was quite well aware of the mutual relation and dependence of the 

 two. In induction, he says, the most characteristic cases are 

 investigated and an inference or hypothesis made in regard to 

 others. But these inferences, or the consequences thereof, must 

 be confirmed by trial in particular cases. Galilei has no sympathy 

 with merely formal, deductive logic, and the appeal, in special 

 cases to the Divine, as a cause, he unhesitatingly condemns; such 

 a method explains nothing just because it explains everything 

 equally easily. 



Now when Kant saw in the sciences of mathematics and 

 physics indisputable results of the harmonious combination of 

 scientific method, results which from the time of Galilei were 

 becoming more and more valuable, he realized the necessity of 

 inquiring more carefully just what that method was and of asking 

 himself how the supposed necessary and universal knowledge 

 in these sciences was possible. And so Kant commenced his first 

 critique by asking the question, how are synthetic judgments a 

 priori possible ? Now what is the significance of this question? 

 Judgments, which merely explicate what is already contained/ in 

 any given concept, are analytic judgments, and, because purely 

 formal, are always necessary and universal, that is, in Kant's 

 terminology, a priori. Such judgments as, for example, all bodies 

 are extended do not, however, add anything to knowledge. But, 

 if there is added to the concept of the subject a predicate not 

 conceived as existing within it, and not to be extracted from it by 

 any process of mere analysis, then a synthetic judgment results. 

 For example, the judgment, all bodies are heavy, is a synthetic 

 judgment, if heaviness be not conceived as a necessary part of 

 the connotation of the subject, bodies. But such a judgment is 

 not necessary or universal. It expands knowledge, but, since it 

 is. based on sense-experience, it is not a priori. It is a posteriori, 

 a synthetic a posteriori judgment. But there are, according to 

 Kant, judgments other than the analytic a priori and synthetic a 

 posteriori. There are judgments which serve to expand knowledge 

 and which likewise are necessary and universal. There are syn- 

 thetic a priori judgments. Mathematics, for example, affords 

 illustrations of such synthetic a priori judgments. All which 

 happens has its cause, is another example of such a judgment. Now 



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