All of Robert4's Comments + Replies

Opps, I made an error when I said: "It is clear that (X->Y)->X does not imply (not X)->X, so your little trick doesn't work." This is false. This implication does exist, so we get:

((not ◻C)->(◻C))

This sentence is true just in case C is in fact provable, so we don't have a problem with your 2=1 cases.

The problem is that while Lob's theorem says that whenever we have ((◻C)->C), C is provable, it does not mean that there is a proof of C from ((◻C)->C). This means that you're use of the deduction theorem is incorrect. You can only say (((◻C)->C)->(◻C)). It is clear that (X->Y)->X does not imply (not X)->X, so your little trick doesn't work.

-3dlthomas
(X->Y)->X and (X->Y)->Y have the same truth table.

This has been mentioned many times, by Peter Singer, for instance, but one way towards moral progress is by expanding the domain over which we feel morally obligated. While we may have evolved to feel morally responsible in our dealings with close relatives and tribesmen, it is harder to hold ourselves to the same standards when dealing with whoever we consider to be not part of this group. Maybe we can attribute some of moral progress to a widening of who we consider to be a part of our tribe, which would be driven by technology forcing us to live and i... (read more)

0Yosarian2
Yes, this is what I was going to say. As time goes on, we seem to add more and more people and groups of people to the catagory we treat morally. Most major changes in morality over time you could describe this way; the elimination of slavery, women's suffrage, laws of war, better treatment for mental illness, even the idea that it's bad to torture cats for your own amusement could all be called "expanding the group of beings who we feel we have to treat ethically".