Truth and knowing.
“What is truth?” — Pontius Pilate, the Gospel of John.
Truth is easy to explain but rather harder to understand. why? Because in its explanation we are trying to form a true statement about what it is to form a true statement. This leads to confusion, and unfortunately to the rejection of what is true truth (so to speak) and the clinging onto those rocks that we do understand (usually scientific truth or religious truth).
Knowledge on the other hand is not easy to explain. To know something one has to belief it is true and have that knowledge accord with something (usually ones perception of reality). Knowledge is also distinct from mere information. In that both concern a truth but knowledge has a purpose or use. It is also usually a learned experience.
So here we have our parameters of investigation. In answering the following questions and drawing the threads of their answers together under a general philosophical theory I hope to cast light into the darkness, or at least classify the dark better.
The questions are:
Are there really different types of truth?
What does it mean to know something, as opposed to just believing it?
Can we really know something is true?
These are of course Titanic questions that Philosophers and Scientists have struggled to answer for generations. A cop out here would be to just fill this post with quotes and analysis of other thinkers works, but i prefer to actually try and think of some answers myself in my admittedly limited capacity to do so.
“Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth.” — Sherlock Holmes (Sir Arthur Conan Doyle)
“I am” is taken as the most fundamental truth of all. But why? Simply because it is the easiest to prove. One can prove “i am” every single time one thinks it and by thinking it one can simply and clearly assert it and by proxy reject it’s negation; “i am not”. Once we have made an assertion that we are clear is true, we believe it. This proposition is now added to the pool of positive propositions, or what i call ideas. This pools of ideas are like bricks building a house. The most simple ideas are the foundation upon which are placed more and more ideas forming a wall. The walls of this house are held up by the simple truths of the provable simple ideas.
So what is a simple idea? Take the following:
I have a rock 0
This idea is simple. Its truth directly relates and relies on the fact it calls in place. I actually have a rock. I perceive that in my hand is a rock. This perception is so solid and consistent that I believe the statement is true because I can prove it in a millisecond by referring to my perception of the object in my hand. As long as that perception remains true, the idea is also true.
Our minds perceive reality all the time through the senses and the beliefs that this perception give rise to are what we take as true.
So, for me truth is a belief in the mental linking of a simple idea to a perception of reality. So, where is the problem with truth? The problem comes with compound ideas:
Say I have a rock 0
And I add another rock 00
Now I call into place a compound idea and, in the form of a special language (maths) that I have learned, i say that i have two rocks. I perceive the rocks in my hand. I say to myself “I have a rock” and “I have a rock”. That means I have two rocks. This is a compound idea, and idea based on language. In this case the language is mathematics.
Mathematics is a shared language with formal rules. I learned mathematical language at school by the teacher communicating the idea, the conceptual idea, of “two” to me. Once I have the idea embedded deep withing my mind, I cannot look at the two rocks without referring to them in this way. The concept “two” is not to be found in the rocks themselves and it doesn’t require i directly refer to reality. It is an idea over and beyond the rocks perceptions and a total construct of humanity. The wonderful thing about mathematical ideas is that because they are a special language they can operate on other concepts and ideas contained within their language. They are a special language because humanity has formulated rigid rules for the linking and further compounding, as well as the operation of these ideas and the creation of further rules and mathematical language.
The operation of this language takes place only in the mind. It manipulates ideas formulated by its rules and operates to produce results upon which we can (if we should need to) refer back all the way to the simple compound idea that we can perceive to correspond to reality. I have a rock.
I have said it before but I will say it again: The communication of ideas is the primary accomplishment of mankind. This combined with the formalisation of mathematics has given mankind a startlingly powerful tool for both the communication and operation of ideas.
So what is the problem here? The problems are that for all it predictive abilities mathematical propositions are only perceived to be true. This is very hard to spot in the simple arena because the operation of math is so fast in our brains and it can always reduce to a simple perception of reality such as “I have a rock”. However, it is the case that at very high levels mathematicians themselves only talk about models. Models are math that is so complex or cutting edge that the reduction to a simple truth is not yet possible*. Mathematicians try and construct math ideas to explain their predictions or perceptions but we cannot actually call them true yet or even at all. Math models depend on variables and mostly what is called a priori variables (or what i would call the communicated shared idea independent of a perception of reality, as i don’t think a priori ideas exist. But then that is no where near as cool as saying “a priori” and i need to find a single word for it, preferably one in Greek!). The modeler tweaks the math until it “fits” or describes his perceptions of what is happening empirically.
This shows a very important thing. Math does not operate on reality only on our perception of reality and some math cannot and will not progress beyond models because the perception of reality is false. Mathematics is inherently incomplete and can involve paradoxes such as: