"Identical with" vs. "Identical to"

[zefan13]

I read a philosophy of mind textbook recently and came across an interesting distinction between the terms "identical with" and "identical to." It suggested that to say that A is identical with B is just to say that A literally is B, i.e., A = B.

To say that A is identical to B, on the other hand, is to say that A is numerically distinct from but otherwise similar to B, i.e., A and B are two different things, but they resemble one another spot-on.

Simply put, "identical with" denotes numerical (or quantitative) identity; "identical to" denotes qualitative identity, according to the reading. I'm wondering if this distinction is widely accepted or assumed by philosophers, or if this is more of a quirk of the author.

[The Voice of Time]

Philosophy of Mind shouldn't really dabble too authoritatively in linguistics. Other languages may not have the same two variations of basically the same concept, and so it's hard to say there's any fundamental truth to it.

I'd say instead that "identical with" and "identical to" are just habitual speak, and people vary in their habits. That said, if I were to distinguish them, I'd use "identical with" to mean "works the same as/has the same significant identifying properties as", whereas "identical to", would mean "is referring to/is the exact same as an original". So in the first, some unsignificant properties may vary, whereas in the second the one would be a complete copy of the other one acting as a model.

But that might be just a random understanding.

[Blaggard]

an electron is identical with another electron but it is not identical to even though all electrons share the same intrinsic properties, makes sense. :S

eˉ = eˉ and eˉ ◅ eˉ

a) eˉ is equal to eˉ and eˉ is a subgroup of eˉ

eˉ # ē

b) eˉ is not equal to all electrons

a⇔b

If a is true b is true if a is false then b is true and vise a versa.

Electrons are identical particles because they cannot be distinguished from each other by their intrinsic physical properties. In quantum mechanics, this means that a pair of interacting electrons must be able to swap positions without an observable change to the state of the system. The wave function of fermions, including electrons, is antisymmetric, meaning that it changes sign when two electrons are swapped; that is, ψ(r1, r2) = −ψ(r2, r1), where the variables r1 and r2 correspond to the first and second electrons, respectively. Since the absolute value is not changed by a sign swap, this corresponds to equal probabilities. Bosons, such as the photon, have symmetric wave functions instead.[80]:162-218

In the case of antisymmetry, solutions of the wave equation for interacting electrons result in a zero probability that each pair will occupy the same location or state. This is responsible for the Pauli exclusion principle, which precludes any two electrons from occupying the same quantum state. This principle explains many of the properties of electrons. For example, it causes groups of bound electrons to occupy different orbitals in an atom, rather than all overlapping each other in the same orbit

electron: wiki

[Advocate]

identical with - indicates the ideas are co-equal in consideration

identical to - indicates one of the ideas was already established