“I would never die for my beliefs because I might be wrong.” -Bertrand RussellI found this quote to be deeply insightful and thought provoking for reasons that may not seem obvious. For one, this quote makes apparent the irony proliferated by theists in their argument for God. As a typical theist would cry, “…but you can’t prove or disprove anything 100% and therefore it is wrong to say that God does not exist!” Considering that theists are willing to die in the name of God, they must believe in his existence to be true and therefore fall into their own trap.But what struck me by surprise was the fact that Russell has no beliefs in which he finds certainly true. How can the guy who helped lay the groundwork of math be uncertain of every belief he has acquired? Is there really nothing we can be certain about? Instead of giving a cop-out answer like “I think, therefore I am” I sought after a more sufficient answer. From my findings, math and philosophy are inadequate in finding absolute truth and/or falsity. Aristotle established classical logic in his attempt to use reason in finding true arguments. This logic allowed him to make propositional expressions true for all input values. All you would need to know is whether the value of your proposition is true or false and using a predefined function variable, you would arrive at a valid prepositional expression. These variables would be defined by truth tables like this conjunction for the p and q.
FAccording to this truth table, if your P is true and your Q is true then the expression ‘P and Q’ is true. Here we seem to have arrived at a way to know something for certain. Using ‘and’ as our truth function, shouldn’t we know for certain that (true P) ^ (true Q) must be a true expression? Shouldn’t this statement be has valid as saying 2 + 2 = 4? Sure, but don’t try extracting any real meaning from these equations and expect a true statement.It turns out that this sort of syntactic manipulation is the closest thing to the truth you will get. Don’t get me wrong, it is quite useful to logically derive true statements via truth functions, but remember that, at most, you’re just throwing around symbols.Whenever we input a value for P or Q, regardless of what logical variable (‘and’, ‘or’, ‘then’, etc) we choose, we are bound to reach a meaningless conclusion. For example, take P to be “I love cake,” which is true, and Q to be “I live in the US,” which is also true. Therefore the sentence “I love cake and I live in the US,” must be true. All right, am I ready to die for my love of cake yet? NopeFor a logical argument to be true, the premises must also be true. If I have one premise that happens to be meaningless and the other true, my functional argument will also be meaningless. Take my love for cake for example. If the cake has fruits on it I will no longer love the cake. Ah, I see my problem is in my weak definition of the word ‘cake’; I’ll just update my definition and be one my way to the truth. “I love cake that doesn’t have any fruits.” Here too I have encountered vagueness in my word choice. If I cut the fruit in half, is it still a fruit? Maybe, but if I cut it down to one atom, is it still a fruit?Maybe I just need to find better word choice to escape vagueness. How about, “If I can lift 200 lbs, then I am strong” This sounds like a true statement, but it doesn’t reveal any truth of what it means to be strong. What if you give me 200 – .001 lbs, would I still be strong? How many times can I remove .001 lbs before I am no longer strong? No matter what proposition I fill in for P and Q, there will always be an undefined answer.Even the mapping of mathematical equations to the natural world proves inadequate in revealing truths. We find the equation 2+2=4 as quite useful, but what does that reveal about truth or certainty in the real world? If I have two pairs of shoes, I'll get four shoes total. But what is a shoe? And what does combining this vague definition of a shoe with our equation even mean? The only thing we can know for certain is the syntactical manipulation in accordance with our predefined connectives.But lets not forget:“When one admits that nothing is certain one must, I think, also admit that some things are much more nearly certain than others.” - Bertrand Russell
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"For a logical argument to be true, the premises must also be true."
ReplyDeleteNot exactly. For a conclusion to be justified by the premises, they must be true (and the inference valid). If the premises aren't all true, then the argument says nothing about the truth or falsity of the conclusion. Then, the premises being true is a necessary, but not sufficient..