1763, distinguishes—­contrary to Crusius—­between logical opposition, contradiction or mere negation (a and not-a, pleasure and the absence of pleasure, power and lack of power), and real opposition, which cannot be explained by logic (+_a_ and -a, pleasure and pain, capital and debts, attraction and repulsion; in real opposition both determinations are positive, but in opposite directions).  Parallel with this it distinguishes, also, between logical ground and real ground.  The prize essay, Inquiry concerning the Clearness (Evidence) of the Principles of Natural Theology and Ethics, 1764, draws a sharp distinction between mathematical and metaphysical knowledge, and warns philosophy against the hurtful imitation of the geometrical method, in place of which it should rather take as an example the method which Newton introduced into natural science.  Quantity constitutes the object of mathematics, qualities, the object of philosophy; the former is easy and simple, the latter difficult and complicated—­how much more comprehensible the conception of a trillion is than the philosophical idea of freedom, which the philosophers thus far have been unable to make intelligible.  In mathematics the general is considered under symbols in concrete, in philosophy, by means of symbols in abstracto; the former constructs its object in sensuous intuition, while the object of the latter is given to it, and that as a confused concept to be decomposed.  Mathematics, therefore, may well begin with definitions, since the conception which is to be explained is first brought into being through the definition, while philosophy must begin by seeking her conceptions.  In the former the definition is first in order, and in the latter almost always last; in the one case the method is synthetic, in the other it is analytic.  It is the function of mathematics to connect and compare clear and certain concepts of quantity in order to draw conclusions from them; the function of philosophy is to analyze concepts given in a confused state, and to make them detailed and definite.  Philosophy has also this disadvantage, that it possesses very many undecomposable concepts and undemonstrable propositions, while mathematics has only a few such.  “Philosophical truths are like meteors, whose brightness gives no assurance of their permanence.  They vanish, but mathematics remains.  Metaphysics is without doubt the most difficult of all human sciences (Einsichten), but a metaphysic has never yet been written”; for one cannot be so kind as to “apply the term philosophy to all that is contained in the books which bear this title.”  In the closing paragraphs, on the ultimate bases of ethics, the stern features of the categorical imperative are already seen, veiled by the English theory of moral sense, while the attractive Observations on the Feeling of the Beautiful and the Sublime, which appeared in the same year, still naively follow the empirical road.