be inconsistent. The datum, Things equal to the same are equal to one another, is an example of guaranteed data; the datum, The object I see exists independently of vision, is an example of unguaranteed data.

4. Another important division of data, viz., into judicial and non-judicial data, will fall to be considered when I treat of Induction (Book II., chap. ii.).

XXXVIII.

An axiom is a guaranteed datum. Axioms are either discoverable or undiscoverable. The axiom, A whole is greater than its part, is an example of the latter. The axioms, A space limit is contained in a space, A time limit is contained in a time, are examples of the former. The thesis, Two triangles that have two sides and the included angle in the one equal to two sides and the included angle in the other are equal, is a discoverable axiom. The mental structure admits of our apprehending a space limit,—a limit of a part of space-e.g. the sky, as though it did not suppose a beyond,-as though it were not essential to it to be contained in a space. A like mental indolence gives room for the apprehension of a time limit,-a limit of a part of time—e.g. the beginning of Cosmos,as though it were not essential to it to be contained in a time, as though it did not suppose an antecedent part of time. To disabuse itself of the error, the mind needs to be roused to scrutiny: over and above seeing, it must look. The scrutiny dissipates the error without the help of evidence, so that intuition, and not infer

ence, is the discoverer of the truth of the theses, A space limit is contained in a space, A time limit is contained in a time. In relation to certitude the theses are axioms, not conclusions. A child is told that above the sky is a region named Heaven. His imagination had bounded this region by another sky which, in advance of scrutiny, had passed with him for a limit not contained in a space,- -a limit that does not suppose a beyond. But scrutiny is challenged, and when he strives to imagine the limit as excluding a beyond, he fails. Another region bounded by another sky emerges. Several other abortive trials of this kind, which perhaps project him into a seventh heaven, terminate in the certitude that there is no end of upward beyonds. So, in the writer, somewhere about his seventh year, originated his idea of Infinity,—an event that constitutes one of the most conspicuous and ineffaceable epochs of his life. He did not distinctly formulate the thesis, A space limit is contained in a space he unconsciously discovered its truth: the event originated unconscious knowledge of the truth of the thesis. One might easily fall into the error that the discovery was a conclusion. It might be supposed that the abortive trials were so many instances of the exclusion of containing spaces by space limits, and constituted evidence for the induction, that all such limits exclude containing spaces; but the discovered thesis is guaranteed, whereas it is not competent to induction to beget discernment of inconsistency of the opposite, and multitude of instances has no weight with deduction. On this more light will be thrown when we treat of Deduction and Induction. Ignorance that it is essential to evidence to be a thesis other than the thesis urged on belief misled Euclid into a counterfeit

of demonstration as regards the thesis, Two triangles that have two sides and the included angle in the one equal to two sides and the included angle in the other are equal. The thesis, although not obvious without scrutiny, convinces scrutiny of its truth without the help of another thesis.

XXXIX.

Fact is intuitable reality. The name, fact, is sometimes used as denoting unintuitable as well as intuitable reality; but, as it is important to distinguish intuitable reality by a special name, the name should be confined to the narrower meaning.

XL.

Reasoning is either communicative or tacit, the former when it is discourse for the enlightenment or deception of another, the latter when it is discovery of truth or argument, or speculation in quest of such discovery.

CHAPTER IV.

THE APPARITIONAL AND INAPPARITIONAL.

XLI.

1. COLOURS, sounds, odours, flavours, ideas of bodies, are examples of objects that are appearances. Identity, familiarity, durability, infinity, necessity, value, polity, are examples of objects that are not appearances. If the term, phenomenon, were applied according to its etymological import, it would be the common name of objects that are appearances, it would be confined to these, while the immediate objects symbolic of identity, familiarity, durability, etc., would not be classed as phenomena. But the distinction between objects that are and objects that are not appearances is now I believe made for the first time, and therefore the term, phenomenon, cannot be supposed to have been customarily restricted, even by philosophers, to the former. For this reason it is presumable that the kind to which Kant applied and restricted the term, intuition, includes objects that are not appearances; that discernment of identity, for example, is, according to this idea, an intuition. Had he confined the term to the denotement of discernment of objects that are appearances, he would have turned its familiarity to

good account, for no species of discernment better deserves a familiar non-descriptive 1 name. 1 To fill the void I distinguish immediate objects that are appearances and the corresponding remote objects as apparitional. The idea of a man is an apparitional idea, and a man (supposing man to resemble the ideal image whereby he is known) is apparitional. The idea of electricity is inapparitional. The ideas of identity, durability, familiarity, etc., are inapparitional, and the things they symbolise are inapparitional. also distinguish as apparitional all discernments of which the objects are appearances, and the opposite species as inapparitional.

I

2. Appearances, whether immediate or remote objects, include all objects of sensational intuition, e.g. colour, figure, solidity, flavour, odour, heat, cold, and the corresponding remote objects; they include all objects of emotive intuition, e.g. beauty, ugliness, virtue, purity, vice, foulness, nobleness, baseness, and the concretes of which these are attributes. They seem to include representations of past consciousness from which we derive what we know of consciousness that is not sensationally or emotively intuited, e.g. representations of remembrance, imagination, judgment, volition, etc. I do not pretend to trace the whole of the boundary that divides between appearances and the inapparitional. I am at a loss in which of the kinds to place our ideas of mental events not originally made known by sensational or emotive intuition, and in which to place the Ego quá object.

1 Non-descriptive names are those that respectively consist of a single word, e.g. man; descriptive names are those that respectively consist of two or more words, e.g. John's horse,