Lecture 2

Cosmos

From Greek kosmos (= order/world), the cosmos is the universe as an ordered world.

(Opposite of kosmos is Greek khaos (= vast chasm, void)).

Archē

Beginning, source or first principle.

The Principle of Sufficient Reason

Associated with the philosopher Gottfried Wilhelm von Leibniz (1646-1716), who argued that it was the principle "by virtue of which we consider that we can find no true or existent fact, no true assertion, without there being a sufficient reason why it is thus and not otherwise, although most of the time these reasons cannot be known to us" (Monadology, sect. 32).

This principle is commonly invoked in the case of causation: for every event, there is some cause of that event. It is never the case that something occurs uncaused, i.e. for no reason. For example, if my car will not start, there is some cause of this. It cannot be the case that, for no reason, it won't start, when everything is working, etc. However, this principle is entirely compatible with our being ignorant as to what the cause is. We can be certain that there is a cause, even if we do not know the cause.

However, the principle extends beyond the case of causation. Leibniz held that for every true statement (including those of mathematics), there was a sufficient reason for why that statement was true (and, indeed, why it must be true).

Note that this principle is not to be understood as the principle that "everything happens for a good reason", and that there are no true accidents. Although Leibniz may have believed this, his principle does not require this to be true.

Reasoning A Priori vs. reasoning A Posteriori

To reason a priori ("from what is before") is to reason in a way that is not derived from, and that is independent of, experience. Also: to reason from causes to effects.

Example: 4 = 4

To reason a posteriori ("from what comes after") is to reason in a way that is derived from, and that is dependent on, experience. Also: to reason from effects to causes.

Example: There are lions in Africa.

Quantitative Change vs. Qualitative Change

A quantitative change is a change in quantity. For example, if I get a new Cadillac, then the number of Cadillacs in my garage changes from 24 to 25.

A qualitative change is a change in quality. For example, if my pink Cadillac is painted white, then it changes from being pink to being white.