In what sense is our world best? The word "best" is somewhat vague -- what exactly does Leibniz mean by saying God's actions are the best? Leibniz compares God to a perfect architect, who, in building a new structure, combines (i) efficient construction with (ii) a beautiful and complete final product in the best possible way. This is a "balancing act", because efficiency requires simplicity, while completeness requires diversity. (A building that is extremely easy to construct will be very plain and boring, while a building that includes everything a building could possibly have would be very complicated.) How does this analogy carry over to God's creation of the universe? In VI, Leibniz characterizes the "most perfect" astronomical creation as one that is "the simplest in hypotheses [roughly, laws of nature]" and "richest in phenomena [roughly, observable predictions]". So God balances simplicity of laws with the variety, abundance, and diversity of the resulting natural world.
- This yields a natural account of miracles. God creates a miracle [= He overrides the usual laws of nature] when the "cost" in simplicity (caused by violating one of the usual laws of nature) is less than the benefit of the goodness or perfection achieved by allowing such an exception.
Simplicity in science. All other things being equal, we prefer our (scientific) theories to be simple instead of complicated. [example: different hypotheses to account for the same set of data points] Why (do we think they are more likely to be true)? Leibniz has given us a reason: because, in general, God uses the simplest means available to achieve His ends, we know that the simplest hypothesis that can explain the phenomena must be (the most likely to be) true.
Why do we need metaphysics? Even if we grant Leibniz that we cannot explain the laws of nature without metaphysics, why think that we need to explain the laws of nature at all? A: Because the substance or essence of a body is more than just its shape and size (i.e., its "extension") and its motion. There is something else, which Leibniz says is analogous to the soul in animals (though of course inanimate bodies aren't conscious), so is called 'substantial form.' - One reason to believe that body is not identical with its extension (a la Descartes): one and the same body can have its shape changed. If Descartes were right, the clay in a ball-shape would not be the same body if it were molded into a cylinder.
Why we need a metaphysical notion of force. Another reason is given in XVII-XVIII. Leibniz gives an argument that the "force" of a body is different from its "quantity of motion" ('quantity of motion' is the mechanical philosophers' term, and it refers to the amount of matter of a body times that body's velocity). Here is the argument:
- P1. The force acquired by a body X in falling from point Y to point Z = the force required to raise X back up from Z to Y.
- P2. Suppose the body B contains 4 times as much matter as body A. Then the force required to raise B up 1 unit of distance will raise A up 4 units.
- P3. Galileo showed that, for falling bodies, distance-squared is proportional to time, velocity is proportional to distance, and that all bodies fall at the same rate regardless of weight.
- Suppose that we lift A four times as high off the ground as B.
- From P3, after one second, A and B will both have fallen the same distance, and both have the velocity of one unit per second. B, the heavier body, hits the ground. After 2 seconds, body A hits the ground, moving at 2 units of distance per second.
- From the definition of 'quantity of motion,' we know that, at their moments of impact, body A's quantity of motion is 1x2= 2, and B's quantity of motion is 4x1=4.
- Therefore, a body's quantity of motion does not = that body's force, since P1 and P2 guarantee that, at the moments of impact, A and B have the same force.
But 'force' goes beyond what the (Cartesian) mechanical philosophers will admit: it is not reducible to shape, size, and/or motion. It is one of those 'incorporeal' entities that the hard-core mechanical philosophers find unintelligible.
Another reason why we must introduce forces is to capture the distinction between merely relative motion and real motion (XVIII). We saw this idea in Newton: if we merely look at changes of distances between bodies, we cannot determine which bodies are moving and which are at rest. But if we know the forces acting on bodies, then we can distinguish between real and apparent motion.
Restoring final causes to physics. A distinguishing feature of the mechanical philosophy is its rejection of final causes as empty and unilluminating (in our readings, Boyle makes this point explicitly). Leibniz suggests that final causes -- in the sense of God's purposes and plans for the world -- may still have some use in understanding our world. Leibniz's basic idea is that final causes and mechanical/ efficient causes are not mutually exclusive, and that without final causes we would (in some cases) have incomplete knowledge. For example, if a historian is studying a battle, if we only have a mechanical- physical explanation of how cannonballs are fired, and the subsequent quantities of motion transferred to the walls of the enemy's castle, causing the walls to break apart, then we have omitted an important part of the story -- the general's strategy. Another of Leibniz's example is the craftsman: to understand his work fully, we should understand BOTH his general plan and purpose, and how he puts the parts together to achieve that purpose. Leibniz suggests that both sides of the story are important:
"I find indeed that many of the effects of nature can be accounted for in a twofold way, that is to say by a consideration of efficient causes, and again independently by a consideration of final causes." (XXI)- Example: Snell's law can be derived from Fermat's principle, which states that light traveling between any two points takes the path that requires the least amount of time. This is a natural consequence of the Leibnizean idea that God does everything in the most efficient way possible.
The concept of an individual substance contains all the properties that belong to that substance. For Leibniz (and others), 'substances' are those things that fundamentally and truly exist.
Most philosophers (and other people who bother to think about it) think that in order to know what a particular substance is, there are some things about that thing you need to know, and others you don't. Call this the "common-sense view." For example, consider me (I am an individual substance). You don't really know what the concept Greg Frost-Arnold means if you din't know that I'm a human (as opposed to a toad, or a rock etc.) But, on the common sense view, you can know fully well what Greg F-A is, even if you don't know what I ate for breakfast this morning.
~ Leibniz denies this common sense view. If you have a complete or perfect concept of Greg F-A, then you know ALL of his properties, past, present, and future. Anything less is an imperfect and incomplete concept. We humans cannot attain such perfect knowledge, but God can and does.
[Note: My eating oatmeal for breakfast today is NOT an essential or "necessary" property of me: for God could have, if He wished, created the world such that I skipped breakfast today, and that would imply no contradiction. L. Says: "Everyone grants that future contingents are certain, since God foresees them, but we do not concede that they are necessary on that account."]
Why does Leibniz reject the common sense view? In short, his argument is this. A sentence in subject-predicate form (i.e., A is B, e.g. "Mary is kind" or "The dog is a mammal") is true if and only if the concept of the predicate is included in the concept of the subject. So if "Greg ate oatmeal this morning" is true, the concept of eating oatmeal this morning must be included in the concept Greg F-A. Leibniz puts the point this way:
"The content of the subject must always include that of the predicate in such a way that if one understands perfectly the concept of the subject, he will know that the predicate pertains to it also." (VIII)
Every substance is a mirror of the world On Leibniz's view, the properties that are part of my substance (for Leibniz, my soul) go well beyond what I happen to have eaten etc.: I have the property of living on a planet with 6 billion humans on it; I have the property of existing 93 million miles from the sun. This is why Leibniz claims "IX: that every individual substance expresses the whole universe in its own manner", and that "every substance is like an entire world and a mirror of God." Also, each substance is independent of everything else except God. As a result of this...
Substances do not, strictly speaking, interact with each other. (XIV-XV) Because every substance already contains all its properties, one thing never changes another. Leibniz of course recognizes that things appear to change one another -- the cold weather appears to be the cause of my sensation of cold, for example. But on Leibniz's view, this is not true, strictly speaking. But then how do all the various human substances agree that (e.g.) a cloudless sky at noon is blue? A: God has arranged all the substances so that the perceptions in their souls 'fit together' or agree. What about when I put my cold hands near a fire -- doesn't the fire cause my hands to warm up? No, says Leibniz -- my substance just starts expressing the property of heat more than it was previously, and it does so at precisely this time because God designed my substance to experience those sensations in that order. In Leibniz's words, "God alone constitutes the relation or communication between substances" (XXXII).
- This leads to Leibniz's epistemology. The usual view of how we come to know things is that our minds receive information from external objects acting upon us. Leibniz, of course, rejects this view, claiming that our minds or souls are not "blank slates" that experience somehow writes upon. Rather, we already have all the ideas inside our minds -- when we learn, we become fully aware of them. Our minds, Leibniz says, have no "doors or windows."