Steel Cage Death Match: Plato vs Aristotle in The Arena of Truth

Plato and Platonic Idealism (428-328 BC)

"Truth" lays in an abstract "Ideal".  We can apply the fundamental principles of mathematical proofs to locate to the True form of these transcendent truths or Ideals

The natural world we perceive through our senses (see, hear, touch etc.) reveals only a fallen, shadow, incomplete versions of this Ideal Truth.

The true "Forms" of natural things or of concepts exist in the way that mathematical truths or forms exist.

Thus attempting to understand the Truth of things by examining the natural world is not only folly, but likely dangerously misleading.

As Truth lies in the abstract and exists more clearly in our minds than in the natural world, philosophical contemplation -- rather than observation -- is the road toward Truth.

Thus: Only those who have a strong control of philosophical Truths should be allowed to make important decisions.

All the other arts, including poetry and argumentation, only confuse us more, tricking us into believing false visions of Truth (example: we mistake what we see on the television for reality; a cunning lawyer can trick a stupid jury into believing the guilty innocent).

In a nutshell: Plato's mystical Idealism will be adopted by subsequent generations of Christians to explain the nature of God.

Aristotle and Analytic Empiricism (384-322 BC)

We can apply the fundamental principles of mathematical proofs to locate to the True form of nature in natural things:

Through the systematic observation and analysis (breaking down and classification) of the natural world, in combination with rigorous logic, we can make "True" statements about the natural world and understand:

1) The nature of essences (what something is)

2) The nature of causes (why things occur)

Unlike Plato, Aristotle also believes that the other arts are very useful for helping us understand things. 
(example: even though tv isn't reality, it helps us understand our own emotions;  juries should be smart enough to differentiate between which lawyer is telling the truth)

In a nutshell:
Aristotle's in-depth treatment of the correct methodology for achieving these types of understanding created what we would now call "science" or the "scientific method".

Augustine (354-430 AD) and Neo-Platonism

Along with other Neo-Platonists, Augustine will translate and transmit Plato's concept of Truth and its relationship to the natural world into Christian terms: this world is a shadow, fallen version of God's eternal Truths, and the pursuit of knowledge has damned humanity (see Genesis 3).  (Similarly, other Jewish and Muslim scholars will transmit Platonic Idealism into Judaism and Islam, both before and after Augustine)

Aquinas  (1225-1274) and Scholasticism

Aquinas's argument:
a) God created an ordered natural world. God also created man's ability to use reason.  Therefore:

b) Rational philosophy (Aristotelian analytical method) is a valid compliment to theology; God created man's intellect and will, thus, celebrating and developing human freedom, intellect and will would promote God's will. 

c) If God created an ordered, natural world, man could and should apply reason to understand the natural world, thereby better understanding and celebrating the will of God as manifest in his creation.

We cannot overstate the effects Aquinas's argument will have on Western Civilization; without him, we would still live in a world without science.  Of course he himself had no concept of where his argument would take civilization.

Raphael's 1510, Renaissance painting, The School of Athens, (Scuola di Atene) represents the relationship between the two philosophers' perspectives:  note Plato (center left) pointing to the heavens and Aristotle (center right) pointing in front of himself, into the natural world.