The Ideal (Platonic) World

Archimedes said that heavier objects fall faster than light objects, because they can more easily push air out of the way as they fall.

Galileo said that all objects fall at the same rate.

Who is correct? (Drop a feather and a hammer at the same time. Do they fall at the same rate?)

"to educe and form axioms from experience ... to deduce and derive new experiments from axioms.... For our road does not lie on a level, but ascends and descends; first ascending to axioms, then descending to works." Francis Bacon (World of Mathematics, p. 731)

"Hence, in order to handle this matter in a scientific way, it is necessary to cut loose from these difficulties; and having discovered and demonstrated the theorems, in the case of no resistance, to use them and apply them with such limitations as experience will teach." Galileo (World of Mathematics, p. 762)

What if we can take the feature to an "ideal world" and do the experiment there, without air resistance?

(see attached video)

Who is correct?

The real world is a very complex place. It can easily get much to complex for precise mathematical analysis. But one can understand what the complicating factors are, such as air resistance, or non-euclidean geometry on a spherical surface. These effects may be too small to affect our calculations within any detectable margin of error. We may be able to minimize their effects be doing our experiment differently. Or we may have to include their effects in our calculations.

Galileo recognized that when calculating the trajectory of a cannonball, the curverature of the earth was so large that the effect on the trajectory is vanishingly small. When Nathanial Bowditch calculated his course from America to Europe, he had to include the curverature of the earth in his calculations. (see "Great Circle")

Galileo also recognized that air resistance did not have a large effect on his cannonball because it was round and smooth. He realized that the shape of an object determines how much it is affected by air resistance much more than the weight of an object.

Plato vs. Aristotle

Here is a good summary of the differences between Plato's and Aristotle's philosophies: http://www.philosophos.com/knowledge_base/archives_9/philosophy_questions_961.html

 

For a start, Plato's writings are poetic and dramatic; he sometimes relies on myth. Aristotle on the other hand is dry and precise. Compare Aristotle's De Anima with Plato's Republic.

1. Metaphysics

Plato wanted to discover the eternal in and immutable in the midst of all change. He held that eternal ideas were more real than what we find in nature. The idea of a horse precedes the particular horses of the sensory world. The particulars are like shadows on a cave wall — shadows of what is real (cf. the allegory of the Cave in Book 7 of Republic). All things in the natural world are reflections of things that exist in a higher reality of 'ideas'.

We are able to work out geometrical truths, even if we have not done geometry before because we are acquainted with their truth before our birth. The meaning of a general term like 'horse' is likewise captured by our being acquainted with the eternal 'form' horse. Nothing in the natural world exists that has not first existed in the realm of ideas. The logic of this position is brought out when you consider what is meant by the word horse? Not any particular horse, but some kind of universal 'horseness'. Metaphysically the meaning of 'horse' is a the ideal form of a horse of whose nature particular horses partake imperfectly. So particular horses are only apparent compared with the reality of the ideal horse.

Aristotle agrees that nothing exists forever — that all is change. He also held that the idea of a horse is eternal; but the idea of a horse is just one that we form after seeing a number of horses. The ideal horse thus has no separate existence of its own. Aristotle holds that ideas in the soul are reflections of natural objects. Nothing exists in consciousness that has not been experienced by the senses first. He criticises Plato by musing where the form of a horse would come from? Is there a third one of which the idea horse is a copy?

There is no ideal form or mold from which the things are made; the form of something is simply the collection of properties belonging to that thing. Forms are therefore in the natural world.

2. Epistemology

According to Plato we cannot have true knowledge of things that always change. We only have true knowledge of that which is grasped by reason. We grasp mathematics and the forms through the exercise of reason. The things we see by sense in the natural world are dark and dreary compared with this world of ideas. We know certain rational truths from before we were born (Meno).

To Aristotle, the highest degree of reality is not what we think with our reason, but what we see with our senses. we have the innate ability of reason to classify things, but not innate knowledge of them. Reason is empty without sensory input.

3. Aesthetics

To Plato, art is dangerous and should be banned (RepublicBook10) because it arouses decadent emotions and subverts reason; it cannot help us understand truth as it is only imitative of reality. It is thus at a third removed from the true reality of the world of ideas. Art is created by inspiration, not because the artist knows about what he is depicting (Ion). It therefore has low epistemological value.

Aristotle held art to be edifying through catharsis. Art is philosophical because it deals with universals -- it invites interpretation in terms of the larger conceptions which structure human experience and understanding. Art represents possible events, so intelligibility depends on plot coherence and unity. The artist has a rational craft or techne(Poetics).

4. Ethics

According to Plato, wrong action is due to intellectual error. The man who adequately understands himself acts wisely. Thus the paradox that nobody does wrong willingly.

According to Aristotle, happiness is the key to living a good life. We achieve happiness through using our abilities and living a balanced life between extremes.

Both Plato's and Aristotle's ethics revolve around the twin notions of arete and eudaimonia -- virtue and happiness, and so there are certain similarities.