A simple kind of necessary truth

Sofar, the quotations have been from the editors' introduction, but from now on they will be from Leibniz, when not explicitly stated otherwise. Since the editors made an abbreviation, the book is not normally paginated, but paginated with reference to the complete work it abbreviates, and these page numbers are in the left and right margins. I will use these page numbers - and so my quotations and remarks do relate also to Leibniz's complete text.

"(...) the case of necessary truths." (p. 49)

A very general definition of "necessary truth re A" is: "what is true in any case A is true" - say, the unconditional consequences of A. In way, these may be identified with A's essential properties, where it should be noted that, as defined, these hold in any and every world A is in. (More formally, one can put it thus: Nec(A) = {B: [(W)(A(W) ==> B(W)] } i.e. Necessary re A = the class of things (in the broad sense of: entities of any kind) which are implied by A in any world in which A is element (irrespective of whatever else is or may be in that world).

The notation used here is non-standard, in that I take A and B to be rendered by statements, while I take statements as attributable to worlds, which I quantify over.).

"While men are capable of demonstrative knowledge, beasts, sofar as one can judge, never manage to form necessary propositions, since the faculty by which they make sequences is something lower than the reason found in men." (p. 50)

Well, animals don't use symbols and don't form propositions. It is difficult to be certain about what animals can and cannot think of, and I, for one, am often impressed by their apparent knowledge, common sense, and inventiveness. UP

If-then notions and sequences

Also, it seems that much of the behaviour of higher animals, including birds, can be explained on the basis of their acquiring some sort of - probabilistically qualified - if-then insights, which I see no reason to deny them on the ground that they cannot put them into words (and I assume humans may put them into words i.a. because they also have non-verbal if-then insights, which forms the basis of their acquisition of language). And I do like the notion that reasoning comes in the end down to forming sequences (that mirror other sequences, say).

"(..) of finding unbreakable links in the cogency of necessary inferences. This last often provides a way of foreseeing events, without having to experience sensible links between images, as beasts must. Thus what shows the existence of inner sources of necessary truths is also what distinguishes man from beast." (p. 51)

If we think without images, we usually think with what are in fact aural "images", i.e. mentally imagined speech. So as before, the difference between men and animals is linguistic. Also, I see no reason why animals could not be aware of necessary truths without being able to formulate them. Indeed, it is difficult to explain the behaviour of bees, pigeons, beavers, spiders etc. otherwise: in some sense they are tuned to some properties of things in their environment we are not, and know instinctively how to use these properties to their advantage. For one simple everyday example, all land-animals have to cope with gravity, and know in some sense what it is to fall. UP

The mind and the body

Of course, it is a moot question whether a cat that balances on a branch to catch a bird has any knowledge of the dynamics or optics involved in its behaviour, especially if it has no way of articulating it in symbols, but on the other hand, its whole existence is built around such knowledge, and its body incorporates it, and its brain uses it and presupposes it in some sense.

"But reflection is nothing but attention of what is within us, and the senses do not give us what we carry with us already. In view of this, can it be denied that there is a great deal that is innate in our minds, since we are innate to ourselves, so to speak, and since we include Being, Unity, Substance, Duration, Change, Action, Perception, Pleasure, and hosts of other objects of our intellectual ideas?"

The actual point being: we have these ideas and they go beyond what experience can teach us. But these ideas seem all to revolve around some generalizations and abstractions. They're also symbolizations. Also, they are pretty abstract, and a more convenient example of an idea that is within us that even a small child can understand is the idea of tomorrow, his or her next birthday, or his or her own fantasies, for each of these is also beyond present experience. Finally, it should be noted that each of Leibniz's example is a term that applies to diverse kinds of things rather than one kind, so that part of the reason that these terms are abstract is that they are defined in terms of a few properties that in any application to real things or experienced things require supplementation of further properties. UP

Leibniz and the unconscious

Leibniz discusses one of his reasons for unconscious perceptions as follows:

"We must be affected slightly by the motion of this wave, and have some perception of each of these noises, however faint they may be; otherwise there would be no perception of a hundred thousand waves (...) (p.54)

This is an interesting idea, but I don't believe it, and much rather suppose we are selectively tuned to bandwidths, and what we hear is sound, not moving droplets. That is: it seems to me in at least some cases what we perceive is rather a statistical abstract from what's there than an actual representation. And in the case of waves of water what we hear is the changes in air-pressures set up by the movement of the water. However, it is an interesting question what we see if we lie under a tree and look up at the thousands upon thousands of leaves that move in the wind: do we in some sense see each and every movement of each and every leaf as the wind moves them? We certainly are not aware of each and every movement, yet we do have some information about statistical ensembles of them, at least, for we do notice oddities in such compositions of movements.

"These minute perceptions, then, are more effective in their results than has been recognized. They constitute that je ne sais quoi (..) (p. 55)

Isn't it more sensible to postulate the workings of a brain or mind than a "je ne sais quoi" (which translates as "I know not what")? Leibniz is here being too empirical, as if what produces experience must be somehow, if only minutely, be given in experience. What produces experience need only have some consequences in experience, that need not at all be like it and also need not contain clues about it.

"In short, insensible perceptions are as important to spiritual science as insensible corpuscles are to natural science (...) (p. 56)

See p. 55 and compare Freud's assertion about the unconscious (Freud made an English recording around 1935 in which he claims to have : #ffff00">discovered the unconscious. This is fraudulent nonsense for many reasons, varying from the ancient Greeks' "Know Thyself" to Leibniz.) UP

Identity and universals and symbolizing what does or cannot exist

"I have pointed out that in consequence of imperceptible variations no two individual things could be perfectly alike, and that they must always differ more than numerically. This puts an end to blank tablets of the soul, a soul without a thought, a substance without action, empty space, atoms, and even to portions of matter that are not actually divided, and also to absolute rest, completely uniform parts of time or place or matter, and hundreds of other fictions which have arisen from the incompleteness of philosophers' notions. They are something which the nature of things does not allow of; nothing could make them acceptable, short of their being abstractions of the mind, with a formal declaration that the mind is not denying what it sets aside as irrelevant to some present concern. Abstraction is not an error as long as one knows that what one is pretending not to notice is there. (p. 57)

First, I deny that "no two individual things could be perfectly alike", since this seems to me to be what universals are, and besides I do not see why, say, two atoms of hydrogen could not be perfectly alike apart from their places - which could be expressed by saying both have the same essential properties: see above note to p. 49 (and have, apart from their location in space and time, no individuating properties).

Second, the notions this would put an end to are thus not put an end to, though this also doesn't establish them, of course.

Third, there is this problem concerning abstractions, illusions, errors etc.: where are the representations (objects) of our false thoughts? In our imagination, but isn't that itself a part of reality? (This is similar to saying "so-and-so is inconceivable" - which is to conceive it and reject its truth.)

In any case, the problems involved in errors are serious and important, for at least two related but distinct reasons: First, if we may make errors, then our thoughts may represent things that are not there, yet are imagined to be there until our error is recognized, and until then we will suppose reality to be as she is not. And second, if one can think of six impossible things before breakfast, then at least these thoughts must exist, and so one's thought seems able to do what reality cannot possibly do, yet one's thoughts are part of reality.

It follows that thoughts are representations, and what is true of representations is not precisely what is true of what is represented - as it may be true of a representation that it does not represent, and that it may be true of a representation that what it represents not only does not represent anything real, but also represents something that could not possibly be real (as Escher's 2-dimensional drawings of impossible 3-dimensional spaces).

"This knowledge of insensible perceptions also explains why and how two souls of the same species, human or otherwise, never leave the hands of the Creator perfectly alike, each of them having its own inherent relationship to the point of view which it will have in the universe." (p. 58)

It seems to me the unique location of any individual thing is sufficient for that.

"(...) the modifications which can occur to a single object naturally and without miracles must arise from limitations and variations of a real genus, i.e. of a constant and absolute inherent nature. (p. 65) (..) So we may take it that matter will not naturally possess the attractive power referred to above (p. 66)

These modifications I explain by essential properties. However, there is the danger, also for Leibniz, that such assumptions are mere prejudice.

"(...) whereas what is natural must be such as could become distinctly conceivable by anyone admitted into the secrets of things." (p. 66)

Yes, insofar as what can be known as real must be known as such by anyone capable of knowing it; no, insofar as appealing to secrets of things introduces a special caste of high priests.

Put otherwise, the only prerequisites to know reality must be intelligence and information about reality that is sufficient given the intelligence to infer - some of the - reality.

This does not exclude the possibility that there are aspects of reality that may be beyond human understanding, although it should at the same time be remarked that this possibility leaves hardly any logical scope for a divinity, since divinities are introduced to understand what reality is like, usually on the basis of an argument to the effect that certain real features of reality cannot be correctly or at all understood without such assumption. UP

Mechanism, qualia and vitalism

Next, there is a fine passage that formulates the problem of how one can account for human experience - feelings, fantasies, desires, true and false theories etc. - on a mechanistic account of reality:

"As for thought, it is certain (..) that it cannot be an intelligible modification of matter and be comprehensible and explicable in terms of it. That is, a sentient or thinking being is not a mechanical thing like a watch or a mill: one cannot conceive of sizes and shapes and motions combining mechanically to produce something which thinks, and senses too, in a mass where formerly there was nothing of the kind - something which would likewise be extinguished by the machine's going out of order. So sense and thought are not something which is natural to matter, and there are only two ways in which they could occur in it: through God's combining it with a substance to which thought is natural, or through his putting thought in it by a miracle." (p. 66-7)

First, Leibniz entirely misses the ideas of information and programming. That is not strange, but one wonders whether he would have said the same had he been aware of these notions.

Second, if information is a natural phenomenon, "thought may be an intelligible modification of matter", and one sensible way of construing information is thus: A informs about B iff B's objects and relations can be inferred from A's objects and relations, which again may be explained in terms of an analogy between A and B.

Third, this does seem to involve a distinction between data and program, in that a program then is a natural process that alters (data about) A to obtain (data about) B, and it does also seem to involve a distinction of representing and represented (or at least the ability to act in appropriate cases to the data obtained about B as if they are about B, and in other appropriate cases to deal with data obtained about B as nothing but data).

Fourth, the notion that "sense and thought are not something which is natural (to matter)" is one that introduces or presupposes a very strong dualism of mind and matter. That may be justified, but the problem from the start is that it goes against parsimony of assumptions. (Ockham's Razor.)

Fifth and last, it should be conceded to Leibniz that there is a deep problem here, namely that the bodies of human beings are made from parts - atoms of hydrogen, oxygen etc. - that themselves are supposed to have no feelings or thoughts or ideas whatsoever. UP