| X (I have gone to Kenya) | Y (The World Explodes) | if X then Y (If I go to Kenya, the World Explodes) |
|---|
| True | True | True |
| True | False | False |
| False | True | True |
| False | False | True |
This is a standard use of a truth table.
However, this is just pointing out the well-known rule of "If X then Y" equals "(NOT X) OR Y", as if you do the same truth table for "(NOT X) OR Y", you also get "true, false, true, true". It's a rather trivial result, as it's very well-known.
So you don't seem to be saying anything here.
Equally well, we could also make the same truth table where X = "I have not gone to Kenya" and Y = "the world explodes", as we'd get the same results.
So "if I go to Kenya, the world explodes" and "if I do not go to Kenya, the world explodes" have the same truth tables.
But then, if we say "if I go to Kenya, the world explodes" is valid, then "if I do not go to Kenya, the world explodes" is also valid, which means that the world would have exploded whether you went to Kenya or not. Hmmm'...has the world exploded?
| Expressions of this table? | What does it mean? |
|---|
| (X is false) OR (Y is true) | I haven't gone to Kenya, or the world exploding, or both |
| Y | The world explodes |
| X is equivalent to Y | I have gone to Kenya, The world explodes |
| X and Y | I have gone to Kenya and the world explodes |
| X is false (not X) | I haven't gone to Kenya |
| (not X) and Y | I haven't gone to Kenya, the world explodes |
| (not X) and (not Y) | I haven't gone to Kenya and the world doesn't explode |
| False | Nothing |
Nice list. But not a truth table. Also, not completely accurate.
#1 is accurate, even though you already demonstrated it a second before.
#2 is accurate.
#3) The left side "X is equivalent to Y" means (X = Y) or "When X is true, Y is true, and when X is false, Y is false", which would mean "Either I have been to Kenya and the world exploded or I have not been to Kenya and the world has not exploded".
The right side: "I have gone to Kenya, the world explodes" = "X and Y", which is #4.
So that's not right.
#4 is correct.
#5 is correct.
#6 is correct.
#7 is correct.
#8 is a category error. If "false" meant "nothing", then "X is false" = "X is nothing". I think you mean that "false" doesn't mention X or Y, and so doesn't say anything about you going to Kenya or not, and doesn't say anything about the world exploding or not.
Plus, "True" would be just as meaningless. So you saying it means "nothing" has got nothing to do with "false" itself.
Even so, all that does, is provide nice explanations for some symbols that are pretty commonplace. You're not proving anything.
Even for those who aren't familiar with those symbols, you got #3 wrong. So those who are trying to learn from your explanations are going to get misled.
Not always the end of the world. But since your explanation of #3 is equivalent to #4, but for #4, you give a slightly different explanation, you can easily mislead people into thinking that "I have gone to Kenya. The world explodes." is a very different statement in logic to "I have gone to Kenya and the world explodes", as those 2 statements already have a different meaning in general English usage. The use of the conjunctive "and" is to join 2 sentences together that could have been said separately. This is often to indicate a connection between them.
So if someone isn't familiar with these terms, they could think that in logic, (X and Y) refers to 2 statements that are somehow connected and relevant to each other, while also in logic, (X is equivalent to Y) refers to 2 statements that are both true but not connected to each other.
Anyone with that notion is liable to have a lot of problems understanding logical arguments where the word "equivalent" is used.
They are also likely to think that if 2 statements X and Y are both true, but not connected to each other, then in logic, "X and Y" is false, which is clearly untrue.
So some of it is wrong, and anyway, it's either trivial or liable to cause serious misunderstandings.
Tell me where the problem in the logic is please.
You seem to be treating logic as if it's a matter of semantics, meaning, that as long as I make a statement that is expressed in the format of a typical logical argument, i.e. it is "well formed", then that makes it valid.
A well-formed argument just means that it is stated in a standardised way that makes it much easier for logicians to figure out if it is true or false. Doesn't tell you if it is true or false.
OTOH, computers use semantics. Modern electronic computers can do additions and all sorts of calculations. But computer circuits aren't known for their power to think. They can just process electrical signals computationally.
However, George Boole, and later, Alsonso Church and Alan Turing, all realised that computational machines like mechanical circuits and electrical circuits could be used to perform logical calculations using semantics, when the inputs and outputs of the relevant electrical circuits compute to the same answers as logical calculations, and thus are logically equivalent. That's how arithmetic works on computers. They don't actually compute logic. But the answers are equivalent, and that's good enough for most people to be able to use their results in a reasonably reliable fashion.
But as I pointed out before, that's not always true, as electrical circuits can't compute square roots without rounding off and creating an error margin. Try it on your calculator: Enter 2. Press the Square Root button. Save in memory. Then multiply it by itself. The answer is usually 1.99999, not 2, which is wrong.
So it's sometimes true that logical semantics computes to the same thing as an actual logical calculation. But only when they are equivalent, i.e. when all the premises are true, then the conclusion is also true, and when some of the premises aer false, then the conclusion is false. But that only happens with sound statements.
So you can say that logical semantics calculate the correct answer when it comes to sound arguments. But that's not always true with unsound arguments, and your argument is unsound.
So if you wanted to prove that logic was faulty, you needed to find an argument that was sound but invalid.
But according to the 2nd video you supplied on this matter, all arguments with invalid arguments are unsound.
So you can't prove that logic was faulty, at least, not the way that you have gone about it.
Plus, if what you were saying was true, then computers would not be trustworthy when it came to arithmetic, and then we would not be able to rely on the results of calculators, because they work on the same premise.
pubmed.ncbi.nlm.nih.gov
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