im online

If we suppose that Ted [Sider] is a person-stage that exists only at instant $\mathrm{t<!--\; -->}$, then it is obviously not true that it was the case that Ted existed at any previous time. That is, at $\mathrm{t<!--\; -->}$, the following is true:

$\neg <!--\; -->\exists <!--\; -->{\mathrm{t<!--\; -->}}^{\mathrm{\prime <!--\; -->}}(<!--\; -->{\mathrm{t<!--\; -->}}^{\mathrm{\prime <!--\; -->}}\mathrm{\text{is earlier than<!-- -->}}\mathrm{t<!--\; -->}\wedge <!--\; -->\exists <!--\; -->\mathrm{x<!--\; -->}(<!--\; -->\mathrm{E<!--\; -->}\mathrm{x<!--\; -->}{\mathrm{t<!--\; -->}}^{\mathrm{\prime <!--\; -->}}\wedge <!--\; -->\mathrm{x<!--\; -->}=<!--\; -->\mathrm{\text{Ted<!-- -->}})<!--\; -->)<!--\; -->$

(‘$\mathrm{E<!--\; -->}\mathrm{x<!--\; -->}\mathrm{t<!--\; -->}$’ means ‘$\mathrm{x<!--\; -->}$ exists at $\mathrm{t<!--\; -->}$’.)

But Sider also claims that ‘Ted was once a boy’ is true. This seems to be equivalent to ‘There was some thing such that it was a boy and it was Ted’. That is, it appears that Sider is also committed to this being true at $\mathrm{t<!--\; -->}$:

$\exists <!--\; -->{\mathrm{t<!--\; -->}}^{\mathrm{\prime <!--\; -->}}(<!--\; -->{\mathrm{t<!--\; -->}}^{\mathrm{\prime <!--\; -->}}\mathrm{\text{is earlier than<!-- -->}}\mathrm{t<!--\; -->}\wedge <!--\; -->\exists <!--\; -->\mathrm{x<!--\; -->}(<!--\; -->\mathrm{E<!--\; -->}\mathrm{x<!--\; -->}{\mathrm{t<!--\; -->}}^{\mathrm{\prime <!--\; -->}}\wedge <!--\; -->\mathrm{B<!--\; -->}\mathrm{x<!--\; -->}\wedge <!--\; -->\mathrm{x<!--\; -->}=<!--\; -->\mathrm{\text{Ted<!-- -->}})<!--\; -->)<!--\; -->$

(Here ‘$\mathrm{B<!--\; -->}\mathrm{x<!--\; -->}$’ means ‘$\mathrm{x<!--\; -->}$ is a boy’.)

These are contradictory claims.