the Critical principles, and would involve the sacrifice only of such pre-Critical doctrines as that of the intuitive character of mathematical proof. Such correction of Kant’s earlier positions is the necessary complement of his own final discovery that sense-intuition is incapable of grounding even the so-called empirical judgment. * * * * * The _Introduction_ to the first edition bears all the signs of having been written previous to the central portions of the _Analytic_.[174] That it was not, however, written prior to the _Aesthetic_ seems probable. The opening sections of the _Aesthetic_ represent what is virtually an independent introduction which takes no account of the preceding argument, and which redefines terms and distinctions that have already been dwelt upon. The extensive additions which Kant made in recasting the _Introduction_ for the second edition are in many respects a great improvement. In the first edition Kant had not, except when speaking of the possibility of constructing the concepts of mathematical science, referred to the synthetic character of mathematical judgments. This is now dwelt upon in adequate detail. Kant’s reason for not making the revision more radical was doubtless his unwillingness to undertake the still more extensive alterations which this would have involved. Had he expanded the opening statement of the second edition _Introduction_, that even our empirical knowledge is a compound of the sensuous and the _a priori_, an entirely new _Introduction_ would have become necessary. The additions made are therefore only such as will not markedly conflict with the main tenor of the argument of the first edition. HOW ARE SYNTHETIC _A PRIORI_ JUDGMENTS POSSIBLE? Treatment of detailed points will be simplified if we now consider in systematic fashion the many difficulties that present themselves in connection with Kant’s mode of formulating his central problem: _How are synthetic_ a priori _judgments possible?_ This formula is less definite and precise than would at first sight appear. The central phrase ‘synthetic _a priori_’ is sufficiently exact (the meaning to be attached to the _a priori_ has already been considered[175]), but ambiguities of the most various kinds lurk in the seemingly innocent and simple terms with which the formula begins and ends: A. ‘How’ has two very different meanings: (_a_) _How_ possible = _in what manner_ possible = wie. (_b_) _How_ possible = _in how far_ possible, _i.e. whether_ possible = _ob_. In connection with these two meanings of the term ‘how,’ we shall have to consider the distinction between the synthetic method employed in the _Critique_ and the analytic method employed in the _Prolegomena_. B. ‘Possible’ has a still wider range of application. Vaihinger[176] distinguishes within it no less than three pairs of alternative meanings: (_a_) Psychological and logical possibility.