Christian Wolff: Reasonable thoughts on the effects of nature (1723) and Ludwig Philipp Thümmig: Attempt to most thoroughly clarify the most remarkable incidents in nature, whereby one will be lead to the deepest understanding of them (1723)

Baroque Cycle of Neal Stephenson contains a lovely scene portraying a typical meeting of the Royal Society. A number of curios and weird phenomena are presented to the audience without any regulated order – one members tells a story of fying fishes living in some oceans, another describes a neat trick with a vacuum pump, while third has just developed differential calculus.

Although such a motley of topics seems chaotic, it reveals what has truly captivated the hearts of men for science – it is the extraordinary that interests us. Consideration of curiosities has for long been a part of science – there is even a pseudo-Aristotelian book Problems, which is nothing more than a collection of what the author considered weird and proposed explanations for these dilemmas. Nowadays weird has been used for good measure in popularisation of science – for instance, in the show Mythbusters dealing with such age-old problems as whether cars truly explode when driven off cliffs.

Versuch einer gründlichen Erläuterung der merckwürdigsten Begebenheiten in der Natur, wodurch man zur innersten Erkenntnis derselben geführet wird is a similar collection of curios, written by Ludvig Philip Thümmig, whom we have already met as an editor of a book of Wolffian essays. Here we finally see some of Thümmig's own work, as he ponders such scientific problems as why a boy sees everything double, why animals with two bodies combined are sometimes born, why some trees grow from their leaves and why does gravity work in different grades across the globe – Thümmig's solution to this question convinced at least his mentor Wolff, who mentions it in his own book on natural science, Vernünfftige Gedancken von den Würckungen der Natur, which is also the second book I am considering this time.

While Thümmig's book is a haphazard motley, Wolff does not fail to give us a work with systematically arranged topics. Here Wolff is once again just following a far older tradition. The nameless collector of the works of Aristotle arranged his books on nature in the following order: first came books on the general principles of natural world, then followed books on the cosmos in general and the heavens in particular, after which came books on atmospheric phenomena and earthly objects, while the story finished with books on living nature. This formal scheme was so well thought out that even Hegel essentially followed it in his own philosophy of nature. Thus, it is no wonder that Wolff himself applied this often used model of natural science.

In his natural science or physics Wolff is quite reliant on empirical information and rarely wonders from presenting the conclusions of the science of his time. One exception where Wolff's physics comes in contact with his metaphysics is the description of animal sensation, where Wolff reminds us of the Leibnizian idea of pre-established harmony: while human bodies go through certain changes in their sensory organs, their souls have corresponding sensations, although bodies and souls do not interact with one another.

A more detailed crossing of physics and metaphysics occurs in the very beginning of the work, in the description of the physical objects as complex substances. An important conclusion of this definition is according to Wolff that all the properties of the complex should be derived from the properties of its constituents and the spatiotemporal structure according to which these constituents have been combined - I have called this the lego-block view of the world. Although seemingly innocent, endorsing this view leads Wolff to some substantial consequences.

Observations suggest that there are some peculiar properties that are difficult to explain through mere spatiotemporal structure of things – for instance, the characteristic of objects gravitating toward the nearest big collection of matter or the property of warmth. Now, if these characteristics are not explainable through the spatiotemporal form of the bodies, it must be explained through the constituents of them – that is, there must be types of matter that cause gravitation or warmth.

The assumption of special matters was not a peculiarity of Wolff, but a common occurence at the time, and even Hegel commented on this habit of scientists. One just saw a peculiar phenomenon – certain kinds of metal attract or repel one another – which was explained by assuming a new type of matter, in this case magnetic matter. While the notion of caloric or heat matter and similar properties as matters sound rather quaint, we should not assume that such reification of properties is non-existent nowadays. One just has to open a book on particle physics to learn about photons or particles of electro-magnetism, glueons or the particles holding the nucleus of atoms together and perhaps even gravitons causing gravitation.

Physicists may well have good reasons for such reification in these cases, but taken to its extremes it will lead to the philosophical theory of tropes – all general properties are actually individual things, like this redness, this sweetness, this roundness. The individual things are then just mere conglomerate of these tropes – for instance, the three tropes of particular sweetness, redness and roundness combine to form a particular strawberry.

The setback of trope theories is that it is difficult to see how all properties could be reified. For instance, do not the tropes themselves have properties, such as being a trope? Is this then supposed to be yet another trope? Furthermore, a trope theorist has difficulties explaining how to account of our thinking about universals. Redness of this particular strawberry should in trope theory be completely different from redness of this particular flag – how can then we describe both of them as red? If we suppose that the two tropes are connected by being similar in some manner, we face yet another dilemma – isn't the similarity yet another property?

So much for the physics of Wolffians. Next time I shall discuss the first of many atheism controversies to come.

Andreas Rüdiger: True and false sense - Sensational mathematics

I have often wondered where Kant got the idea of dividing judgments into analytic and synthetic, analytic referring to judgments where the content of the predicate was included in the content of the subject and synthetic referring then obviously to judgements where this inclusion did not hold. It's not any difficulty in the definitions I am speaking of, but of the nomenclature that would have in Kant's days reminded the reader of two different methods of reasoning, analysis and synthesis.

Originally analysis and synthesis were used by Greek geometers as referring to processes that mirrored one another. In analysis, one assumed that the required conclusion – proposition to be proved or a figure to be constructed – was already known or in existence. One then had to go through the conditions of this conclusion in order to find self-evident principles on which the conclusion could be based.

If analysis moved from conclusions to premisses, the synthesis moved the other way. One began from some principles already assumed or demonstrated to be true and from methods that one already knew how to use, and from these principles and methods set out to prove some new theorem or to draw a new sort of figure.

A certain step in the evolution of the mathematical methods into Kantian judgement types is symbolised by Rüdiger's notion of analysis and synthesis. Just like in the tradition, Rüdiger uses analysis for a method moving from consequences to principles behind them. Yet, he also calls such method judicial and separates it from synthetic method, which he describes as invention. That is, analysis does not produce any new information, just like in Kant's analytic judgement predicate does not reveal anything that wouldn't already be in the subject. Instead, analysis merely determines whether a given proposition is clearly true or at least probable.

Rüdiger's account of synthesis or invention of new and informative truths includes even more aberrations from the traditional account. For Rüdiger, synthesis might involve also mere probable conclusions that are based on the correspondence of various sensations – for instance, by seeing that a certain effect follows always from certain conditions, we may conclude that a new occurence of similar conditions would probably lead to similar effects. Here we see Rüdiger's empiricist leanings, but he does not restrict synthesis to mere empirical generalisations – in addition he also accepts necessary demonstrations.

Rüdiger divides demonstrations into three classes, according to three components required for thinking. One type is based on the verbal form of thinking and grammar: for instance, we deduce from the statement that Jane hit Mary the related statement that Mary was hit by Jane. The second type contains various forms of reasoning, such as traditional syllogisms, but the common element Rüdiger suggests is that all of them are based on the relations of ideas – we might name these forms logical.

By far the most interesting is the third type of reasoning, the mathematical. Leibniz and Wolff had thought that mathematics was based on inevitable axioms and even empiricists like Hume grouped mathematics with logical reasoning. Rüdiger, on the other hand, clearly separates logic and mathematics. Logical reasoning is based on the relations of ideas, while mathematics is based on the sensuous element of thinking.

Rüdiger's position shares some interesting similarities with Kant's ideas on mathematics. Both Kant and Rüdiger are convinced that mathematics are not mere logic, but synthetic or inventive. True, Kant speaks of mathematics as based on intuitions, while Rüdiger speaks of sensations, but this might not be as great a difference as it first seems. Rüdigerian concept of sensation is clearly more extensive than Kant's and would probably include also what Kant called pure intuitions. Indeed, Rüdiger also separates mathematical reasoning from mere empirical generalisations – mathematical truths are not mere probabilities.

The reason behind Rüdiger's desire to separate mathematics from logic is also of interest. Once again Spinoza is the devil that one wants to excommunicate. Spinoza's Ethics is supposedly philosophy in a mathematical form, but Rüdiger notes that this is intrinsically impossible. Mathematics can rely on certain sensations, when it constructs its definitions and divisions – it can tell that triangle is a meaningful concept, because it can draw triangles. Philosophy, on other hand, does not have a similar possibility for infallibly finding sensations for its concepts – a very Kantian thought.

So much for Rüdiger this time. Next time we are back with Wolffian philosophy.