In the former he notes that philosophy is more universal, history more particular. In the latter he explicitly argues that Man is not a mathematical creature, thus common sense - not logic - must make up the foundation of political science.
History was not mathematical for Aristotle because it was history as Thucidides conceived it; a story about humans. Philosophy was its polar opposite, rooted directly in mathematics as the apprehension of the reality of ideal forms.
Pythagoras had first called himself a philosopher, Plato's five solids defined the essence of Being in geometric language presented in a literary dialogue called Timaeus. Aristotle disagreed with Plato about the relation between matter and idea, but not about the preeminence of ideas.
In his Politics, Aristotle does, however, utilize mathematics in order to analyze non-mathematical Man. Deductive reasoning, being the general definition of mathematics, is the basis for Aristotle's political philosophy. It is deductive reasoning which allows Aristotle to connect popular opinion to philosophical truth in political science, since political science is the attempt to scientifically understand the non-scientific human animal.
Paradoxically, for Aristotle, that which makes us capable of scientific thought makes us unscientific in our activity: reason. Rational animals deliberate and exercise will. Non-rational animals never make mistakes (though they do suffer accidents) because their actions are not the result of deliberation, only instinct. Humans, because we are capable of deliberating, can deliberate poorly or even not at all. Thus we say of some people that they act irrationally. Though capable of science, we are often content to remain ignorant.
Yet Aristotle's thinking does not lend itself to poetry. It is a precursor of the dry analytical dogmas of the German and English mind. The German mind has since liberated itself from Aristotelian thought and adopted a kind of pure poetry in the work of phenomenology (which is likewise an attribute of French thought). The English, combining an empirical science which substitutes induction for deduction, have expanded the horizon of boredom hinted at by Aristotle into a never ending Hell of data and conjectures.
This state of affairs may in turn be the root of our modern prejudice regarding the distinction between literature and mathematics. We instinctively believe the two if not incompatible, then at least polar opposites.
To recollect that such is not the case requires that we turn to a student of mathematicians who adored math and was more than capable of embedding it within a literary context in such a way as to make the two almost indistinguishable: Plato.
The Platonic solids, just to give one example, emerge (as do all truths in Plato's work) within a literary dialogue. It would be preposterous to try and separate Plato's math from his poetry.
The key to grasping the relationship between literature and mathematics is recognizing that neither is random. Random literature, no less than random numbers, is rather ugly. The modern world will quickly agree that a random sequence of numbers and mathematical symbols is not math. Yet the relativist prejudice now prevalent in the humanities is quick to abstain from such harsh judgment in the realm of literature (and perhaps even modern art).
Of course if the author of random scribbles or paint smudges were known to be a 4 year old, then why of course we would reject any but the most coincidental claims regarding the high value of the work. But should an adult present this sort of silliness, we are expected to probe the silliness thoroughly for hidden meaning. This might explain the poor state of literary criticism.
This is certainly not to say that a good book should have all the attributes of a linear equation. Mathematics itself is full of wonderful paradoxes of the kind we likewise enjoy in good literature. The key here is not to drown in data but to revel in imagination.
Mathematics is the great sojourn into worlds seen in the mind's eye and reflected in shadows of the cosmos. Literature is in some senses a higher form of geometry. The material world is an interplay of complex shapes animated by a variety of impulses of which the human ones are the greatest.
Note: Photograph courtesy
Note: Photograph courtesy