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 $U\square\phi$.
Arguing for logical realism and discussing the logical structure and constitution of the world.
Non omnes formulae significant quantitatem, et infiniti modi calculandi excogitari possunt. (Leibniz)
Monday, February 26, 2024
Problems with tense and modality in Topics 145b
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