course, does not mean the defendant is, as a matter of actual fact, innocent. Is this state of a airs
captured accurately when we use "not" in the mathematical sense? (i.e., Do "Not guilty" and ~guilty" mean the same?) What if we change the question to ask if "Not proven" and ~ proven"
mean the same?
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The truth table for ~ ~ Φis clearly the same as that for Φ itself,
so the two expressions make identical
truth assertions. This is
not necessarily true for negation in everyday life. For example, you might
find yourself saying “I
was not displeased with the movie." In terms of formal negation, this has
the form ~(~ pleased), but
your statement clearly does not mean that you were pleased with the
movie. Indeed, it means
something considerably less positive. How would you capture this kind of
use of language in the formal framework we
have been looking at?
(thought for the day): In English, two negatives make a positive. In some languages, such as Spanish, two negatives make a stronger negative. There is no language where two positives make a negative.
ReplyDeleteYeah, right.... (said with a sneer)
In the first question, "Not guilty" is definitely not the same as "innocent." In mathematics something is true or false; 2 + 2 = 4 is true; 2 + 2 = 8 is false. There are no other options.
ReplyDeleteIn life, though, we use "fuzzy logic." You tell your son to be home before 10:00 PM. He comes in at 10:03. Is this wrong? Yes, it is a violation of your rule. Will he be punished? Probably not. What if he came in at 10:10? 10:30? At what time does the rule violation make a difference?
I think of many very famous people who were found "not guilty" of a crime. (Not mentioning any names here, but the long list could include former US presidents, sports figures, celebrities, and others). Often they were guilty of something -- poor judgement, poor choices, or a different crime than what they were actually charged with).
Is this the same as "not proven" and "Proven"? I would argue that even this is not cut and dried. There may be a fuzzy logic area between the two.
I was watching America's Got Talent on Wednesday. For those of you who have not seen the show, 12 acts performed on Tuesday. The top five performances, as voted on by social media, got to go on to the finals. The acts placing 6 and 7 were voted on by the judges as to who would go on.
These two acts were both children -- and 11 year-old girl with an adult's singing talent, and a 12-year-old and 13-year-old dancing couple with adult skills. As the judges began debating, I said to my husband, "There aren't any wrong choices here -- they are both so talented!"
Just because one of the acts were voted through and the other was not doesn't mean is was "Proven" that they were better; it's just the way the voting came out.
Nancy here really:
ReplyDeleteI am stuck on second one. using % for the negation symbol, it seems that:
%%0 does not equal % (%0) but I don't get it.
and yeah is it two negatives make a positive as in math OR two negatives really underscore that something stinks???
The point our prof is making here is that language is much more fluid than math, and we often can make inferences in English which we can't show in mathematics. I mentioned on another thread the topic of "fuzzy logic." We can make inferences based on our experience that we cannot show based on mathematics. Is he tall? Short? It depends on our own perceptions and standards. Although I am not tall myself (5' 4" if I stretch), I was surrounded by large men as I grew up. I was well into adulthood before I knew that the average man was NOT 5' 11" (the height of my shortest brother.)
ReplyDelete"That person is not stupid" does not necessarily mean "that person is smart." It all depends on the circumstances and our past experiences.
Another example: I recently adopted a new dog because we had to put an old dog down, and our chow chow was really lonely. We got a new dog that neither tried to attack the chow, nor was attacked by the chow. (It took us several hours at the local animal shelter.) Can I say that the two dogs like each other? I can say, "Alf did not attack Meg" and "Meg did not attack Alf." Other than that, I can say, "The two dogs did not dislike each other." But, we haven't had Meg long enough to say, "The two dogs like each other." After a week together, they just tolerate each other. No mathematical sign for that!
I thought of the last question as a Venn diagram, where, in my mind, the thought of %%pleased /\ %pleased did cross in the median to include a thought that was both pleased and not pleased instantaneously, without defining extra variables or making a scale system to define a 'zero state'. I am having a hard time getting any consensus in real life discussion on this one, though, as is shown by the other variables and zero state comment - which I have been presented with as other ideas.
ReplyDelete