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Sense and Reference: The Question

This man is about to step out in front of a bus.

This man is Ben.

Therefore:

Ben is about to step out in front of a bus.

Andrea is in her office speaking on the telephone to her friend Ben. As she looks out of the window, Andrea notices a man on the street below using his mobile phone. He’s not looking where he’s going; he’s about to step out in front of a bus. Andrea does not realise that this man is Ben, the friend she is speaking to. She bangs the window and waves frantically in an attempt to warn the man, but says nothing into the phone.
\citep[adapted from][p.~439]{Richard:1983rl}

Andrea is in her office speaking on the telephone to her friend Ben. As she looks out of the window, Andrea notices a man on the street below using his mobile phone. He’s not looking where he’s going; he’s about to step out in front of a bus. Andrea does not realise that this man is Ben, the friend she is speaking to. She bangs the window and waves frantically in an attempt to warn the man, but says nothing into the phone.

adapted from Richard, 1983 p. 439

All I’m saying at this point is that we’re getting into a mess ...
recall this quote from personal identity ...

‘Identity is utterly simple and unproblematic.

Everything is identical to itself; nothing is ever identical to anything else except itself.

There is never any problem about what makes something identical to itself; nothing can ever fail to be.

And there is never any problem about what makes two things identical; two things never can be identical.’

Lewis, 1989 pp. 192--3

‘Identity gives rise to challenging questions which are not altogether easy to answer.’

\citep[p.~209]{frege:1948_sense}

Frege, 1948 p. 209

What doesn’t Andrea realise?

That this man is Ben.

Numerical identity.

‘This man is Ben’ expresses a fact about numerical identity.