Empiricism is the view that the ultimate source of knowledge is from experience, beliefs that conform to this are known as a posteriori. Empiricists believe that we are born without any innate knowledge (a priori knowledge) but instead learn everything we know from our senses. This is in opposition to Rationalism which is the view that the source of our knowledge is ultimately reason, such beliefs are known as a priori, or without prior experience and so are innately within us from birth.
Empiricists such as Locke argue that there are “no innate ideas” and so we are born with no knowledge, we only have knowledge of a pencil or gravity because we have experienced it. However a Rationalist could respond with the example of our ideas of mythical creatures such as Hippogriffs or Chimeras. However, Empiricists argue that even though we may not have experience of a hippogriff, ultimately we have.
This is because a hippogriff is a complex idea built from simple ideas, namely the experiences of different animals such as the beak of an eagle and the feathers of an owl, which combine to form a complex idea, and so we may never have experienced an actual hippogriff, our experiences are enough for us to create a complex idea, but ultimately it remains a posteriori knowledge. However the main problem with empiricism has been its reliance on inductive reasoning, which as Rationalists are keen to point out is weaker than reaching conclusions deductively.
Even Hume, an empiricist himself, admitted that causal relationships have no reason to be the same in the future as what they had been in the past. This poses a problem as ideas come from experience and so the belief that something such as the sun rising tomorrow may not necessarily occur. Even though it is likely that the sun will rise tomorrow as it is based on many past instances of the same occurrence, albeit based on an inductive argument, there is an even greater problem for Empiricists to overcome.
That is that we may not necessarily be able to trust our senses. As Descartes points out as the start of his Meditations, he is unable to trust his sensory data as there are any number of reasons why it could be false or at the very least an untrue perception of the world; we could be dreaming, we could be being tricked by a demon, or our senses could simply give us only half the picture, such as with Descartes’ wax argument. Mathematics can also be used as an argument against empiricism by rationalists.
The debate is over whether mathematics is a priori or a posteriori. Empiricists argue that mathematics is a posteriori as no one is born a mathematician and it mathematical ability requires learning skills. However the counter to that would be that someone used their reason to make a discovery of that skill, Pythagoras had to use his reason to discovery his theorem, he did not learn it and therefore mathematics can be seen as a priori.
However an empiricist’s response to that would be to argue that such discoveries are merely complex ideas built from simple ideas, and so ultimately it was made from experience, after all would we really be able to reason mathematically without having learnt numbers and basic skills such as addition and subtraction? However the rationalist’s response would be to define what is being used to make the discovery in the first place, and a rationalist would argue that it was not the combination of simple ideas that led to Pythagoras discovering his theorem but through use of his reasoning which is independent of experience and so a priori.
However I would argue that if you believe mathematics is ultimately complex ideas formed from simple ideas (numbers) then of course it is a posteriori as all mathematics is based on numbers, however rationalists could argue this to be unfair as numbers do not in themselves lead to reason and so the fact that we use reason to reach complex ideas arguably shows maths to be a priori. In any case Plato’s story of Socrates and his slave boy illustrates the rationalist view that mathematics is a priori.
Socrates decided to see whether mathematics was a priori by trying to see if an uneducated slave boy could work out Pythagoras’ theorem for himself. Socrates managed this, albeit using quite suggestive questions which prompted the slave boy towards the conclusion but it nevertheless illustrates the principle that mathematical conclusions can be reached through a priori means and so mathematics is a priori.
However others, such as Hume, who was an empiricist, argued that some concepts were a priori but only because they are also analytic. An analytic statement is one where the predicate is contained within the subject, such as “all bachelors are unmarried”. A synthetic statement describes propositions in which the predicate is not contained within the subject, such as “this book is purple”. Hume argued that some beliefs were a priori and others were a posteriori.
However there some flaws with Hume’s fork, such as the Cogito which does not seem to fit into the fork. Overall, I agree with Hume, in thinking that knowledge altogether is either a priori or a posteriori but more a mixture of the two. Mathematics would be a good example of knowledge that is a priori, whilst language would be an example of knowledge that is a posteriori. It would be foolish to think that all knowledge was either one or the other.