The original parent posited that we have multiple identities, as in: multiple sets of attributes, each of which uniquely identify us within a certain context.
> Let's assume we define "identity" to mean "any set of attributes of Alice", so widening it essentially as far as possible. Then "is a human", being an attribute of Alice, would become an identity of Alice.
> That doesn't make much sense, does it?
If Alice is the last surviving human being in the universe, it does.
If Alice isn't the last surviving human being in the universe, than the premise of "is a human" as an identity is already nonsensical (because it no longer identifies), hence also any conclusions you derive from that premise are also nonsensical.
> In order to check that you are the person on a picture I have of you, all I need is the picture, no need to have a replica of you.
You haven't checked that it's me, you've checked that it is someone who looks like me.
Within any given context, that may or may not be treated as my identity. Hence, we're back at multiple identities, each in their own context.
> In order to check that you are in the possession of a private key, all I need is the corresponding public key, not the private key.
Which says nothing about identity, only about possession. Whether this possession is taken to be sufficient proof of identity again depends on the context.
> Also, if it were the case that identity verification were in fact impossible ... what would be your point then? You don't like the (hypothetical) fact that it is impossible, therefore it is possible?
Do you believe this hypothetical example to be true? If not, what's your point?
> The original parent posited that we have multiple identities, as in: multiple sets of attributes, each of which uniquely identify us within a certain context.
In which case it's just not a refutation of the tautological impossibility at all. Either something uniquely identifies someone, or it does not. Uniquely identifying someone while at the same time being (trivially) being replicated by somebody else is just a contradiction.
> If Alice is the last surviving human being in the universe, it does.
Seriously?
> If Alice isn't the last surviving human being in the universe, than the premise of "is a human" as an identity is already nonsensical (because it no longer identifies), hence also any conclusions you derive from that premise are also nonsensical.
Which is exactly why "was able to tell us the DoB of Alice" as an identity is nonsensical, and hence any conclusion of the form "therefore, Alice's identity was stolen" is nonsensical as well, correct.
> You haven't checked that it's me, you've checked that it is someone who looks like me.
Which contradicts the claim that the verifier does not need a replica of you how exactly?
> Within any given context, that may or may not be treated as my identity. Hence, we're back at multiple identities, each in their own context.
Which still cannot be stolen. So?
> Which says nothing about identity, only about possession. Whether this possession is taken to be sufficient proof of identity again depends on the context.
Which contradicts the claim that the verifier in a context where it is taken to be sufficient proof of identity does not need the private key how exactly?
> Do you believe this hypothetical example to be true? If not, what's your point?
My point is that I am responding to your argument that was about an implication from that hypothetical case.
> Let's assume we define "identity" to mean "any set of attributes of Alice", so widening it essentially as far as possible. Then "is a human", being an attribute of Alice, would become an identity of Alice.
> That doesn't make much sense, does it?
If Alice is the last surviving human being in the universe, it does.
If Alice isn't the last surviving human being in the universe, than the premise of "is a human" as an identity is already nonsensical (because it no longer identifies), hence also any conclusions you derive from that premise are also nonsensical.
> In order to check that you are the person on a picture I have of you, all I need is the picture, no need to have a replica of you.
You haven't checked that it's me, you've checked that it is someone who looks like me.
Within any given context, that may or may not be treated as my identity. Hence, we're back at multiple identities, each in their own context.
> In order to check that you are in the possession of a private key, all I need is the corresponding public key, not the private key.
Which says nothing about identity, only about possession. Whether this possession is taken to be sufficient proof of identity again depends on the context.
> Also, if it were the case that identity verification were in fact impossible ... what would be your point then? You don't like the (hypothetical) fact that it is impossible, therefore it is possible?
Do you believe this hypothetical example to be true? If not, what's your point?