Susan Brown
@susanhypoluxo.bsky.social
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Advocate for safe, healthy, efficient homes. Laughing beats crying all day long.
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Reposted by Susan Brown
![\begin{frame}{Leibniz's Identity of Indiscernibles}
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\highlightp{\textbf{\Large``}}Two objects are identical iff they have the same properties.\highlightp{\textbf{\Large''}}
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Mathematically: $x$ and $y$ are objects in $\Mcal$. Then $x = y$ iff $\Mcal \models \phi(x) \iff \Mcal \models \phi(y)$ for every property $\phi$.
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\item $\Mcal \models \varphi(x)$ is model theorist speak for \highlightv{$x$ has property $\varphi$ in the structure $\Mcal$}.
\item
It's circular to have a property like ``identical to $x$''. We only mean properties you can express in the \highlightv{language} of the structure, e.g. the language of rings.
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\end{frame}](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:73hkwya2rrrfg26vdcwnmo6p/bafkreiagbuhluk6tgqyy7gyboxjbbyl4p65w4edxifawoj7bfq6gg5chne@jpeg)
Reposted by Susan Brown
