One of my favorite topics in philosophy is knowledge. I've thought about the definition of knowledge for countless hours... What does it mean to know something? How do I know that i know something? What role does knowledge play in in what we perceive as intelligence?
Personally I believe that knowledge is our capacity to understand the things around us. If I understand a concept then I would be comfortable saying that I am knowledgeable in that specific thing or concept. I haven't made it far and there is already a problem with my theory; if I don't understand knowledge then do I really know anything? If i know nothing am I intelligent?
Another way to think of knowledge is to not think of it if that makes sense... Replace knowledge with logic. Rather than saying I know this or I know that, we can use our understanding of a certain concept to come to a logical conclusion. A good example of this would be looking both ways on a one way street; I understand that a one way street only goes one way therefore I do not need to look both ways before crossing because I logically deduced a car cannot come from the other way.
Logical fallacies are very common with our everyday reasoning. A logical fallacy is flawed logical reasoning that illegitimizes your conclusion. There are many naturally occurring things that create logical fallacies like for example the concept of time and numbers, although these aren't actually natural things as they required human thinking to create them I would still count them as natural as they define a natural occurrence.
Lets take numbers as an example since I think its a little shorter. Lets take out language as a factor here since I'm not talking about definitions for example "if we decided to use the word 5 to describe 1 then 5 would be 1" or whatever, I'm going to talk about actual natural numbers.
Before humans came along to put labels on things and define the world around them using limiting auditory communication, there were still numbers. Imagine yourself as a sort of third person looking at the world before humans; There were still multiple blades of grass and multiple trees or whatever there may have been no matter what we use to describe that number, it still exists. Numbers like almost everything in the world will create these fallacies for example a more or less famous one being 1 = 2.
let a = b.
that would mean a^2 = ab
a^2 + a^2 = a^2 + ab
2a^2 = a^2 + ab
2a^2 - 2ab = a^2 + ab - 2ab
2a^2 - 2ab = a^2 - ab
2(a^2 - ab) = 1(a^2 - ab)
cancel out the (a^2 - ab) from both sides and you get 2 = 1.
The problem arises obviously from the cancellation of the (a^2 - ab), although it may seem like the logical thing to do based on your understanding of math to get rid of a multiplication you must divide. Cancelling out would equate to this equation in a way 1 x 0 = 2 x 0 therefore 1 = 2.
Logical thinking may seem like a good answer to the never ending question of knowledge, but logic itself can lead to very misleading conclusions. I wonder if we will ever truly be able to prove what knowledge is and what makes one person more intelligent than another.
Very interesting post @robertmacdonald. Knowledge is powerful and without it we wouldn't know and understand the world around us that's for sure.
Thanks, I feel like knowledge and intelligence is one of the biggest misteries to us but at the same time is what drives us a species.
Knowledge is to cut, divide, separate (etymologically).
Logic is to collect (etymologically).
Knowledge requires logic to arrive at truth.
I think the above demonstrates a rule that is previously ignored which would prevent the tool of logic from leading someone off course. The user uses a tool but if the rules of how to use it aren't known, then it can be misused. Logic will work on a soundly constructed origin.
But when using a=b, that violates the law of identity. It's not explicitly shown, but that's what the above states. 'ab' can only equal 'a^2' if a=b. Constructing a false setup and using logic on a false setup will produce a false result. The logic isn't the problem. In the end, with the false result, one can recognize its falsity through logic that collects and compares the data for consistency and non-contradiction.
The logical problem in my example of 1=2 would actually be the last step mathematically. I agree that it may violate the law of identity, but in math, if a = 1 and b also = 1 then a would be equal to b. The problem is to cancel out the a^2 - ab you would need to divide each side. Technically this would be a division by 0 which causes the problem. We cannot divide by 0 since we cannot define the quotient, so it's not legitimate to divide by 0. My post was mainly to prove what you stated, "Constructing a false setup and using logic on a false setup will produce a false result". I'm more of a programmer than a philosopher, but I personally feel like philosophy and programming share similar roots. Philosophy being the love of wisdom or the seeking of wisdom. I think that we find answers to questions we cannot fully answer by using logical deduction to achieve the best possible answer and widen our understanding of things. Thank you for explaining your point of view, I read your stuff often and it is quite interesting.