1.1.7.1 Analytic Propositions

Version 1.4 September 2019                                  (Previous Version)

Some things appear to be true á priori – before we have to look at the world itself.

·       For instance, a triangle has three sides.  We know that because that’s what ‘triangle’ means.

·       Two plus two equals four.  2 + 2 = 4.  That comes out of the laws of arithmetic.

Analytic knowledge arises out of definitions and how we use language, and the meanings of words, true by virtue of meaning.  Analytic propositions can’t be proved right or wrong by looking at the world.  We call this being NOT contingent, or we say they are necessary.  it's obvious.

The “opposite� of analytical knowledge is synthetic knowledge, such as “the sky is blue�.  Most of the stuff we know is actually synthetic in this sense.  We have to check the real world to know if it is true.  So synthetic knowledge seems to be less reliable than analytical knowledge.  It seems synthetic knowledge is much less certain than analytic knowledge.

Mathematics is analytical knowledge.  It involves symbols and manipulation of symbols that are unrelated to the real world.  It is amazing that we can use mathematics to describe the world, as we do in physics, chemistry, engineering, biology and medicine.  In fact the link between mathematics and reality is a happy coincidence that we had no right to expect, but fortunately it works.

However, not all mathematics has immediate applicability to the real world. 

Some people have hoped that one day we would find a way for all knowledge to be like á priori knowledge, or somehow derived from it, so that we would know for certain what is always true.  They have tried to make epistemology the foundation of all philosophy and all knowledge.  For instance, the philosopher Kant claimed his categorical imperative (act as if the maxim of your actions is universal) was compelling, and derived from pure reason.  The quest for the foundations of all knowledge drove so called analytic philosophy and the logical positivists.  But this quest has been in vain: unfortunately life is too complex.

Analytical knowledge, the things that we know á priori, are relatively trivial or largely irrelevant to most people’s daily lives, and don't help with life’s major questions or to find meaning or purpose.  Analytical knowledge is not uniquely different to other forms of knowledge.

Although mathematics and logic are essential tools, they are only useful when we link them to the real world, practical problems, such as how much to pay for goods, how to best educate our children, whether to invest in the stock market, or how to synchronise signals from orbiting satellites.  There are many ways mathematics and logic can be linked to real world problems, and most of them are probably wrong.  We only know which ways are useful by actually trying them out.  There is nothing á priori about the application of analytical knowledge.

There are other substantial problems with the idea of analytic knowledge as being obviously true.

1.     Philosophers explain the difference between analytic and synthetic propositions by describing how we know about them.  

a.      They describe the mental processes that lead us to understanding analytical propositions, and hence realising they are true.  They talk about mental concepts and meanings and what is immediately before the mind and so on.  

b.     But understanding the mental process, understanding the causes for our beliefs, does not explain how or why the belief is true.  If someone thinks the world always looks rosy, and we can explain that they do so because they always wear rose coloured glasses, we know their belief that the world is rosy is not necessarily true.

c.      And also, philosophers also explain synthetic knowledge by how we acquire other beliefs, by looking at the world, by our sensory perceptions, and how we develop and understanding of synthetic propositions.  And we know appearances can be deceptive, and our inferences wrong.  

d.     So both analytic and synthetic knowledge is defined by how we acquire it.  There is no reason to believe that the way we acquire so called analytic knowledge is so special that it always leads to the truth.  There is nothing in that method that makes it a truth generator.  Our minds and intuitions can be as misled as our eyes and ears.  The distinction between analytic and synthetic knowledge is false.

 

2.     In fact, for thousands of years philosophers thought Euclidean geometry, analytic knowledge, accurately reflected the world and so was “trueâ€�: it corresponded with reality.  And it does – approximately, when things aren’t too big or small or too fast or slow.  But now we know Riemannian geometry provides a better correspondence to the real world in 4D space-time.  There are lots of mathematical ideas that have no relation at all to reality.  Are they True? 

 

3.     Recently philosophers have also asked what happens if you translate an analytic proposition into another, very different language.  Perhaps the other language doesn’t have exactly equivalent words.  Perhaps it has no word for triangle.  Translators, from say Hindi to English or English to Mandarin often have difficulty finding a direct translation.  An obvious truth in one language may not be so obviously true in another language.  In fact, it may not even be comprehensible in the other language.  But the idea of analytic knowledge is that it is necessary, ie it must be true.  But it might not be in some other language with slightly different meanings to words.  So we can't rely on analytic propositions as the foundations of knowledge.

 

We phrase our current conclusion on this issue as follows: