Vicariate Apostolic of Dahomey
Father Damien (Joseph de Veuster)
Antoine-Elisabeth Dareste de la Chavanne
Victor Augustin Isidore Dechamps
Feast of the Dedication (Scriptural)
Defender of the Matrimonial Tie
Definitors (in Religious Orders)
Dei gratia Dei et Apostolicæ Sedis gratia
Ferdinand-Victor-Eugène Delacroix
Ambrose Lisle March Phillipps De Lisle
Prefecture Apostolic of the Delta of the Nile
Johann Nepomuk Cosmas Michael Denis
Jacques-René de Brisay Denonville
Heinrich Joseph Dominicus Denzinger
Jean Desmarets de Saint-Sorlin
Deus in Adjutorium Meum Intende
Francisco Garcia Diego y Moreno
Melchior, Baron (Freiherr) von Diepenbrock
Dionysius the Pseudo-Areopagite
Institute of the Divine Compassion
Daughters of the Divine Redeemer
Johann Joseph Ignaz von Döllinger
Emmanuel-Henri-Dieudonné Domenech
Ferdinand-François-Auguste Donnet
Juan Francesco Maria de la Saludad Donoso Cortés
Clemens August von Droste-Vischering
Louis-Guillaume-Valentin Dubourg
Phillippe-Charles-Jean-Baptiste-Tronson Du Coudray
Daniel Greysolon, Sieur Du Lhut
Felix-Antoine-Philibert Dupanloup
Archdiocese of Durango (Durangum)
(Lat. de ducere, to lead, draw out, derive from; especially, the function of deriving truth from truth). The topic will be treated in two sections:
I. As an argument or reasoning process: that kind of mediate inference by which from truths already known we advance to a knowledge of other truths necessarily implied in the former; the mental product or result of that process.
II. As a method: the deductive method, by which we increase our knowledge through a series of such inferences.
I. AS AN ARGUMENT OR REASONING PROCESS
The typical expression of deductive inference is the syllogism. The essential feature of deduction is the necessary character of the connexion between the antecedent or premises and the consequent or conclusion. Granted the truth of the antecedent judgments, the consequent must follow; and the firmness of our assent to the latter is conditioned by that of our assent to the former. The antecedent contains the ground or reason which is the motive of our assent to the consequent; the latter, therefore, cannot have greater firmness or certainty than the former. This relation of necessary sequence constitutes the formal aspect of deduction. It can be realized most clearly when the argument is expressed symbolically, either in the hypothetical form:
or in the categorial form,
The material aspect of the deductive argument is the truth or falsity of the judgments which constitute it. If these be certain and evident the deduction is called demonstration, the Aristotelian apodeixis. Since the conclusion is necessarily implied in the premises, these must contain some abstract, general principle, of which the conclusion is a special application; otherwise the conclusion could not be necessarily derived from them; and all mediate inferences must be deductive, at least in this sense, that they involve the recognition of some universal truth and do not proceed directly from particular to particular without the intervention of the universal.
AS A METHOD
When, starting from general principles, we advance by a series of deductive steps to the discovery and proof of new truths, we employ the deductive or synthetic method. But how do we become certain of those principles which form our starting-points?
This ascent from the particular to the general is called induction, or the inductive or analytic method. Comparatively little attention was paid to this method during the Middle Ages. Apparatus for the accurate observation and exact measurement of natural phenomena was needed to give the first real impetus to the cultivation of the physical, natural, or inductive sciences. In these departments of research the mind approaches reality from the side of the concrete and particular and ascends to the abstract and general, while in deduction it descends from the general to the particular. But although the mind moves in opposite directions in both methods, nevertheless the reasoning or inference proper, employed in induction, is in no sense different from deductive reasoning, for it too implies and is based on abstract, necessary truths.
P. Coffey.