Page 318

Just a bit of concern here:

we're given 3 valid formulas on page 314 . THey are always true in all worlds in all models.
Then on page 218 we are given formulas which are not valid, but should hold for certain interpretations of BLOCK and DIAMOND

now the decision on whether these hold, seem very very subjective.

for instance: It ought to be true
it says that if things ought to be true, then it should be permitted. hence saying if BLOCK p --> DIAMOND p (ie. if all should be permitted, then we should have at least one)

Are these interpretations fixed, should we know them based on the table on p 318. Or are they just given to help us understand the reasoning behind them?

many thanks

Danie van Eeden
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Sorry, just saw your question on this now...

To be honest, I don't think that we have to know the table (Table 5.7) by heart, but more use it as a tool to understand the content... From my understanding of the scope of the situation, the table is used to indicate the different meanings of the modal connectives in the different modes of truth. In other words, simply showing that by changing the meaning of the mode of truth that block and diamond represent, a formula that may be valid in one mode of truth is not necessarily valid in another.

I've had a quick look through the table, and it may be helpful to understand what the differences are, how the validity differs between the various modes of truth, etc. But I don't see how learning the differences is going to be helpful...