Logic Statements 127-1.5

Logic Statements 127-1.5


This video is going be about logic statements,
and basically what I wanted to do discuss the kind of things that you can and
can’t use in logical arguments and also talk a little bit about
negation. So here’s some examples of valid
statements for a logic argument. I’ve got “a square has four equal sides”, “George Washington was left-handed”, “5 + 2=11”, and “Paris is the capital of France.” Now not all these statements are true. 5 plus 2 obviously does not equal 11. But the thing they have in common is we
can determine whether each of the statements is true. There’s no middle area.
They’re either true or they’re not true. So we can say “a square has
four equal sides” is a true statement. “George Washington was left-handed”…. I don’t know if he was left-handed, but we could find out. He either
was a left-handed or he wasn’t left-handed. “5 + 2=11” is not a true statement, but since we can determine that it’s not a true
statement, then it’s a valid statement for an argument. “Paris is the capital of France”… Well we can check that and make sure
it’s true. Or maybe find that it’s false. (It’s true.) So here are some statements that cannot be used: “Did it rain yesterday?” This is not a statement it’s a
question, and questions are neither true nor false. “Don’t eat that cookie.” This is a command, and commands are neither true nor false. “Chocolate and vanilla.” This is not even a statement, it’s just the names of two flavors. “Picasso was the world’s greatest painter.” This is a statement, but it’s not valid in an argument because it’s an opinion, and whether one person thinks
Picasso was the world’s greatest painter doesn’t make that person’s opinion true or
not. okay there Now here are a couple more that seem like they
should be good, until we go deeper into it. “5 + x=17.” The problem with that is we don’t know
what x is, so without any context we can’t determine whether this is a true
statement or not. We have to be able to decide whether
it’s true and we can’t do that with this statement. He is my brother. This is also a statement with no context.
We don’t know who I’m talking about, so that person might be my brother or
might not. Unless we can determine who I’m talking
about, we can’t use this as a valid statement. So now we come to the issue of negating statements. In other words, we want to take a statement and
say that no, the opposite is the case. Typically we’re going to use the word ‘not’. So if I have a statement like “a square
equal sides,” I can just say “a square does not have for equal
sides.” If I have “George Washington was
left-handed,” all I have to do is is say “George
Washington was not left-handed.” “5 plus 2 equals 11,”… We negate that with “5 plus 2 does not equal 11.” The same thing with “Paris is
the capital of France.” I’m just going to say “Paris is not the capital of France.” The problem we have is when the
statements contain some words like ‘all’ or ‘no’ or ‘some’ or ‘each’ or ‘every’, in which case we can’t
negate them as simply. If I have a statement like “all roads
lead to Rome.”…. Now this is a valid statement, but the negation of this would not be “no roads lead to Rome.” The negation would happen if I could find at least
one road that doesn’t lead to Rome. So if I have a word like ‘all’, my negation is probably going to
include some word like ‘some’… “Some roads don’t lead to Rome. If I have something like ‘no’…. “No roads lead to Rome”… all I have to do is find at least one road that does lead to Rome and this statement will be negated. So if I start with “No roads lead to Rome”,
I can just say “Some roads do lead to Rome,” or “There is at least one road that leads to
Rome” and that would negate this statement. If I start with ‘some’, I’m gonna go the other
way. Some pigs can fly”. Well, if you tell me that some pigs can fly
and I want to disprove that, I want to say that’s not true, I’ll have to say that ‘there are no pigs that can fly’ or
just ‘no pigs can fly.’ If I start out with a statement like ‘some
pigs can’t fly’ and I want to prove that that’s not true, I’m going to have to say
‘all pigs can fly’. So when you’ve got words like ‘all’, ‘no’, or ‘some’, or variants of them, ‘each’, ‘every’, then you’ve got to be careful
before you decide what the negation is. If you’ve got it ‘all’, all you have to do is
say that there are some that are the opposite. ‘All roads lead to
Rome’ – ‘Some roads don’t lead to Rome.’ If you’ve got ‘no’,… ‘No roads lead to Rome’, once again we’ll
use ‘some’,… ‘Some roads do lead to Rome.” And if you’re starting out with ‘some’, you may use ‘all’, as in ‘Some pigs can’t fly’ — ‘All pigs can fly’ would be the opposite. ‘Some pigs can fly’…
the opposite of that would be ‘no pigs can fly.’ So you might want to think about this last
section a little bit before you dive into any problems, just to make sure you don’t get tricked.
Okay, that’s about it, take care, I’ll see you next time.

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