What really distinguishes the analogical from the syllogistic inference is not so much the progress from the particular to the particular in contradistinction to the descent from the general to the particular, as the difference in the certainty about the inner connection of the conceptions that are given in the premises. When one instance (as in a geometrical figure) really gives us the inner connection between certain attributes and certain others, we do not need any more an analogical inference to conclude about the connection of these attributes in other or new instances, but may do this syllogistically. The Inductive conclusion does not present us with anything new in relation to the analogical inference; it only extends the consequence which analogy draws for one case to the whole class of objects which agree with the former objects in the definite relation which made the analogical inference possible.
PSYCHOLOGICAL.
Mental acts have intensity, a definite magnitude, and so are conceivably measurable. But for measurement proper, the amount of difference between them must be ascertainable. This is not given by immediate judgment, but must be sought through circuitous means taught by psycho-physics.
It is not to be admitted that only rough measurements of mental acts are possible. Practice brings considerable accuracy in determining both the quality, e.g. of the situation of musical notes on the scale, and of intensity, e.g. of the light of the stars, and of intellectual attainments or ability, e.g. under the marking system.
Fechner starts from the principle that if several values are given as increasing and decreasing, it is possible to judge of the equality or inequality of any two, and so to determine a number of equivalent magnitudes. On this principle all physical measurement is based. In that sphere there is the difficulty that equivalent units cannot be determined with perfect accuracy. The errors thus arising are diminished by artificial means of observation, and by repetition of the measurement. The arrangement of the stars in classes according to their degrees of brightness shows that equality in sensations of light may be perceived, and the amount of inequality measured. Hence every psychical difference may be regarded as a definite multiple of the difference between two adjoining degrees on a scale of intensity. A psychical measure may thus be obtained from determinations of equality in different parts
