Leibniz's Law

In philosophy there are three generally accepted laws of thought: identity, noncontradiction, and the excluded middle. The law of identity asserts that a thing is itself and not something else; A is A. The law of noncontradiction asserts that something is not itself and something else, A is not B if A is A. The excluded middle asserts that A cannot be both A and non A (B), it is either A or non A (B). These laws are generally accepted in western philosophy, although there is great disagreement over where and what they apply to, and if such distinctions exist in the natural world. Other laws have been proposed to also be laws of thought, one of them is the principle of sufficient reason PSR which says that there is a reason or cause for everything. This one is quite controversial because of its metaphysical implications. 

The Identity of Indiscernibles is another one of the candidates for being a law of thought, but one which appears to follow the traditional laws of thought more than the PSR because it deals with identity and not relation. The Principle of the Identity of Indiscernibles, also called Leibniz's Law, states that if two things share the same properties, then they are the same things. If everything that can be said about one thing can be said about the other, then they share the same identity. 

Leibniz puts it in his essay On the Principle of Indiscernibles: "there are no purely extrinsic denominations, because of the interconnexion of things, and that it is not possible for two things to differ from one another in respect to place and time alone, but that it is always necessary that there shall be some other internal difference."

Sounds reasonable enough, but why is it called the identity of Indiscernibles? Because the things in question are supposed to be able to differ extrinsically, in time space or number, and still be able to be the same thing. Just because the Earth exists in different spaces and at different times during the year does not mean it isn't the same thing the whole year. Position in space, motion, time, number etc. are different modes of the physical world, what could be called physical substance. Though physical things may differ in certain respects, that doesn't mean they do not share the same quality of being physical, all existing in space and time. To be truly different from something else, the subject must also differ in other predicates like color, taste, or smell. 

When I first tried to understand Leibniz's Law this way, by reading a straight definition, I didn't quite grasp it or its importance. The best way to understand the principle is understanding what could have motivated Leibniz to formulate the principle. He goes on to say in his essay "this overthrows the whole of purely corpuscularian philosophy. First, there cannot be any atoms, otherwise there could be two things which differ only extrinsically. Then, if place by itself does not make a change, it follows that there cannot be any change which is merely local."

Corpuscularian philosophy refers to a type of atomism put forth by 17th century thinkers like John Locke and Robert Boyle active in the scientific revolution which differs from atomism in that the tiny units which make up everything can in principle be infinitely divided, but also while existing in a void (which Descartes denied). They can be infinitely divided because the qualities that objects have are not just the configuration of atoms, but are also the products of the powers of interacting corpuscles. These additional powers come from the quality of solidity, where the void between corpuscles is filled. In that way everything sensual can be more than just the motion of atoms as they can join together. This meant that objects have two kinds of qualities, primary qualities which are due to atomic arrangement and secondary qualities which were the result of interaction with the senses. Primary qualities were said to reflect the corpuscles as they really are; having the qualities of extension, motion, figure, solidity, and number which are common to all objects of sense. Secondary qualities do exist to the corpuscles but are caused by their interaction. Color, taste, smell, and sound the way we experience them do not exist in the objects themselves but are produced by the acting on our senses, they are purely subjective. This distinction was problematic from the beginning, but is crucial to the corpuscularian philosophy. If everything is physical in nature, subjective things like pain can explained as an emergent property, much as in chemistry where elements behave differently together than individually. 

Leibniz's Law suggests that this distinction is untenable. Secondary qualities are in a sense real attributes which demarcate different kinds of things, and are not just products of the action of physical things. "Just as shape is to extension, and derived force is to an entelechy, so are phenomena to light; light is in a way the matter of images. This cannot be located in the mere power of acting, since action is again something relative to a state which varies." Light is not just the power of photon particles to produce electrical signals through the eyes to the brain. If that was true then there would be no means of differentiating light from any other corpuscles, which differ only extrinsically. 

The implications of this law or principle are profound. Materialism or physicalism would be downright false, as they claim everything is physical which would mean differing only extrinsically. Non-physical things like the ideas of love or freedom which are quite different than physical things cannot be reduced to physical sensations, brought on by physical objects. They are something in themselves, perhaps. Leibniz's Law has been used to support dualism, that mind and body are different. The qualities of consciousness are that it is subjective and not reducible to a time and place, the mind is continuous for as long as it exists, and has intention behind its actions. Since physical objects are known to a third party, are reducible to time and place, and do not have intentionality it follows that mind and body are somehow different or separate because of their different properties. 

Critics of the implications of Leibniz's Law invoke the masked man fallacy. If my father is accused of being a masked thief, I can say he does not appear to have the character of being a thief and isn't wearing a mask so he is not the masked thief. Or, Clark Kent cannot be Superman because Superman has been observed flying and Clark Kent has not. The qualities shared must be intrinsic to the nature of what we're talking about, the true properties of these objects, and not just appearances. Critics of dualism would assert that it seems as though mind has different properties than matter, but that is just because we don't fully understand how it works given the difficulty of studying consciousness from a third person point of view. Much like it was thought that the sun circles the Earth, "the sun can't be the center of the solar system because it moves in the sky while we stand still." 

Still Leibniz's Law is something to think about as artificial intelligence advances. Does behaving intelligently demonstrate consciousness, if consciousness is defined by its subjective nature?