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Tarski and truth conditions
  1. Metaphysics
  2. Meditations on First Philosophy
  3. The Subject Matter of First Philosophy
  4. The Solution to the Problems of Science

Leibniz's conception of God, however, may seem to cause more problems than it solves. For example, if the complete concept of any being, such as a human being, is known for all time, and was chosen by God for existence, then is such a being free? It seems that what one means by "freedom" is that the outcome is not predictable, as opposed to, for example, the way in which the operation of a washing machine or the addition of two numbers is predictable.

Further, what must one make of morality and sin? While Leibniz's philosophical system demands a certain sense of determinism about the universe, he does not want to deny the existence of free will.


In order to accomplish this, Leibniz distinguishes between several ways in which things might be determined in advance. Whatever is determined is clearly true.

An encyclopedia of philosophy articles written by professional philosophers.

Truth, however, comes in several varieties. Much of the following is taken from the set of distinctions Leibniz makes in "Necessary and Contingent Truths;" Leibniz makes similar but rarely identical sets of distinctions in a variety of texts. A person's actions are, therefore, not necessary by definition regardless, at this point, of which type of "truth of existence" they fall under. Leibniz further writes:. But whose fault is that?

Does it have anyone to blame but itself? By "indifference," Leibniz means a physical indifference--that is to say, there is no universal-physical truth, as defined above, which governs human action. For Leibniz, this means that human action is further freed: the will has the power to suspend its action with respect to the physical sequence of efficient causes, but also even with respect to what would otherwise be seen as a decisive final cause. Leibniz states: "For they [free or intelligent substances] are not bound by any certain subordinate laws of the universe, but act as it were by a private miracle" "Necessary and Contingent Truths".

Minds, then, are different from mechanical causes. As it will be shown below, Leibniz goes against the trend of 17th and 18th century thought by reintroducing the Aristotelian and Scholastic notion of a final cause and, indeed, substantial forms. Although Leibniz occasionally uses the analogy of a machine to describe the soul, the kinds of forces and causes operative in the former are simply inapplicable to the latter. Thus, if by individual free choice one means an individual action that cannot be known in advance by even an infinitely subtle application of the laws of physics, chemistry, or biology, then humans have free choice in that sense as well.

Leibniz also offers the following additional arguments for his particular conception of human free will:.

Meditations on First Philosophy

But this makes no sense, for free choice is not randomness. Caesar's free act, for example, has a cause--namely, Caesar. Why should one complain when the individual concept of Caesar intrinsically determines what Caesar does? Isn't Caesar free if he is the source of his action, and not anyone or anything else?

Again, grasping the full explanation of any predicate that lies in the complete concept is an infinite task. To help illustrate the distinction between contingent and necessary truths, Leibniz makes a famous analogy with the incommensurability of any whole number or fraction with a "surd" for example, the square root of two, the value of which cannot be represented numerically by any finite series of numbers. For finite human minds, that incommensurability is a positive fact, just like contingency--no matter that for God neither calculation is impossible, or even more difficult.

Thus contingent truths can in principle be known from all time, but necessarily not by a human being see, for example, "On Freedom". It should be pointed out that this is somewhat more than an analogy, since it is closely related to the kinds of problems infinitesimal calculus was designed to deal with--and Leibniz takes the possibility of a calculus as having real metaphysical implications. One can just be a sloth, and let the universe happen. Leibniz thinks this is absurd--indeed, immoral.

The will of an individual matters. If John Doe is the kind of person who is a sloth, then everything else being the same the course of his life will indeed be quite different than if he is the kind of person like Caesar who takes events by the scruff of the neck. For Leibniz, this is impossible.

Leibniz thus claims that philosophers of a more radical sense of freedom do not take seriously the extent to which the universe is an integrated network of explanations, and that this in turn has implications for the idea of contingency see the discussion of Adam in Leibniz's letter to Landgraf Ernst von Hessen-Rheinfels, April 12, Thus, contingent events, even one's free acts, must be part of the perfection of the universe.

Although, that does not mean that all contingent events are so in the same way. According to Leibniz, any remaining objections to this idea of free will only result from a metaphysically incoherent idea of what freedom means.

The Subject Matter of First Philosophy

There is no question that Leibniz introduced a spirited and powerful position into the age-old philosophical debate concerning free will. Which position is "metaphysically incoherent," however, remains under debate.

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For more on the philosophical debate of free will, see " Free Will ". Leibniz's approach to the classic problem of evil is similar. The problem of evil, for Leibniz, can be put in the following way: If God is supremely good, and the creator or author of the best possible universe, then why is there so much pain and sin in the world? Leibniz claims that this apparent paradox is not a real problem. Leibniz coined the term "theodicy" to refer to an attempt to reconcile God's supremely benevolent and all-good nature with the evil in the world. However, his thoughts on the issue are to be found spread over many texts.

To judge it full of misery on this small fraction is presumptuous. Between and , at the request of Caroline, Princess of Wales, a series of long letters passed between Leibniz and the English physicist, theologian, and friend of Newton, Samuel Clarke. It is generally assumed that Newton had a hand in Clarke's end of the correspondence. They were published in Germany and in England soon after the correspondence ceased and became one of the most widely read philosophical books of the 18th Century.

Leibniz and Clarke had several topics of debate: the nature of God's interaction with the created world, the nature of miracles, vacua, gravity, and the nature of space and time. Although Leibniz had written about space and time previously, this correspondence is unique for its sustained and detailed account of this aspect of his philosophy.

It is also worth pointing out that Leibniz and after him Kant continues a long tradition of philosophizing about space and time from the point of view of space, as if the two were always in a strict analogy. Newton, and after him Clarke, argued that space and time must be absolute that is, fixed background constants and in some sense really existent substances in their own right at least, this was Leibniz's reading of Newton.

The key argument is often called the "bucket argument. With linear motion, the frame does not matter as far as the mathematics are concerned, it does not matter if the boat is moving away from the shore, or the shore is moving away from the boat ; even linear acceleration changing velocity but not direction can be accounted for from various frames of reference. However, acceleration in a curve to take Newton's example, water forced by the sides of a bucket to swirl in a circle, and thus to rise up the sides of the bucket , could only have one frame of reference.

For the water rising against the sides of the bucket can be understood if the water is moving within a stationary universe, but makes no sense if the water is stationary and the universe is spinning. Such curved acceleration requires the postulation of absolute space which makes possible fixed and unique frames of reference. Similar problems made Einstein's General Theory of Relativity so much more mathematically complicated than the Special Theory. Leibniz, however, has a completely different understanding of space and time.

In short, an empty space would be a substance with no properties; it will be a substance that even God cannot modify or destroy. But Leibniz's most famous arguments for his theory of space and time stem from the principle of sufficient reason the principle that everything which happens has, at least in principle, an explanation of why it happened as it did and not otherwise.

Leibniz is fond of using leaves as an example. Two leaves often look absolutely identical.

The Solution to the Problems of Science

Leibniz's support for the principles of the identity of indiscernibles primarily derives from his commitment to the principle of sufficient reason in the following way. If any objects are in every way the same, but actually distinct, then there would be no sufficient reason that is, no possible explanation for why the first is where and when it is, and the second is where and when it is, and not the other way around. If, then, one posits the possible existence of two identical things things that differ in number only--that is, one can count them, but that is all , then one also posits the existence of an absurd universe, one in which the principle of sufficient reason is not universally true.

Leibniz often expresses this in terms of God: if two things were identical, there would be no sufficient reason for God to choose to put one in the first place and the other in the second place. Note that Leibniz's argument relates to a scholastic debate centered on the notion of "Buridan's Ass. Similar considerations apply to Newtonian absolute space. The first concerns the violation of the principle of the identity of indiscernibles.

Suppose that space is absolute. Since every region of space would be indiscernible from any other and spatial relations would be construed as extrinsic, it would be possible for two substances to be indiscernible yet distinct in virtue of being in different locations. But this is absurd, Leibniz argues, because it violates the principle of the identity of indiscernibles.