Gottfried Leibniz (1646 - 1716) was a polymath, who turned his hand to philosophy, mathematics, law, philology and many other subjects. He made huge adcvances in mathematics, simultaneously with Newton, coming up with Calculus. He worked out ways to algebraize logic. He made advances in the areas of computation, sometimes described as the first computer scientist.
Here we are concerned with a work he wrote, in response to John Locke, called New Essays on Human Understanding.
Leibniz accepted Locke's position that universal agreement was not sufficient evidence for innate knowledge. Even if everyone were to agree that the world was created yesterday, that wouldn't mean that it was either true, nor that we were born with such knowledge.
He did, however, disagree with Locke in thinking that we could have knowledge of which we were not aware. Leibniz thought that ideas and truths are innate in us as inclinations, dispositions, tendencies, or natural potentialities and not as actual things being thought. They are like a ‘vein in marble’ that means that it is inclined to take a particular shape.
He argued that we can know things of which we aren’t aware because we have to retrieve things from our memory. Recollection needs some assistance. Something must make us revive one rather than another of the multitude of items of our knowledge, since it is impossible to think distinctly, all at once, about everything we know. He compared an individual memory to the sound of an individual wave crashing amidst the whole sound of the sea.
Leibniz also gave an argument for the existence of innate knowledge based on necessary truths.
He distinguished between contingent truths - sentences that just happened to be true, and necessary truths - sentences that are always and everywhere true - like 'all triangles have three sides'.
Can you work out the rest of the argument from these premises before scrolling down?
Here are the main ideas that make up Leibniz' argument:
Necessary truths
Single examples
Things we learn through experience
Things we know innately
So how does he connect up all these ideas to get from this premise to the conclusion?
Things we learn through experience are single examples
...
∴ Necessary truths are things we know innately
Leibniz argued that there is no way that we can know that 'all triangles have three sides' from experience because we can't possibly see every triangle. Therefore, our knowledge that they have three sides must come from somewhere else. For Leibniz, this means it must be innate.
The source of knowledge of a truth is either the senses or innate
We can know necessary truths (e.g. Mathematics, Logic, Metaphysics, Morals)
All knowledge comes from the senses, only if the senses can be the source of necessary truths
BUT from the senses, we can only know an instance (or instances) of that truth
∴ the senses cannot prove every instance of a truth
∴ the senses cannot be the source of necessary truths
∴ All knowledge does not come from the senses
∴ Innate knowledge is the source of necessary truths
...necessary truths, such as we find in pure mathematics...must have principles whose proof does not depend on instances nor...on the testimony of the senses, even though without the senses it would never occur to us to think of them...[S]o the proof of them can only come from inner principles described as innate. It would indeed be wrong to think that we can easily read these eternal laws of reason in the soul, as the Praetor's edict can be read on his notice-board, without effort or inquiry; but it is enough that they can be discovered within us by dint of attention...[W]hat shows the existence of inner sources of necessary truths is also what distinguishes man from beast.
—Leibniz, New Essays on Human UnderstandingIs the only explanation for our knowledge of universal truths that they're innate? Is there any other possible explanation?
What about Locke's point that not everyone understands mathematical truths?
Leibniz seems to think that mathematical truths are descriptions. Are they?
Explain the difference between a necessary and a contingent truth.
Explain why Leibniz thought that we must have innate knowledge.
Think of an objection to his argument.
Evaluate his argument. Explain your answer.
Leibniz also relies on the distinction between necessary and contingent truths in his proof of the existence of God. He lays out this argument in The Ultimate Origin of Things. The argument also lays out the famous Principle of Sufficient Reason - the idea that every fact about the world must have an explanation.
We can formalise the argument as follows:
Any contingent fact about the world must have an explanation. (Principle of Sufficient Reason)
It is a contingent fact that there are any contingent things.
∴ The fact that there are contingent things must have an explanation.
The fact that there are contingent things can’t be explained by any contingent things.
∴ The fact that there are contingent things must be explained by something which is not contingent.
∴ There is a necessary being.
Beyond the world, i.e. beyond the collection of finite things, there is some one being who rules, not only as the soul is the ruler in me (or, to put it better, as the self is the ruler in my body), but also in a much higher way. For the one being who rules the universe doesn’t just govern the world but also builds or makes it. He is above the world and outside it, so to speak, and therefore he is the ultimate reason for things. ·That follows because he is the only extramundane thing, i.e. the only thing that exists out of the world; and nothing in the world could be the ultimate reason for things.
I now explain that second premise·. We can’t find in any individual thing, or even in the entire collection and series of things, a sufficient reason why they exist. Suppose that a book on the elements of geometry has always existed, each copy made from an earlier one, ·with no first copy·. We can explain any given copy of the book in terms of the previous book from which it was copied; but this will never lead us to a complete explanation, no matter how far back we go in the series of books. For we can always ask:
Why have there always been such books?
Why were these books written?
Why were they written in the way they were?
The different states of the world are like that series of books: each state is in a way copied from the preceding state—though here ·the ‘copying’ isn’t an exact transcription, but happens in accordance with certain laws of change. And so, ·with the world as with the books·, however far back we might go into earlier and earlier states we’ll never find in them a complete explanation for why there is any world at all, and why the world is as it is.
—Leibniz, the Ultimate Origin of ThingsLeibniz also gives us an interesting extension of the idea of necessary truths in his definition in terms of possible worlds.
In trying to defend the idea that God exists from the problem of evil, he argues that (despite appearances) this world must be the best of all possible worlds.
This idea of possible worlds gives him a definition of a necessary truth: something that is true in all possible worlds.
53. Now as there are an infinity of possible universes in the ideas of God, and but one of them can exist, there must be a sufficient reason for the choice of God which determines him to select one rather than another.
54. And this reason is to be found only in the fitness or in the degree of perfection which these worlds possess, each possible thing having the right to claim existence in proportion to the perfection which it involves.
55. This is the cause for the existence of the greatest good; namely, that the wisdom of God permits him to know it, his goodness causes him to choose it, and his power enables him to produce it.
—Leibniz, Monadology