Now synthesis was explicable neither by reference to pure thought, the logical or elaborative faculty, which in Kant's view remained analytic in function, nor by reference to the effects of external real things upon our faculties of cognition.
The analytic method sought to express the moon's motion by integrating the differential equations of the dynamical theory.
The systematic Introduction is a characteristic production of Germany and has done excellent service in its day, though there are signs that the analytic method hitherto mainly practised is beginning to give place to something more synthetic or constructive.
In the analytic process these specific data, called elements of the distance.
In this way the Presocratics and Sophists, and still more Socrates and Plato, threw out hints on sense and reason, on inferential processes and scientific methods which may be called anticipations of logic. But Aristotle was the first to conceive of reasoning itself as a definite subject of a special science, which he called analytics or analytic science, specially designed to analyse syllogism and especially demonstrative syllogism, or science, and to be in fact a science of sciences.
They afford yet another great advantage in that the derivation of the results requires only the analytic operations of the infinitesimal calculus.
Hamilton's significance for the history of logic lies in the stimulus that he gave to the development of symbolic logic in England by his new analytic based upon his discovery or adoption of the principle of the quantification of the predicate.
Leaven, which some deem the soul of bread, the spiritus which fills its cellular tissue, which is religiously preserved like the vestal fire--some precious bottleful, I suppose, first brought over in the Mayflower, did the business for America, and its influence is still rising, swelling, spreading, in cerealian billows over the land--this seed I regularly and faithfully procured from the village, till at length one morning I forgot the rules, and scalded my yeast; by which accident I discovered that even this was not indispensable--for my discoveries were not by the synthetic but analytic process--and I have gladly omitted it since, though most housewives earnestly assured me that safe and wholesome bread without yeast might not be, and elderly people prophesied a speedy decay of the vital forces.
Really, we first experience that particular causes have particular effects; then induce that causes similar to those have effects similar to these; finally, deduce that when a particular cause of the kind occurs it has a particular effect of the kind by synthetic deduction, and that when a particular effect of the kind occurs it has a particular cause of the kind by analytic deduction with a convertible premise, as when Newton from planetary motions, like terrestrial motions, analytically deduced a centripetal force to the sun like centripetal forces to the earth.
He gave analytic accounts on his recovery.