The concept of change, or the concept of same? Both seem essential to how we think about the world.

It is common to reduce a problem to it ` s parts, and solve the parts. In this case, if you define "the same", to another concept " change", then a solution to the former is obtained given the solution to the latter.

The concept "change" don` t seem to be necessary to me.

All right, but lets hope that you will change your mind.

But the conversation has to be about something, and not consist in just random thoughts about some supposedly philosophical topic. Have you any idea how to draw the distinction (if there is one) between essential and accidental properties? How about presenting it?

But it is not the same organism qualitatively,

how is it not the same organism qualitatively if they share the same identical DNA?

The two copies may be the same in quality, but of course, not in quantity.

How are two copies of the same bacteria the same in quantity if they are two separate individual organisms? You must be hallucinating if you are confusing two distinctly unconnected bodies as one.

I think that you are not reading straight, and that you are reading what you want to read, not what I have written.

But they are the same organism quantitatively, since the baby and the adult are one and the same individual. You have it exactly backwards.

If two organisms share the same DNA they may still not be qualitatively the same if they have qualities other than their DNA, for they may differ in those qualities.

4.04 In a proposition there must be exactly as many distinguishable
parts as in the situation that it represents. The two must possess the
same logical (mathematical) multiplicity. (Compare Hertz's Mechanics on
dynamical models.)


4.041 This mathematical multiplicity, of course, cannot itself be the
subject of depiction. One cannot get away from it when depicting.

Wittgenstein ain't always right, in my opinion. (Are we allowed to say this?) But this is interesting. Sometimes Wittgenstein seems nothing like a Platonist & at other times quite so.

I venture to suggest that no two things in nature are identical or the same. I suggest that perfect identity is intuitive, a sort of Platonic Form. Having thought about this sort of thing constantly for months, I suggest there is no better way to see if I'm right. Books are nice, of course. But I sincerely think they can get in the way in a case like this. It's the simplest too obvious things we are dealing with.
:detective:

An accidental property is supposed to be a property that something does have, but which it need not have in order to be what it is. An essential property is a property that something must have in order for it to be the thing it is. Water may be a solid, or a liquid, or a gas. So whether it is a solid (say) is accidental. But if a substance is water, then it must contain oxygen. So oxygen is an essential property of water.

The concept of the same is one of the central philosophical concepts with truth, knowledge, and good. What is central is how something can remain the same thing though change (persistence through change). The person is the same person although he is a baby, and adult, and an old person. The beginning of wisdom here is to take note of Wittgenstein's advice not to confuse the concept of the same with the concept of identity. How does something remain self-identical, although, at the same time, it changes?

Thoughts about what? Words by themselves seem to trigger you off. The issue, as I have already said, is how to draw the distinction between accidental and essential properties. And that question supposes that there is a real distinction in the first place.

Our intuitive understanding of identity, is not 'too obvious' to me.

Perhaps we should define x=y as
Necessarily[(x exists) & (y exists) & (all F)(Fx <-> Fy)].

Our intuitive understanding of identity, is not 'too obvious' to me.

I agree that two different things cannot be identical.
If there is a property that x has and y does not have then they are not identical.
That physical objects occupy different space-time locations, however similar they are otherwise, provides proof that different physical objects are not identical. (some F)(Fx & ~Fy) -> ~(x=y).

'perfect identity' only occurs to itself, ie. a=a and only a=a.
If (a,b,c,..) are each unique and different values (names) of the individual variable, then only (a=a) because, a=b or a=c etc., are false.

x is identical to y, means, a property of x is equivalent to the same property of y, for all properties. ie. x=y defined (All F)(Fx <-> Gx), (Leibniz, I think).

Even this definition of identity has exceptions. ie. It seems to be restricted to extensional properties.

For example:
The number of planets is eight and Necessarily (eight is greater than seven) therefore, Necessarily (the number of planets is greater than seven) ..is false.

(the number of planets) = 8 & [](8>7), implies, [](the number of planets > 7)..is false.

Wittgenstein denied the use of (=) between different names. TLP *5.
But, in the case of described objects, we still need the identity sign (=).

2=2 is not informative, but (1+1=2) or (the sum of 1+1) is 2, is informative.

Another exception to LL, x=y -> (all F)(Fx <-> Fy), is...
(the present king of France)=(the present king of France).

(the present king of France) has the property F <-> (the present king of France) has the property F, is tautologous for all F. But, (the present king of France)=(the present king of France) is contradictory according to Russell's description theory.

(the present king of France)=(the present king of France) <-> (all F)(F(the present king of France) <-> F(the present king of France)), is contradictory.

'Similarity' also seems to be difficult to define. ie Similarity is neither too obvious nor too simple.

Russell defines natural number as: the class of those classes that are similar to it, where similarity is a one to one relation such that.....
That is, 1=(the class of classes that have exactly one member).
X is a unit class, implies, X is a member of 1.

Perhaps we should define x=y as
Necessarily[(x exists) & (y exists) & (all F)(Fx <-> Fy)].

Whatdoyouthink?

What about analogies? When to things are compared through analogy does this point to a sameness of some kind? I would say yes it does. For example an analogy can point to a sameness of appearance or a sameness of structure.

I was thinking about metaphor/analogy last night. We circle two objects. We use "is" as an equals sign. Or as an approximately equal sign. And this forces us to abstract what these things have in common, and leave behind what is not in common? basically a Venn diagram --which Euler invented it seems....

Nor to me; questions such as this cast me back into a "blooming, buzzing confusion", and I find it easier to type out a passage from Wittgenstein or criticise a point in Frege than to venture any thoughts of my own. So let's have a go at one of yours.

I'm out of my depth here, and won't attempt to comment either on Leibniz's definition, your prefixing 'Necessarily' to it (if it's not there already), or Wittgenstein's rejection of identity as a binary relation. But I do note that you seem to be taking existence as a predicate. Do you mean this?

(Also, any true instance of your x=y would even seem to imply that x, i.e. y, exists necessarily!)

Or to compare a woman to a rose. There's no genetic or causal connection. They look nothing like each other. Yet both have the power to fascinate and are pleasant to look at. Both are beautiful.

Yes indeed, to analogize is to think abstractly. It is to abstract sameness from two or more things.

Also notice that there's no difference between the points on a circle until you place an x-y axis over it. Now the points can have unique identity. Take away the axis and the circle is once again defined as a line where all the points are equidistant from the center. But there's no way to distinguish between the points on the line. So unique identity is dependent on the application of the axis or cross.

Twirlip:
"But I do note that you seem to be taking existence as a predicate. Do you mean this?"

Yes. x exists, has x as its subject and exists as its predicate.

x exists, is defined as, there is some property which x has.

(x exists) <-> (some F)(Fx), where F is a primary predicate (property) of x.

(some F)(Fx) <-> (Gx v Hx v Kx v ...) <-> (x exists).

Gx -> x exists, for all x ...If x has the property G then x exists.

If (I think) then (I am), is tautologous.