For this question, it might help to parse what type-identity theory means and what multiple realizability means.

#type identity# The idea is that a type, i.e. a mental state, maps onto a physical brain state in a numerically identical fashion.

Translated into plain English, this is the view that any mental state is exactly and in every respect one brain state.

#multiple realizability multiple realizability is the claim that the same mental state can be realized in multiple physical ways.

Regardless of how, this would imply that the identity is broken, because the same thing can occur in ways that differ.

It might help to think of a pair of six-sided dice.

Let's first consider the number 2. The only way to get the number 2 on two dice is 1 and 1. Thus, there's an identity between rolling a 2 and having the physical state of two dice each showing 1. These two things are thus identical.

But then let's consider the number 6. We can get 6 by having a 1 and 5, 2 and 4, or 3 and 3. Thus, rolling a six is multiply realizable. This means its non-identical with any of these particular physical arrangements of dice.

Thus if multiple realizability is true about mental states, then type identity is false. And if type identity is true, then multiple realizability is false.

For this question, it might help to parse what type-identity theory means and what multiple realizability means.

type identity

The idea is that a type, i.e. a mental state, maps onto a physical brain state in a numerically identical fashion.

Translated into plain English, this is the view that any mental state is exactly and in every respect one brain state.

multiple realizability

multiple realizability is the claim that the same mental state can be realized in multiple physical ways.

Regardless of how, this would imply that the identity is broken, because the same thing can occur in ways that differ.

It might help to think of a pair of six-sided dice.

Let's first consider the number 2. The only way to get the number 2 on two dice is 1 and 1. Thus, there's an identity between rolling a 2 and having the physical state of two dice each showing 1. These two things are thus identical.

But then let's consider the number 6. We can get 6 by having a 1 and 5, 2 and 4, or 3 and 3. Thus, rolling a six is multiply realizable. This means its non-identical with any of these particular physical arrangements of dice.

Thus if multiple realizability is true about mental states, then type identity is false. And if type identity is true, then multiple realizability is false.