Monday, 24 February 2014

Truth and The Bounds of Reason


100th Article! 
There never comes a point where a theory can be said to be true. The most that one can claim for any theory is that it has shared the successes of all its rivals and that it has passed at least one test which they have failed. - A.J. Ayer

Language

       Language is a powerful tool  for an organism, it enables it to communicate vital information to other organisms, which may or may not be in its own species. Languages differ in complexity according to the spectrum of evolution, the further back you go on the evolutionary timeline the means of communication between organisms will be much simpler. Language is therefore evolutionary advantageous to have and it primarily functions as a tool to increase chances of survival and reproduction.

       However an organism might exist with a highly evolved and functioning brain which has the capability to develop a complex language which has functions which are not strictly related to pure survival or reproduction. Humans are the only example that we know of at present which exhibits this linguistic characteristic. Our language of course fits the evolutionary trend, we need it to communicate about food, sex and other mundane things but the complexity of our language has evolved so that we can communicate about abstract concepts.

       One of the most intriguing and important aspects of our language is that some statements can be true or false. We are told many things everyday, about daily life, in the classroom, by the news reporters on the television and in the books that we read. Is there a simple, logical and rational method to quickly decide what is true and what is false?

         Statements Within A Logical System

      What I mean by a 'logical system' is a set of pre-determined rules and definitions, a statement within such a system can obey or disobey these rules and definitions. For example the easiest logical system to use is mathematics. 1+2 = 3 obeys the definitions and rules of numbers, 1+5 =9 disobeys the rules and definitions. Another example is this; A married man has a wife or husband  obeys the definitions which we assigned to the word married i.e. anyone who is married has a wife or husband. One can quickly see that a statement obeying these rules is equivalent to the statement being true and disobedience to these rules is akin to falsehood. This is simply trivial. What this means is that to decide whether statements in a closed logical system (only determined by a set of axioms or 'rules' ) are true or false, one only needs to check if they obey the rules. The truth or falsehood of these statements are either certainly true or certainly false, that means we cannot have any doubt either way.

     So it seems all mathematics is simply trivial. Apply the rules and you can work out all the truths in the system... so it should be easy right? Wrong. The system of mathematics is extremely complex and even if a human creates a set of simple axiomatic rules, to prove a statement within that system may require completely different logic or thinking power. For example Fermat's last theorem can be easily stated but it took Andrew Wiles 10 years to solve it and it required studying of many different areas of mathematics which seem completely unrelated. This is the oddity or beauty of mathematics.

     We now have a method to determine the truth of statements within a logical system.... but these are trivial and not related to the real world. So how can we decide what makes a statement about the real world true?

Statements about the real world 

   If I state something about the external world, there must be a way to somehow check that what I have said relates to something in the world. If I said all swans are white, I can go out and see if they are really are white or not... if they are my statement is true if not my statement is false. Is this truth certain and 100%?  No, because I can only observe a finite amount of swans... there may be swans which are black but i have not yet observed them. Because I cannot possibly observe all objects everywhere and at all times there may be an opportunity that I could observe an object which makes my statement false, it is this doubt which makes all truths about the world APPROXIMATIONS. This is the essence of empirical... or scientific truth. In the infinite future there may be a possibility that we could witness something which prove us wrong.

   However to state that swans are white is true, in the sense that, if you observe a swan there is an extremely high probability that it will be white.  Most people state empirical truths as if they are certain but it is in fact impossible for such truths to ever become certain.

  This implies that as you do more observations to justify a statement and accumulate more evidence for it, the statements empirical truth becomes stronger. It is exactly the same for scientific theories (which are just collections of carefully worked statements) the more evidence in favor for a theory... the more 'true' it is.

   People state that if we apply mathematics to the real world we could get certain truth. This is not true however because certain truth only exists in closed logical systems. The universe is not closed or more precisely our knowledge of the system (the universe) is finite which means we do not know all the rules to the system... which as you guessed it implies that there could be a rule which overturns certain present truths = uncertainty.

   This method of verifying statements with observation seems simple yet we witness confusions and controversy when it comes to the existence of supernatural things. We must be consistent and apply our method to all statements about the world. We all know that the moon exists because we have all observed it and astronomers have measured its gravitational effects, this is the same of all common objects. However if I claim that an object exists which governs the world and is its creator I would expect to collect evidence of its existence before my claim would hold any truth value. There is no present evidence to verify claims about supernatural beings like God, ghosts or vampires so any statements claiming their existence are simply meaningless. Note that these claims are not false because a statement about the world can only be false if evidence contradicts its claims. There is no evidence either way about statements about God etc. so we render such statements meaningless... which in my opinion is worse than false statements. False statements at least lead us in the direction of truth by ruling out ideas and what not.

The bounds of reason

   We must realize that when we observe the real world we are using our sensory equipment and our cognitive tools which have been carved out by natural selection. So how we perceive the real world is relative to how our bodies interact with the world. 

   One could argue that as language is a construct built upon the structure of an organisms brain... and if truth exists in the world of language does this imply that truth itself is relative to the organisms brain? This is a hard question. If the answer is yes then physicist who look for universal laws of nature are simply looking for universal 'human relative' laws of nature... does this mean there search is pointless?

   I believe that as nature fits so well with mathematics i.e. the natural phenomena that we see in the world obeys nice mathematical systems.. could imply that the universe is itself a closed logical system. The laws which we discover via science are merely the uncovering of the laws of closed logical system of the universe. We can only approximate to these laws. So in this sense we are really working out something external but which we are still a part of. This is a very hard concept to get your head around. 

   There is an idea, promoted by string theorist Leonard Susskind, that the universe itself is a hologram of a mathematical construct... a hologram in the eyes of observers in the system? We don't know... we don't even know if questions like this make sense or are even worth talking about.

   So the physical limits of our brains could pose a boundary to how much we can reason from nature. We are doing pretty well so far and with the advancement of complicated, huge and intricated experiments such as the LHC and with the progress of computers we could witness AI which surpass our own cognitive limits. 



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