It is somewhat peculiar to notice that almost all notable German philosophers of the period wrote a textbook on logic. Considering that there had been no notable additions to Aristotelian syllogistic, one might think that the market would have quickly been saturated with these books. Of course, one would then be forgetting that logic books of the time contained something beyond syllogisms and were more like books on methodology. Thus, they even gave the philosopher a chance to share his opinion on the proper means to do philosophy. Hence, it is not surprising to find Bilfinger in his Praecepta logic attacking Rüdigerian idea that mathematical and logical method would not be equivalent terms.
Bilfinger continues the trend of putting logic itself in logical form, that is, of using the formal schema of definitions, propositions and corollaries. An interesting part of his exposition is the heavy use of problems, that is, of practical propositions suggesting solution to some task, which especially emphasises the methodological part of the book. This methodological feeling is also heightened by an appendix concentrating in the use of logic in academic disputations – Bilfinger gives quite practical advise, for instance, on the means by which a defender or opponent of a thesis can look for arguments for or against some proposition.
As is often the case, the most interesting part of the book is the first one dealing with the ideas or concepts. Bilfinger's notion of idea is quite representational – idea is like a picture of something, although it might indeed be quite an obscure picture. The primary source of ideas for Bilfinger is our sense or experience, but we can then produce new ideas out of these first ones, e.g. through recombination, analogies and abstraction. Especially abstraction is a potent source of mistakes, because it might lead to embodiment and substantialisation of mere properties. This might happen e.g. in physics, where we speak of wind, which is nothing else but movement of air, or in psychology, where different capacities of mind are thought of as distinct entities, like Aristotelian souls.
The practical aim of Bilfinger with ideas is their clarification, that is, making them better tools for identifying things which they represent. This means for Bilfinger primarily making them more intuitive, that is, connecting them to ideas that are directly connected to what they represent. Most of our ideas are mere signs for other ideas – this is especially true of words, but also e.g. of some written symbols (like + and -), inflections of speech etc. Words should be defined, so that we could find marks which help to distinguish things signified by these words from other things.
Mere definitions are still not enough for Bilfinger. Even if we would have a definition of, say, God as the most perfect entity, we still wouldn't know from this mere definition whether there really could be possible things represented by this definition – for instance, even if we had a definition of a biangled figure, there still couldn't be any biangled figures. Thus, Bilfinger notes, the so-called Cartesian proof of God's existence (what Kant later called an ontological proof) wouldn't work if we weren't sure about the possibility of the notion of God. A better foundation for reliable information, according to Bilfinger, is a real definition, which gives an account of causal processes that would generate things signified by certain words. Because all things are ultimately generated by God, perfect real definitions would show how things are connected to God.
Ideas are connected to form judgements or propositions, and at this point Bilfinger's account starts to become more and more formulaic, with all the different forms of judgement. A more interesting thing is what methods to use for accepting propositions. Experience is, according to Bilfinger, undoubtedly a starting point of all cognition, whether it is formed through passive observation or through active experimentation. Still, experience is not the whole basis of cognition, Bilfinger continues, because we must still make some deductions to move from particular experiences to generalisations – for instance, although we can see light revealing a rock, we need still something more to conclude that light is a general cause for seeing things. Deductions might even lead us to things we cannot observe straightaway, Bilfinger says, for example, when we deduce the existence of caloric matter from observing its effects or heat.
After moving from propositions to syllogisms, Bilfinger's exposition becomes even more formulaic, although it does have its moments, especially in discussion of problems, for instance, when Bilfinger points out that a solution to a problem must be 1) a possible solution (perpetuum mobile is a solution to nothing), 2) a real solution of the problem, 3) a full solution (diligence alone is not enough for becoming a scholar) and 4) accurate (phases of the Moon are not an accurate enough criterion for deciding when to sow the seeds).
Despite these interesting tidbits, Bilfinger's logical lessions contain nothing surprisingly novel. Indeed, the same verdict can be pronounced on his whole philosophical career. He was undoubtedly a historically important figure, because he both introduced Chinese philosophy to a serious discussion in German culture and also started a move within Wolffian school to a more Leibnizian way of thinking. Yet, in both cases Bilfinger was again merely a follower of other philosophers and not an imaginative and creative thinker.
This is as much as we'll see of Bilfinger. We shall continue with logical treatises and this time check whether Darjes has anything new to say about it.