Monday, February 26, 2024

Problems with tense and modality in Topics 145b

 Aristotle asks if  the statement: at the present it is not possible for $A$ to be $B$ entails or not that it is not possible for $A$ to $B$ at all times.  That is, is the modality involved a virtuality of the present or is it inherently temporal as well, wherein 'being not possible' means at all times it is never the case that $A$ is $B$. If we take $P$ to be the present operator and $U$ to be 'at all times', then we have $PU\phi \rightarrow \phi$.  However there are sentences like 'at the present it is not possible for me to understand this'  in which the embedded modality has no temporal implication. In this case $P\square\phi$ does not imply that $U\phi$ or $U\square\phi$.

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