I have been thinking about translating an assertions into a suitable formal logical language :" If they have vanilla, then I'll also have that, but otherwise I'll have chocolate." Since I am not sure what "But" really means, I tried two ways to translate it. V represents they have vanilla; C represents I'll have chocolate. The first way: (V-->V) and C. The second way: (V-->V) or (C and not V). Can anyone help me out? Thank you very much.
Asked
Active
Viewed 18 times
1 Answers
1
Long story short, "but" is "and" with value judgement.
The natural language "but" is often used as a list-connective with an indication that the things being joined are of opposition in some sense.
"We have some bad news, but we have some good news too." The news that is had is a union of bad news and good news.
More to the point, it is also used to conjoin conditionals with opposing antecedants (and usually disjoint consequences). Such as in: "I will do this thing if I can, but I will do that thing if I can't."
So, "If they have vanilla, then I'll also have that, but otherwise I'll have chocolate," might be represented as: $$\big(H(t,v)~\to~ H(i,v)\big)~\wedge~\big(\neg H(t,v)~\to~ H(i,c)\big)$$
Graham Kemp
- 129,094
-
Thank you very much for your explanation. If "But" always means "and"? How about this assertion:"If we leave the window open, then water will get in, but only if it rains." If I apply the same reasoning, I would translate it as (O-->W) and (not W--> not R) – Deepsea234 Aug 31 '17 at 02:38
-
I also think "but only if" as "if and only if" Therefore, O--> (W <--> R). Can anyone explain it more? Thanks. – Deepsea234 Aug 31 '17 at 03:09
I also think "but only if" as "if and only if" Therefore, O--> (W <--> R). Can anyone explain it more? Thanks. – Deepsea234
– Deepsea234 Aug 31 '17 at 12:13