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This form is called a

or more propositions. sorites.

III.

clusion has

The premises must be certain in order that The conthe conclusion may be necessary and apodeictic. the same If they are only probable, the conclusion will also value as be probable; if they are hypothetical, the con- mises. clusion will be the same.

The doctrine of probability is manifold and most important.

the pre

“All probability,” says Rosmini, “is, in the last analysis, based upon this reasoning: I apprehend a certain thing. I have observed that several times when such a thing was, there was also this other, that is, the being (thing) affirmed in the possible judgment. Hence, when this being is affirmed, although I do not apprehend it, still there is probability that it is. Such is the universal foundation of probability. The index or sign of the being affirmed, that is, of the truth of the proposition, is of many sorts, as many as there are possible connections and relations between one being and another. It would be too long a matter for our present purpose, though an important one, to stop in order to classify them. We will merely observe that, since probability has for its basis the connection (not known as necessary) between two entities, one of which is apprehended and the other conjectured from it as its mark, it rests no less on those connections which exist between the nature and the accidents of two entities, than on those which are given in experience, although the connection arising from the nature or the accidents is not seen. Hence there are rational probabilities and experimental probabilities, according as the connection in question is rational or purely experimental. ...

“ The rational probability which is derived from know

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ing the nature and accidents of two connected entities may be called philosophical ; the probability which is inferred from similar cases may be called mathematical. These two kinds of probability are frequently found intermingled. Philosophical probability, arising from the consideration of two entities connected together, does not lend itself to mathematical calculation, but is discovered through meditation, and this is one of the chief reasons why the calculation of probabilities has a limited sphere, beyond which when mathematicians try to go, they fall into error. And these errors may be attributed to three special causes. Either, first, the calculation does not seize the rational probability; or, second, the calculation tries also to seize the rational part and errs through the difficulty of reducing it to figures; or, third, it frequently happens that the similar cases which form the basis of experimental probability are the effect of the nature of the two connected entities and represent it; hence every time there is added to the calculation any figure to express the rational probability, the same thing is made to enter twice into the calculation. Sometimes, again, the number of similar cases results from diverse causes, that is, from the connection based upon the nature of the two entities and from other causes foreign to these ; and it is most difficult to determine how much of the frequency of similar cases is due to the one source and how much to the other. Every time, therefore, that mathematicians, not content with basing their calculations on the number of similar cases, presume to base it also on the causes that may have produced them, they almost inevitably fall into error. And they do the same, if, omitting to include in the calculation the probability which arises from causes, they deal merely with the number of similar cases, because most frequently this number cannot be derived from experience save in a very imperfect and often irregular manner" (Logic, S$ 1073-1076). The logical relation of the calculation of probabilities to the distributive judgment has been treated with great clearness by F. A. Lange in his Logische Studien, pp. 99 sqq.

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112.

sources

of truth is

The heuristic or inventive method teaches Three how truth may be obtained from the sources from

which a within the reach of man. These sources are, knowledge generally speaking, three: first, authority and derived. tradition ; second, observation and experience; and, third, reasoning-each of which may, again, be subdivided into many. The question of how the various human faculties must be applied to these sources in order to draw from them pure and abundant knowledge, and the question of how certain external means, which direct and aid these faculties, are to be applied, afford abundant material for this part of logic.

I13

didactic

The didactic method is general or particular, The according as it contains the general principles for method the communication of truth, or particular rules for general or

particular. the teaching of special sciences.

is either

I14.

three

Each of these three methods has a supreme Supreme

principles principle which directs it. That of the apodeictic of the method is : Given a proposition which is certain, methods. all that is implicitly contained in it is also certain. That of the heuristic method is : The idea of being, which is the light of reason, when applied in the proper way to new feelings or to cognitions

already possessed, produces new cognitions. That of the didactic method is : Let the truths which it is desired to teach be arranged in such an order that those which precede do not require those which follow in order to be understood.

SCIENCES OF PERCEPTION.

Psychology and Cosmology.

Why Ideology and Logic were called Sciences of Intuition.

115. IDEOLOGY and Logic were called Sciences of Intuition, because they treat of the means of knowing, and this is ideal being, which is intuited. After we have come into possession of the means of knowing, we have still to apply it to the various beings that present themselves to us, and to try to discover their ultimate grounds. But the first application which we can make of the means of knowing to beings, we make by means of perception. Since the only function of the intellect is that of intuition, there remain for the reason the two functions of perception and reflection. Now, we cannot reflect upon anything relating to real beings unless perception supplies the material. The abstract sciences, therefore, cannot be legitimately built up, except through reasoning based upon material supplied by perception.

In answer to the question, “What means has the human reason for knowing essences, or for forming the ideas of things ?" Rosmini says, " These are four: (1) perception; (2) analysis and synthesis ; (3) the perception of natural

or conventional signs, and chief among these latter words, (4) integration" (New Essay, vol. iii. $ 1220 ; cf. under § 103). Rosmini entirely agrees with Kant, that nothing respecting the nature of reality can be known except through feeling; but he differs from Kant in holding that we can infer by reason the real, and not alone the ideal existence of certain beings-for example, of a First Cause or God.

116.

is

external

the two sciences

Now, what are the beings which we can per- What we ceive ? All those, and only those, which fall under can per our feeling, wherein alone we find reality-our- and the selves and the external world. Hence the philo-edela. sophical sciences of perception are Psychology and Hence Cosmology.

Pyschology and

Cosmo“The science of the world, or Cosmology, is unquestion- logy. ably a science of perception and observation, and if by world is meant all that is created, Psychology itself becomes a material part of Cosmology, since, after all, man is a member of the world. But it is one thing to consider sciences from the point of view of their subject matter, another, to regard the fountain from which they spring. If Cosmology be considered in relation to the source from which man draws it, it is readily seen to rise out of Psychology, inasmuch as it is a science of perception and observation. ... In the feeling of the soul there is a duality, there is a subjective element, and there is an extra-subjective element, which through reflection respectively change into Ego and non-Ego. . . . Hence it is the feeling of the soul that enables us to know the material universe ... Thus Psychology furnishes the first rudiments to Cosmology. Cosmology is, in truth, conceived in the womb of Psychology, as the known world exists in the bosom of the soul ” (Psychology, SS 24-26).

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