"Truth" lays in an abstract "Ideal"

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, civic decisions (ie contribute to the republic).

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 to explain the nature of God.

We can apply the fundamental principles of mathematical proofs to locate to the True form of 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" (valid) 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.  Relevant to our course is that he believes argument -- or dialectic -- is a key ingredient for people reaching understandings: by arguing over issues the truth and falsity of the claims becomes increasingly apparent, where Plato might have believed that honing such rhetorical arts only confuses the matter (sophism).  (For 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 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).