His Studies in Deductive Logic, consisting mainly of exercises and problems for the use of students, was published in 1880.
If their view is correct, the theory appears to be a remarkable example of deductive reasoning.
All we aspire to add is that, in order to attain to real truth, we must proceed gradually from sense, memory and experience through analogical particular inference, to inductive and deductive universal inference or reasoning.
The work as a whole is a striking example of the weakness of treating economic problems from a purely a priori standpoint by the deductive method.
These attempts at the unification of algebra, and its separation from other branches of mathematics, have usually been accompanied by an attempt to base it, as a deductive science, on certain fundamental laws or general rules; and this has tended to increase its difficulty.
For De Maillet not only has a definite conception of the plasticity of living things, and of the production of existing species by the modification of their predecessors, but he clearly apprehends the cardinal maxim of modern geological science, that the explanation of the structure of the globe is to be sought in the deductive application to geological phenomena of the principles established inductively by the study of the present course of nature.
It was counteracted to some extent by the study at the universities of the deductive logic of Aristotle and the inductive logic of Bacon, by parts of Mill's own logic, and by the natural realism of Reid, Stewart, and Hamilton, which met Hume's scepticism by asserting a direct perception of the external world.
But he laid too much stress on reasoning as syllogism or deduction, and on deductive science; and he laid too much stress on the linguistic analysis of rational discourse into proposition and terms. These two defects remain ingrained in technical logic to this day.
Similar views were arrived at by Goethe, though by the deductive rather than the inductive method, and were propounded in his famous pamphlet, Versuch die Metamorphose der Pfianzen zu erklren (1790), from which the following is a quotation: The underlying relationship between the various external parts of the plant, such as the leaves, the calyx, the corolla, the stamens, which develop one after the other and, as it were, out of one another has long been generally recognized by investigators, and has iii fact been specially studied; and the operation by which onc and the same organ presents itself to us in various forms has been termed Metamorphosis of Plants.
Lastly, the science of inference is not indeed the science of sensation, memory and experience, but at the same time it is the science of using those mental operations as data of inference; and, if logic does not show how analogical and inductive inferences directly, and deductive inferences indirectly, arise from experience, it becomes a science of mere thinking without knowledge.