Introduced the idea of kinetic energy (vis visa) into physics and proved that kinetic energy is conserved in inelastic collisions
Truths of Reason vs Truths of Fact
Two Great Principles of Reasoning
Cosmological and Ontological Proofs
Theory of Monads
A Busy Man
“Leibniz was a man of medium height with a stoop, broad-shouldered but bandy-legged, as capable of thinking for several days sitting in the same chair as of traveling the roads of Europe summer and winter. He was an indefatigable worker, a universal letter writer (he had more than 600 correspondents), a patriot and cosmopolitan, a great scientist, and one of the most powerful spirits of Western civilization.”
Leibniz did not build a philosophic system, like Descartes and Spinoza. But he left his thoughts on a range of philosophic topics.
Truths of Reason and Truths of Fact
Leibniz introduced calculus into mathematics, kinetic energy into physics, and the fundamental distinction between truths of reason and truths of fact into philosophy.
Leibniz, from the Monadology Part II 33
“There are two kinds of truths, those of reasoning and those of fact. Truths of reasoning are necessary and their opposite is impossible: truths of fact are contingent and their opposite is possible. When a truth is necessary, its reason can be found by analysis, resolving it into more simple ideas and truths, until we come to those which are primary.”
Truths of reason are logically necessary, their negations self-contradictory. For example:
All husbands are married
2 + 2 = 4
Everything is what it is and not something else.
Truths of fact are contingent truths, their negations logically consistent. For example:
Some molecules have three atoms;
Harper Lee wrote To Kill a Mockingbird;
The total energy of a closed physical remains constant.
The distinction between truths of reason and truths of fact is different from that between knowable a priori and knowable a posteriori.
Truths of reason and truths of fact concern the internal structure of propositions.
A priori and a posteriori have to do with how propositions can be known.
Rationalists and Empiricists disagree on the existence of contingent truths knowable a priori, with Rationalists providing examples:
Descartes’ principle that what is clearly and distinctly perceived is true.
Spinoza’s axioms and propositions.
Leibniz’s Principle of Sufficient Reason.
Two Great Principles of Reasoning
“Our reasonings are based on two great principles, that of contradiction… [and] that of sufficient reason.” (Monadology 31–32)
The Principle of Contradiction governs truths of reason:
“We judge false that which involves a contradiction, and true that which is opposed or contradictory to the false” (Monadology 31 )
Thus to establish a truth of reason you prove its negation leads to contradiction.
The Principle of Sufficient Reason governs truths of fact:
“No statement of fact can be true unless there is a sufficient reason why it should be so and not otherwise.” (Monadology 32)
For every truth of fact there is a sufficient reason why it’s true.
Leibniz loved PSR
The principle “must be considered one of the greatest and most fruitful of all human knowledge, for upon it is built a great part of metaphysics, physics, and moral science.”
PSR is the basis of Leibniz’ Cosmological Argument
Leibniz developed two proofs of God’s existence: the Cosmological Argument and a version of the Ontological Argument.
Reconstruction of Leibniz’s Cosmological Argument, Monadology 36-38:
The existence of the universe, whether it always existed or began, is a truth of fact.
There’s a sufficient reason why a truth of fact is true. (PSR)
There is thus a sufficient reason why the universe exists.
“The sufficient or final reason must be outside of the sequence or series of particular contingent things.” (Monadology 37)
“Thus the final reason of things must be in a necessary substance …. and this substance we call God.” (Monadology 38)
There’s a gap in the argument between a sufficient reason beyond the universe and a necessary being. The gap can be filled:
A sufficient reason, by definition, cannot be an infinite sequence of reasons; reasons must stop at some point, at a final reason.
A final reason must be a sufficient reason why itself is true.
Only the necessary existence of being is a reason why itself is true.
Therefore, a necessary being exists.
Whether Leibniz had this argument in mind, it plugs the hole.
It’s logically possible that God exists
If God exists, He necessarily exists
Therefore it’s logically possible that God necessarily exists.
If it’s logically possible that God necessarily exists then God necessarily exists.
“Thus God alone (or the necessary Being) has this prerogative that He must necessarily exist, if He is possible. And as nothing can interfere with the possibility of that which involves no limits, no negation and consequently no contradiction, this [His possibility] is sufficient of itself to make known the existence of God a priori.” (Monadology 45)
Therefore God necessarily exists.
Theory of Monads and Pre-established Harmony
The ontology (or ontological commitment) of a theory consists of the kinds of entities it postulates. Descartes’ ontology is mental substance, physical substance, and God. Spinoza’s ontology is God-Nature. Leibniz’ ontology consists of monads.
“In Leibniz’s system of metaphysics, monads are basic substances that make up the universe but lack spatial extension and hence are immaterial. Each monad is a unique, indestructible, dynamic, soullike entity whose properties are a function of its perceptions and appetites. Monads have no true causal relation with other monads, but all are perfectly synchronized with each other by God in a pre-established harmony. The objects of the material world are simply appearances of collections of monads.”
Bertrand Russell in the preface to his book on Leibniz:
“The Monadology was a kind of fantastic fairy tale, coherent perhaps, but wholly arbitrary.”
Voltaire, who enjoyed satirizing Leibniz:
“Can you really believe that a drop of urine is an infinity of monads, and that each of these has ideas, however obscure, of the universe as a whole?”