It seem to follow from Leibniz' notion of a complete concept that if you could express the complete concept of a substance you could deduce from that everything about the substance.
Leibniz didn't think you could read off the complete concept just by looking. Study, including observation and experiment, would be needed in many cases before the complete concept could be fully articulated.
But once you knew the complete concept, you could define terms so as to reflect these complete concepts.
Once you had revised language in that way, your language would reflect the world, and all truths would be analytic.
Let me explain a little
Hobbes had suggested that it was possible for one representation to relate to another in the way that one part of a package relates to the package as a whole.
Take a seasonal analogy: Father Christmas has lots of packages in his sack.
Representations can be like that.
Take this picture of the street Leibniz lived on.
It is a representation of a street which contains a representation of a house, which contains a representation of a window.
Then take a representation of one of the windows. We can say that this representation is contained in the representation of the street scene.
We are asserting an identity between the picture of the window and one of the components in the picture of the street scene.
Reasoning on this view is a matter of handling identities like that between ideas.
For example, reason might consider a number of ideas and judge that another idea that it is given to consider is nothing but those separate ideas joined together. Or it might consider a complex idea and what would be left should certain component ideas be taken away from it.
By analogy, what would be left if you took the picture of the houses away from the picture of the street scene?
Hobbes puts these points like this:
'When a man [sic] reasoneth, he does nothing else but conceive a sum total, from addition of parcels; or conceive of a remainder, from subtraction of one sum from another."
Hobbes Leviathan, Ch. 5.
This was the picture that Leibniz elaborated. (Eg in Leibniz, 'Of the Art of Combination', in Leibniz, Logical Papers, ed. G.H.R. Parkinson, Oxford, 1966, Clarendon, Ch 1.)
When we say something is true, in Leibniz' view, we are very often bringing out what is already there in the representation of the subject we are talking about. In terms of one of his own examples, when we say that
'Man is an animal'
we are, he thinks, doing no more than bringing out the fact that the representation animal is contained in the representation man.
Because it contains component representations in this way, Leibniz calls man a complex representation. He thinks animal complex in this sense too, since it contains the representation living thing; and also that, in its turn the representation living thing contains component representations as well.
But ultimately he thinks such regresses come to an end and we encounter representations which are simple: while they may be contained in representations, they themselves contain none.
He called these unanalysable representations 'first terms', and his suggestion was that a complete list of them would represent a kind of alphabet out of which all other concepts were constructed.
The fact that a certain representation is contained in a certain other, Leibniz claimed, is usually obscured by ordinary language
It is not obvious from the words used, for example, that man contains animal.
He argued that thinking, as well as communication across languages, would be very much aided if this situation were rectified.
We need to pause to ask about language and how the revolutionaries were able to think of it in the Modern period.
As a result of the revolution, we have established the picture of two worlds, the world of objects, and the world of the mind. In the mind are ideas, and ideas are representations of the world of objects.
Words were thought of as representations also. they represented ideas.
Locke was to say that words 'are the signs of internal conceptions' (Human Understanding III,1,ii)
In many ways, words were bundled along with ideas, since both were representations.
Foucault: 'The language of the classical age is caught in the grid of thought, woven into the very fabric it is unrolling. It is not an exterior effect of thought, but thought itself.' (The Order of Things, p.78.)
Once it had become established that thinking was a matter of the inner eye inspecting representations, language, which represented those representations to the thinker, and to those he or she wished to communicate with, took the guise of a glass that could distort the objects viewed through it.
Once it was established that words represented ideas, and it became possible to think they might do so well or badly.
Ideally you would want a word to express as plainly as possible the idea it was being used to represent.
A perfect language would be one that reflected accurately the structure of the thoughts it was used to express.
( John Wilkins and George Delgarno, both working in the mid-seventeenth century, were two of the many who took up the challenge of devising such a language, and reached the point of publishing proposals. (L.J.Cohen, 'On the project of a universal character,' Mind, 1954, pp 49-63))
Leibniz' contribution was to look towards a 'universal polygraphy' - an all-purpose system of writing.
In the system he proposed, a complex representation was symbolized by stringing together the signs that severally stood for the various component simple representations it contained.
I have explained that ideas for Leibniz are simple or complex, and that complex ones are made up of simple ones You should, he thought, be able to devise a complete set of signs for the simple ideas.
Once you had these, the signs for complex ideas would simply be combinations of the relevant signs for the simple ideas of which each one was composed.
Leibniz recommended that the signs for the simples be designed, to the extent that this was feasible, so as to picture what they represented, rather in the manner of the Chinese ideographs.
There would be room for choice then - and indeed scope for ingenuity - in determining the signs for the 'first terms'. But the signs for complex ideas would follow once the choice of signs for first terms had been made.
Leibniz called his proposed system a 'characteristica universalis' .
Leibniz apparently took some inspiration from the colourful thirteenth century visionary Raymond Lull (Martin Gardner, Logic Machines & Diagrams, Brighton, 1983, Harvester, Ch. 1).
His new system, he thought, would, just by-pass the imperfections of ordinary languages. It would be 'intelligible to anyone who reads it, whatever language he knows'. Leibniz, 'Of the Art of Combination', in Leibniz, Logical Papers, ed. G.H.R. Parkinson, Oxford, 1966, Clarendon, p.10.
Leibniz thought, as I have explained, that a perfect system would present to the reader the correct analysis into component simple representations of each of the complex representations it expressed. That way, thoughts would be represented without distortion. But what of the accuracy of the representing done by thoughts themselves?
Leibniz thought that a substance's characteristics flowed from its nature, and that the characteristics of an aggregate made of substances flowed from the nature of the substances that made it up.
It was part of, or at least flowed from, the nature - or 'essence' - of gold, for example, that it should dissolve in some acids but not in others, just as it flowed from a creature's being a horse that it should have four legs.
There are many cases, Leibniz thought, in which it was by no means obvious what a substance's nature was; in these cases 'induction' was called for - what we now call empirical research.
Particular historical truths (for instance, 'Augustus was emporor of Rome') are on kind of example. He gives as another, 'All European adults have a knowledge of God'. (Leibniz, 'Of the Art of Combination', in Leibniz, Logical Papers, ed. G.H.R. Parkinson, Oxford, 1966, Clarendon, p. 5,6.
Once our knowledge of things' essential natures was complete we would be in a position to allocate to each its correct representation: that is, one consisting of just those simple representations which corresponded to what our research had discovered or confirmed to be the several essential qualities of the thing.
That would bring the scientific enterprise to fulfillment: not only would our knowledge by complete, but would be laid out with maximum clarity in language. It would, thought Leibniz, take quite some time: but if we got properly organized we could finish in five or six decades.
Leibniz, 'Of the Art of Combination', in Leibniz, Logical Papers, ed. G.H.R. Parkinson, Oxford, 1966, Clarendon.
Once you took the perspective on representations and reasoning Leibniz arrived at the idea of a mechanical reasoning device becomes thinkable. Reasoning is a matter of spotting whether such and such a concept is contained in such and such another.
You need to find a way of representing the first terms mechanically - as different positions of a cogwheel, for example. When you've done that you will be able to represent in the machine every complex concept as well as every simple one. You then need a mechanical way of testing whether such and such a component of one concept is present in such and such another. The principle is just the same as in mechanical calculators, which are able to tell whether two representations of numbers are the same or not.
Leibniz dream was for 'logical calculation' to replace argument. There would come a point he hoped when the advice to disputants locked in a disagreement that they are finding irresoluble would be that they should 'take up their pens and calculate'. Once we had got the point of a definite set of procedures for calculating out arguments, mechanising the process would swiftly follow. In this way mechanical reasoners would follow mathematical calculators, of which Leibniz himself was of course a pioneering designer.
[Much of this derived from Thinking Machines, chiefly chapter 5.]
Last revised 22:01:04
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