same time. Thus,the two cars of the same model are discernible - they occupy two different places at the same time.

Ignore time for the moment and we come to the realization that one object can be in two places e.g. Lewis Carroll was in Daresbury and then in Guildford. In other words, in only a spatial sense, the fact that cars of the same model were in two different locations neither implies that the cars are identical nor that the cars are not identical. Space, by itself, isn't a discerning feature.

If we now include time in the picture a problem arises. Lewis Carroll was in Daresbury but not at the same time he was in Guildford. This is the principle you're using - one object can't be in two different places at the same time - to assert that two models of the same car are discernible.

However, what does "at the same time" mean? Simultaneity, according to Einstein, is relative in the sense that what's simultaneous to one observer is not to another and vice versa. What this means is that what you observed as two different temporal events - 1832 in Daresbury and 1898 in Guildford for Lewis Carroll - are actually simultaneous events for an observer in a different frame of reference. In essence then it's possible for one object to be in two different locations at the same time. The principle that one object can't be in two different locations at the same time is untenable.

Ergo, spatio-temporal properties can't, shouldn't, be part of the criteria for discerning one object from another.

Pfhorrest

Even in relativistic spacetime, two spatiotemporal coordinates (two events) are still clearly distinguishable as two events.

This begins to raise very thorny questions about identity over time. In an extremely literal sense, by the time I finish typing this sentence I won't be the same person as I was when I began typing it; the me at the end time is a different event than the me at the beginning time. Also, me now is physically different in many different ways than me 20 years ago, so being discernible, we can't literally be identical to each other. Diachronic (trans-temporal) identity as we usually use it in day-to-day life thus has to be a different thing than the literal logic identity we're discussing.

tim wood

What needs to be understood is there's no logical contradiction, ergo it's possible, — TheMadFool

Logically possible. Seventh-cousin thrice removed from reality, from possibility. Logic a tool, reality - possibility in reality - the engine. On the way from tool to engine, the very best one can do, if it's a very good tool, is make some inferences about the engine, which may be, or may not be, true.

Leibniz Buys One Car Too Many

Welcome to The Philosophy Forum!

Categories

More Discussions