Leibniz's rationalism and rationalism

The editors classify Leibniz as a rationalist, and explain this as follows:

"Leibniz was a 'rationalist' at least in thinking that every intelligible 'Why?' question has a true and satisfying answer." (p. xvi)

The key-word is clearly 'intelligible', and given that one can add: and unintelligible questions have the answer they are unintelligible. One may well ask, though, whether 'Why does this very question have no true and satisfying answer?' is intelligible, and add: 'Why has every intelligible question a true and satisfying answer?'.

One problem with rationalism, as described, is that both questions and answers seem, first and foremost, linguistic entities, whence it follows that what may be, linguistically, a perfectly correct question and answer may be, conceptually, incomprehensible. This may be due to many reasons: the length of the question, the terms used, or the logic involved. An example of the last is as follows: "If a paradoxical question is one which can neither be truly nor falsely answered, then why is this paradoxical question not paradoxical?" Up

Rationalism in terms of principles of inference

In any case, I prefer the abductive position that anything whatsoever can be shed light on by specifying a context in which it happens, a content of what happens to what, and a characteristic of whatever does or could happen.

This is a methodological characterisation of rationalism: to proceed rationally is to seek to explain in terms of assumptions that entail what is to be explained. "Abduction" (like "hypothesis") in the present context is a term of Peirce that stands for any principle of inference that concludes assumptions that entail what is to be explained. It may be explained as follows:

"Abduction. (..) "Hypothesis [or abduction] may be defined as an argument which proceeds upon the assumption that a character which is known necessarily to involve a certain number of others, may be probably predicated of any object which has all the characteristics which this character is known to involve." (5.276) "An abduction is [thus] a method of forming a general prediction." (2.269) But this prediction is always in reference to an observed fact; indeed, an abductive conclusion "is only justified by its explaining an observed fact." (1.89) If we enter a room containing a number of bags of beans and a table upon which there is a handful of white beans, and if, after some searching, we open a bag which contains white beans only, we may infer as a probability, or fair guess, that the handful was taken from this bag. This sort of inference is called making an hypothesis or abduction. (J. Feibleman, "An Introduction to the Philosophy of Charles S. Peirce", p. 121-2. The numbers referred to are to paragraphs in Peirce's "Collected Papers".)

I shall later return to the distinctions between abduction, deduction and induction, that may here be briefly explained as:

• abduction is inferring a premise for a conclusion (with probability, but that the conclusion follows from the premise must be deductively valid),

• deduction is inferring a conclusion from a premise (with certainty, as a conclusion follows deductively from a premise only if the premise cannot be true without the conclusion also being true), and

• induction is inferring a new probability for a premise (that was inferred abductively) from a conclusion that follows deductively from it.

Whether the abduction or hypothesis reached is "a true and satisfying answer" will depend on the ends one has and criterions one uses. In general, if it is an empirical hypothesis, it requires testing and inductive confirmation (by deducing consequences that turn out to be facts).

One remark that must be made here is that these are three different kinds of principles of inference, and that historically what is here called "abduction" has often been equivocated with "induction". Thus "Whewell maintained that the formation of an explanatory hypothesis was the induction, and since the facts explained could then be deduced from the hypothesis, induction and deduction were not different kinds of reasoning as Mill thought" ("The Concise Encyclopedia of Western Philosophy and Philosophers", Ed. J. Urmson, article on Whewell).

Whewell and Mill were prominent 19th Century English philosophers (Whewell was predominantly a scientist) and the quotation shows how confused these terms were and often are used. As I use the terms an abduction is tested by deduction but differs from it in that it adds hypotheses, while deduction does not; while induction is a deductive mode of reasoning that is specifically concerned with the probabilities of hypotheses.

I shall return later to a fuller explanation of abduction, deduction and induction, since these concepts are of fundamental importance for understanding what is really involved in any kind of human explanations, and I shall also return later to the triple of terms context, content and characteristics, since these are of fundamental importance for understanding any kind of human arguments.

It may be remarked here that this triple of terms is meant in a perfectly everyday sense: The content of something happening is a description of what is supposed to happen; the characteristic of something happening is a description of those properties and relations that are sufficient to re-identify what is supposed to happen; and the context of something happening is a description of what else happens round about the place or time of the happening.

The reason to insist on the importance of these concepts is that any explanation of things seem to involve these, indeed usually combined with the - normally tacit - principle that any content and any context have some finite characteristic that may be formulated and understood by human beings. Up

Whether there is a reason for every fact

To return to the editor's introduction to Leibniz. There is talk of

"...the explanatory-rationalist principle that there is a reason for every fact." (p. xvii)

a principle which was used i.a. by Schopenhauer and Einstein, but which seems to go against there being real chance, if this is defined to amount to there being facts that have no prior reasons. For example. it is clearly stated by e.g. Dirac, in his text on quantum mechanics, that the quantum mechanical facts he discusses are such as to have no particular reason: a radio-active particle emits quanta of energy without any reason, though collections of these quanta plotted in time do have particular statistical distributions. If this is true - as most physicists believe - "...the explanatory-rationalist principle that there is a reason for every fact." either is not true or needs qualification. Part of Einstein's objections to quantum mechanics were based on this principle.

What complicates the problem is that chance itself can be used to provide a reason for a fact, both in explaining why it may happen unpredictably or not, and why - given a certain distribution of chances - a certain kind of facts, although each of the individual facts is unpredictable, is more common than another kind of facts.

Finally, it seems to me that it is quite implausible if not outright inconsistent to assume that, at least when we restrict ourselves to reasons presented in arguments, in the context of which reasons normally appear and are given, every fact has some reason, simply because we need to make assumptions to have any conclusion, and we will not provide reasons for out assumptions other than that they imply what we want to explain.

Also, this does not mean that these first assumptions are arbitrary or cannot be justified, for such first assumptions are made in order to deduce certain consequences one wants to explain, and these first assumptions are supported by having further consequences that turn out to be true. Up

The role of the free will

It should also be noted here that free will may require that the present and not the past determines the future, in cases where free will does apply. Since most human beings believe they have a free will, and indeed the whole corpus of the law - as used in courts of justice - is based on the assumption that human beings have a free will, here we have another commonly accepted belief that is difficult to combine consistently with the belief that every real fact can be fully explained - "causally", as the term is - by preceding facts. This is also a topic I shall later return to.

The reason to stress the term 'prior' in the previous section is connected (among other things) to the related problem of free will: It is at least conceivable that, whereas this or that does or does not happen with necessity because of prior reasons, it is conceivable that something happens with necessity because of prior and present reasons, present reasons involving, for example, a person's present choice. (Here it may be determined or necessary that this person given his prior beliefs and values comes to such and such action, and no other action, while it is not determined by prior facts that this person does make up his mind - but if he does, which is up to him, knowing him one can say he will do such and such. Whatever its ultimate validity, this is a type of reasoning people very often rely upon when dealing with each other. Also, to give the term 'present' some more content: A quite typical case of what I have in mind occurs when a person is reminded or reminds himself that he has made a promise that involved some commitment, and the person was not consciously aware of this before.) Up

The mind as experienced or as what produces experience

Here is one of the fundamental differences in outlook of Locke and Leibniz:

" Locke tends to allow only such mental activities and structures as one is consciously aware of, whereas Leibniz held that most mental events do not come within the reach of awareness (aperception) because they are too small and confused with more vivid mental content. Leibniz holds that something can happen in one's mind without one's being aware of it (...)" (p. xviii)

To some extent one can construe this as being about how experience is to be analysed. One problem is that both Locke and Leibniz seem too strongly inclined to use "mind" as "what one is aware of" - for as we shall find Leibniz also tends to talk as if his "minute perceptions" of things we don't really sense - like the sound of one of the drops in one of the waves in the sea we hear - could be conscious if they are not, whereas the principal point is whether our experiences may be explained by something that produces them and is not itself experience, even if it is in part or completely derived from it.

To me the basic points are

1. whether or not there is something behind and not (fully) given in experience that produces experience, which one may call the mind, and if so, and on that terminology,

2. whether the mind is like or may be inferred from experience or not.

And if there is a mind one can say something like: the existence of a mind entails the existence of both conscious and unconscious truths, without thereby answering the second question (although if abduction is a valid form of inference, the mind may be inferred from experience, since it is a consistent explanation for it).

My own position is that there is something behind experience that produces experience and is not fully given in experience, and that it may be inferred abductively from experience, to account for experience, but should by and large not be expected to be like experience (just as the brain is not like the thoughts it supposedly thinks). Up

Self and self

Another way of phrasing a similar kind of distinction is between Self (as what produces one's given experiences) and self (the experiences the Self produces that one is conscious of). Here one is not conscious of the former, and conscious of the latter, although one may add that the latter is like the former, and contains clues about it (or so one would naturally assume).

This distinction is somewhat narrower than the distinction between mind and experience, in that it is natural to provisionally identify the Self with everything in one's memory one attributes to oneself, and the self with everything in one's consciousness - which always is here and now - that one attributes to oneself.

Another way of describing what is here called Self is: the character people built in the course of their lives by the choices, interpretations, judgments and evaluations of their experiences that they retain in their memories.

To return to the principal difference between Locke and Leibniz we discussed. The editors correctly identify a difference between Locke's and Leibniz's use of the term "mental" and cognate terms like "mind" as follows:

"Locke held that the human mind's only innate endowment is a set of skills or aptitudes - no knowledge or beliefs and no 'ideas' (..)"(p. xix)

Given this, the disagreements about whether there are any "innate ideas" ought to have been about what is the meaning of "ideas". But in any case, Locke's position is very implausible, for it is rather obvious that all animals are born with preferences for and against foods and kinds of animals, and it seems mistaken or very odd to call these preferences skills or aptitudes rather than ideas: if one is born with - say - an abhorrence for blue food, snakes, or the shape of a flying falcon, one seems born with some sort of ideas.

Also, if one is born with a set of skills or aptitudes, to say, as Locke did, that the mind starts out like a "tabula rasa" or empty blackboard seems false or misleading. Up

Necessary truths

The editors have a problem with Leibniz's position, namely

"Leibniz still has to explain what it means to say that I knew P before I was aware of doing so." (p. xx)

One better answer than the editors' text gives is this: The innate truths (that one knows without being aware of them) are those whose denials are inconsistent with one's innate capacities. The idea here is that one's innate capacities are like a set + a valuation-rule in a model, as in mathematical logic. An example might be ducklings, who treat the first moving object of a certain size they see as parent.

"The link between 'P is necessarily true' and 'P is to be found in the depths of my soul' is not explained." (p. xxi)

The previous remarks provide an outline-answer I will return to later.

We turn to another aspect of the difference between rationalists and empiricists:

"Leibniz often admonishes Locke for conflating 'idea' with 'image', as when he says against Locke that there is no danger of confusing the ideas of a chiliagon and of a figure with one side less, any more than of confusing the numbers 1000 and 999, though of course the corresponding images may be hard to tell apart." (p. xxi)

This raises a problem: Leibniz may be able to infer the properties of chiliagons from the definition of them, but he may not be able to decide whether anything seen or imagined is a chiliagon.

The problem here is in fact that of theoretical entities and what they represent and how they do that. Linguistically, one easily introduces "the property of F-ing", but what if this is illustrated in experience only by fairly remote non-linguistic empirical consequences, that can be deduced only in conjunction with further assumptions? It seems the best line of reasoning here is abductive: such an abstract property of F-ing is - presumptively - real if its consequences would not exist without its existence (on our knowledge), and this is also the justification for introducing such an abstract property or theoretical entity: without it we cannot explain our experiences at all, or cannot explain them as well as with it.

The difference between rationalists and empiricists is also put thus:

"Leibniz insists that an idea is not 'the form of the thought', but rather 'the object of the thought' - something that does not come into existence with the thought or perish with it." (p. xxii)

I agree thoughts have objects (what the thoughts stand for) but what if - as with "speaking elephant" - there are no such objects in reality? Where is the object of a thought whose object happens not to exist? Answer: in the imagination (or "fantasy"), where "imagination" (or "fantasy") also included non-images, like chiliagons. However, at least for humans, this does seem to require that whatever is in the imagination is either an image or a coded image (i.e. a symbol) and whatever is in the imagination represents (symbolises) something or nothing.

Note also that this relates to the earlier remark on the mind: thoughts are experiences, specifically experiences of ideas, which themselves either correspond to something real or not.

This leaves it open whether there is any intersection between thoughts and ideas, though such a non-void intersection would make the experiencing of one's ideas easier.

However, as I use terms I assume that one's ideas stand to one's thoughts as assumptions or causes stand to consequences or effects. And to explain conscious thoughts one must assume, it seems, ideas one has without being conscious of them, while being conscious of their consequences or effects.

"Leibniz holds that the ultimate constituents of reality must be simple, without parts. He rejects atoms, i.e. extended things which cannot be split into parts; so for him everything extended is divisible, and thus no extended thing is a substance or ultimate constituent of reality.(p.xxiii)

I disagree with Leibniz's argument for the rejection of atoms, and shall return to the topic later. In passing I also note that the real as a collection of non-standard reals ("non-standard reals" in the sense as used in recent new treatments of the calculus, based on ideas of Abraham Robinson, that do admit infinitely small entities) is an interesting notion, since here we do have a mathematically precise idea of the infinitely small that lies at the basis of all that is or may be. In this context:

"The true substances, according to Leibniz, are monads - sizeless entities of which minds are the only accessible examples. Not every monad is a mind; but the states of any monad are just its perceptions, in which the states of all the other monads are represented." (p. xxiii)

The problem here is that perceptions seem to be in monads and seem to - at least - be in time and normally about spatial entities. This is a problem because it is not at all obvious why and how a non-extended entity should represent and perceive reality as if it is extended (in some interval of time, about some spatially extended entities).

An important idea in Leibniz's epistemology is the notion of unconscious perceptions (which incidentally shows that Freud's claim to have discovered the unconscious was fraudulent, like so much else in Freud's teachings):

"Sometimes, he says, a perception may be too unvarying or too small (too 'minute', in our translation) for its owner to be aware of it (..) (p. xxiii)

Of course, this was an important idea, but as stated there enters the possibility of confusing what are in psychology called jnd's ("just noticeable differences"), which are, say, the smallest possible perceptions or thoughts, and the ideas which are their objects, which one simply cannot become aware of, whatever one tries.

Another important idea in Leibniz's metaphysics concerns the relation of identity. The editors remark

"(..) no two items could differ only in their spatial relations with other things, that being part of his case against atoms" (p. xxiv)

I reject Leibniz's case against atoms, and to me universals are just that: different items that differ only in their spatial or temporal relations with other things, being both here and there, or then and now, but otherwise are exactly the same - like this patch of white and the next patch of white, which to me are indistinguishable except by reference to their places.

Leibniz would deny there are two distinct things which are the same, but that is not the point, although it would be difficult to tell the difference between this and that atom of Helium, say. The point concerns properties and relations rather than substances: I am a son of my father in precisely the same sense that any other man is a son of his father, even though he and I are different and his and my father are different. In this sense "to be a son" and "to be a father" etc. are universals: identically the same through varying instances. Also, Leibniz's position becomes very doubtful as soon as one considers such terms as 'approximately circular', 'greenish' etc. that stand for whatever they represent in the same way, yet do not require that anything they stand for have more in common than being approximately circular, greenish etc. And this and that may very well share the property of being approximately green, while not being of the same colour.

Yet another important idea in Leibniz's metaphysics is his notion of pre-established harmony, which Leibniz needs to explain why, in his system of assumptions, one monad (such as me) can perceive what appears to be a reality that seems in many ways the same as what another monad (such as you) perceives, where part of the difficulty for Leibniz resides in his assumption that monads do not really communicate:

"It is a contingent, God-contrived fact that the perceptions of each monad are systematically correlated with those of every other, so that the entire structure of the universe is, though 'harmonious', not held together by real forces of any kind." (p. xxiv)

This is, of course, a great and miraculous mystery, that Leibniz had to introduce to account for the agreement between, say, the perceptions of different persons, on his assumption that persons (like other entities) are fundamentally unconnected with other things. It is a very curious assumption we shall have to discuss later, and all I can say here in its defence is that in the context of Leibniz's other assumptions it does seem required.

But it gives his system a rather absurd appearance, since it is based on a mystery that cannot be explained except by appealing to the benevolent intentions and doings of an also mysterious God. In defence of Leibniz it may be added that other philosophical systems also make mysterious assumptions that are hard to explain or understand, and that philosophies for which there are neither mysteries nor miracles must be very trivial indeed.

And there is another point to be made that shows that Leibniz at least was aware of a fundamental problem that is not very often discussed: That the similarity or identity of this person's experience and that person's experience in the end depends on some assumption, since experiences are completely private (apart from ESP), and that generally people simply assume that their experiences resemble those of other people - which, in spite of being an ordinary assumption, is therefore not less metaphysical, since it assumes far more than is given in one's own experience, and also assumes something that, by its very assumption, is untractable, precisely because it is generally assumed (again apart from ESP) that one's experiences are private, and hence cannot be compared, except indirectly, by talk about it. Up

Pre-Established Harmony and reality

The editors discuss another hypothesis of Leibniz about the mind:

"(...) the astonishing hypothesis not merely that 'every created intelligence has an organic body' but that every monad whatever has an organic body." (p. xxv)

Leibniz's reason seems to be fundamentally Aristotelian: to exist is to exist as a substance or as a form of a substance (but never as a mere form, just as with relations and properties), and in Leibniz's system monads play the role of forms. So this seems to me not as astonishing as it seems to the editors: Leibniz apparently reasoned: monads and intelligences are (as) forms of the substantial bodies they are the monads or intelligences of, and since forms cannot exist without bodies, every monad or intelligence that exists can exist only as the intelligence of some substantial body. Note also that (approximately) for Leibniz the following chain of identities held: substances are monads are mental entities are entelechies (are things that desire and believe). Up

Monads

"(..) he is ascribing to each of them [monads - M] the role of a dominating member of an infinite colony of monads - in some sense of 'dominating' which does not imply 'causally controlling'." (p. xxv)

See the end of the previous remark: desires are teleological rather than causal, and whereas causal relations may be explained in terms of antecedent conditions that first come into being and are followed by (or perhaps sometimes simultaneous with) subsequent consequences, teleological relations start with (desired ideas of) ends, sometimes followed by (ideas of) means to realise these ends.

One problem I have with Leibniz's monads, that also relates to Leibniz's rationalism, is that monads seem to be a generalization from human experience, and I see little reason to assume that reality is much like our experience of it, and much reason for the opposite: that to account for the facts as we know them, we are bound to make assumptions that go beyond our experiences or do not square with them, one example being the principle of inertia (that Aristotle could not believe since it did not square with experience, but that Galileo correctly saw as required for explaining movement of bodies). Up

Choice

"Leibniz rejects choice out of equilibrium, and choice against the preponderance of causes or reasons (..)" (p. xxvii)

Like the other points raised in the introduction, this will be more fully discussed later on. Here I only note that Leibniz, accordingly, rejected choice as caused by or arising from having no preference and also rejected choices for things one prefers less than others.

It may be added that for me the free will of a person a involves there being something in a person a, given to a as a's desires, say, that are more relevant to a's acts than anything else there is. Note that this also applies to a's desires (which accordingly are more relevant to a's desires than anything else, if indeed they are the reason for a's choice).

"It is a recurring theme of Leibniz's that although we cannot alter our beliefs or desires 'at will', we can deliberately act upon them 'as though from a distance' (..) (p. xxviii)

More precisely: we make our future beliefs and desires by our present thinking and deciding (which likewise, in so far as they are not innate, were made by our past thinking and deciding). Up

Essences and empiricism

"Locke does not grant real essences much importance (..)" (p. xxxi)

Which is rather odd, since without them - in the minimal sense of: the properties and relations that identify a kind of things as that kind of things and no other - anything seems arbitrary. However, Locke's ideas about essences derive from his ideas about epistemology, and have some plausibility in that context. Still, the problem that without essences - to be understood as analogous to those properties that make you and me human, for example - what things really are is arbitrary remains, as Leibniz notes:

"'I don't know why [Locke] always wants to make virtues, truths and species depend on our opinion or knowledge. They are present in nature, whether or not we like it.'" (p. xxxii)

I agree with the conclusion. The reason why Locke wants to make categories depend on the human mind is his empiricism, and the mistake is the same as Kant's "Copernican Revolution": to presume that what is real depends on what you (could) know to be real, rather than the other way around: you can only know what is real if what you believe is really so. And succesful technology - TV, electric light - based on science that involves the assumption of things we cannot experience seems we do know some of the properties and relations of some real things. For else it wouldn't work in practice.  Up

The special status of human beings for human beings

"(...) humanity is for him a special case - a kind whose inner nature we can not only name but even recognise, often, through its outward manifestations.)"

By imaginatively taking another's place, indeed. I agree with that, but add that it seems all animals seem to be similarly placed vis à vis animals of their kind: they are able to infer emotion from behaviour, on some presumably instinctive assumption of likeness. Whether they do so in fact seems to depend on their brain-power: chimps and dogs do, apparently, and amoebae don't, presumably (but as all animals seem to have some sort of idea of what may be edible and what may be mated with, all animals seem to be born with some notions, however crude and hormonically driven.). Up