In this post I want to take a look at some interesting comments by G.W. Leibniz (1646-1716) about the nature of propositions and how their ability to combine the way they do makes them different from physical objects. His insights have interesting implications for our understanding of the mind and God.
Many philosophers agree that the proper bearers of truth and falsity are propositions which are, roughly, the meanings of statements that declare something to be the case. For example, this sentence in English, which can be true or false and which declares something, expresses a false proposition:
‘The United States entered WWI in 1920.’
Now Leibniz pointed out that “any two propositions can be connected to prove a new one, when the means of joining them have been added” (see Leibniz: the Shorter Leibniz Texts, Continuum Publishing, p. 182). Perhaps Leibniz has in mind the rule of inference known as addition which is:
2. Therefore, P or Q.
It is raining.
Therefore, either it is raining or it is sunny out.
In other words, given a certain proposition p, we can connect any other proposition to it to form a new disjunctive (either/or) proposition. So, to take the example from above, we could have the following false disjunction comprised of two false disjuncts:
‘The United States entered WWI in 1920 or the Earth is the largest planet.’
And we could, if we so desired, go on and on adding disjuncts to this disjunction.
Now, because all propositions can be combined in this fashion, Leibniz thinks it must be the case that they are “not distinguished by time and place” (p. 182). If they were, we would presumably find it impossible to, for example, (1) combine some from one region with others from another or (2) some from the past with some from the present. All kinds of spatial and temporal limitations would arise that would prevent us from making the propositional combinations we make so easily. However, Leibniz points out that physical things are distinguished by time and place and thus can’t be combined in many cases. If this is the case then propositions aren’t physical.
Moreover, the type of combining Leibniz is talking about is the kind that ends up proving something. When we reason one mental state seems to cause another mental state by virtue of its propositional content or meaning. We grasp the meaning of the proposition ‘It is raining’ and then grasp the valid inference that ‘Therefore, either it is raining or it is sunny out.’ But physical causation is a matter of energy interacting in accordance with the basic forces and laws of nature – not propositional content and logical inference. It would seem, as Edward Feser nicely put it, “that the electrochemical properties of the neural processes with which the thoughts are associated are entirely sufficient to bring about whatever effects they do bring about. The meaning or content of the thoughts is irrelevant” (see his Philosophy of Mind p. 152). Tyler Burge elaborates:
“[R]eason is a constitutive structural feature of causation by propositional psychological states and events. According to the natural sciences, reason is not a structural feature of material composites. The causation by material parts of material composites, operating in their physical relations to one another, must suffice to alone compose causation by material composites. It is hard to see how the causal powers and causal structure of material components could alone compose the causal powers and causal structure of causal transactions that hinge on the rational, propositional structures of propositional states and events. So it appears that rational, propositional, psychological causation is not the causation of a material composite.”
“The second concern about compositional materialism is similar, but does not feature causation. Here it is: the physical structure of material composites consists in physical bonds among the parts. According to modern natural science, there is no place in the physical structure of material composites for rational, propositional bonds. The structure of propositional psychological states and events constitutively includes propositional, rational structure. So propositional states and events are not material composites.” (see his article “Modest Dualism” in The Waning of Materialism, eds. Koons and Bealer).
If these points are correct then no combination of physical objects could ever result in an argument. Propositions can only be connected and inferred when, as Leibniz claimed above, “the means of joining them have been added”, namely, a mind with the capacity to reason. Such a mind would have to be non-physical in order to think universal concepts, establish propositional bonds between them, make judgments, and infer one proposition from another. James Royce, in his book Man and His Nature (McGraw-Hill, 1961), provides a helpful elaboration:
“My concept of a triangle cannot be measured. I can have larger and smaller images, but the idea of what a triangle is applies equally well to all triangles, large and small, which could not be possible if the idea had size itself. My idea of an elephant is no bigger than my idea of a flea, for neither is quantified. Ideas do not occupy space: not having parts, they cannot extend over quantified matter. Nor does a simple idea occupy many parts of the brain at once, for then we would have many ideas, not one, of any one thing. A judgment means recognition of identity or non-identity of two concepts; but if one concept is in one space, and the other in another part, I could never get the two together in a judgment. The only conclusion is that the ultimate subject of such simple operations is itself simple.” (313)
Leibniz concurs when he opens his Monadology by asserting that a monad or soul is “nothing but a simple substance, which enters into compounds. By simple is meant without parts.” So we see Leibniz’s insights about propositions have interesting consequences for our understanding of the mind (for my argument that a commitment to propositions strongly suggests we have a soul, go here).
They also offer us insights into the nature of God. Leibniz claimed that “a plurality of truths joined with each other produce new truths. And there is no truth which does to produce a new truth when untied with any other truth. Therefore anything in any truth that exists objectively from eternity is united with any other truth” (Leibniz: the Shorter Leibniz Texts, p.183). Here we see Leibniz introducing eternity: all these truths and their relations to one another are eternally true. But if this is the case then truths, which for Leibniz are just modes or properties of a subject (how can we have true thoughts without a thinker?), would have to exist in some subject or subjects even when humans did not exist: “The reason why a necessary proposition is true when no one [no human] is thinking must be objectively in some subject.” And: “If no one thought, the impossibility of a square larger than an isoperimetric circle would still exist. And since it is only a mode, it is necessary that its subject be something.” (pp. 182-183). In On the Ultimate Origination of Things Leibniz argues there can only be one ultimate source of these truths: [I]t [the ultimate source for the reality of eternal truths] can be sought in but one source, because of the interconnection among all these things [necessary truths]” (Hackett, 45). Robert Adams explains: “According to Leibniz’s argument, for any plurality, P, of (necessary) truths or natures, there necessarily exists a necessary truth, T, grounded in a relation, R, among all the members of P; in order to sustain T in being there must eternally and necessarily exist at least one mind that understand R. But a mind that understands R must be one that understand the members of P, a mind…if those are the natures in which T is grounded; understanding all that, it will presumably be a mind that understands T itself. The conclusion of this argument is that for any plurality, P, of (necessary) truths or natures, there eternally and necessarily exists at least one mind that understands all the members of P.” (Leibniz: Determinist, Theist, Idealist, 182).
In sections 43-44 of his work The Monadology (1714) he argues that the eternal subject in which the eternal truths reside is God:
43. It is farther true that in God there is not only the source of existences but also that of essences, in so far as they are real, that is to say, the source of what is real in the possible. For the understanding of God is the region of eternal truths or of the ideas on which they depend, and without Him there would be nothing real in the possibilities of things, and not only would there be nothing in existence, but nothing would even be possible.
44. For if there is a reality in essences or possibilities, or rather in eternal truths, this reality must needs be founded in something existing and actual, and consequently in the existence of the necessary Being, in whom essence involves existence, or in whom to be possible is to be actual. (Translation by Robert Latta)
In sum: propositions, the bearers of truth and falsity, are not physical aggregates according to Leibniz. Any proposition can be combined with any other to prove another but (1) many physical objects, distinguished as they are by time and place, can’t be combined and (2) even if they can be combined such combinations can’t prove anything since physical aggregates determined by natural laws have nothing to do with the logical entailments of justifications. This account offers us a way to challenge the view that everything is physical or at least material. It also offers us the tools to argue for immaterial minds and even God’s existence.
For more on Leibniz’s insights about the mind and his famous mill thought experiment go here.
For my post that explores Leibniz’s critique of atoms in relation to a few of his principles, go here.
For my post that explores Leibniz’s view of the soul and its immortality, go here.
For St. Augustine’s argument for God from eternal truths which is a precursor to Leibniz ‘s argument, go here.