thought properly so called. Their analytical character is a necessary consequence of the constitution of the thinking faculty, and is so far from being a proof of the unsoundness or frivolity of logical speculations, that it is the strongest evidence of their truth and scientific value, and leads to most important consequences, both in Logic and in Psychology.

The nature of these judgments, as well as of those distinguished as metaphysically necessary, will be examined in the following chapters.

CHAP. V.

ON THE PSYCHOLOGICAL CHARACTER OF METAPHYSICAL NECESSITY.

A DISTINCTION between necessary and contingent matter is found, somewhat out of place it is true, but still it is found, in most of the older, and, among English writers, in most also of the recent treatises on Logic. The boundaries of each, however, are not in the majority of instances determined with any approach to accuracy. Among the schoolmen, the favourite example of a proposition of the highest degree of necessity was omne animal rationale est risibile, an example consistent enough with the medieval state of physical science, but which in the present day will scarcely be allowed a higher degree of certainty than be

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Matter in this sense must not be confounded with the modality recognised by Aristotle and by most of the modern German Logicians. The former is an understood relation between the terms of a proposition; the form of the proposition being in all cases A is B;" and is supposed to be of use in determining the quantity of indefinites. The latter is an expressed relation; the form of the necessary proposition being "A must be B;" and this is applicable to universal and particular propositions indifferently. The admission of the latter is still a point of dispute among eminent authorities: the admission of the former will be tolerated by no Logician who understands the nature of his own science.

longs to any other observed fact in the constitution of things. An eminent modern Logician gives as an example of a proposition in necessary matter, “all islands are surrounded by water," an example which is only valid in so far as the predicate forms part of the notion of the subject, and which, therefore, has no other necessity than belongs to all analytical judgments, a necessity derived from the form, not from the matter. The distinction itself, though altogether out of place when Thought is considered merely in its relation to Logic, is, in a psychological point of view, of considerable importance. The following remarks will, it is hoped, throw some light on its true character.

All analytical judgments are necessary; but they cannot properly be said to be in necessary matter. They are all ultimately dependent on the Principles of Identity and Contradiction, "Every A is A," and "No A is not A:" principles, the neces

Examples of this kind were indeed indiscriminately admitted by the scholastic Logicians, who held any proposition to be in necessary matter, in which the predicate was part of the essence, or necessarily joined to the essence, of the subject. But this classification, though tenable perhaps in connection with realist metaphysics, is inconsistent with an accurate discrimination between the matter and the form of thought.

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Kant, Kritik der r. V. p. 133. Proleg. §. 2. He derives all analytical judgments from the Principle of Contradiction. It would be more accurate to distinguish this principle from that of Identity, and to derive the negative judgments from the former, the affirmative from the latter.

sity of which arises solely from their form, without any relation to this or that matter. That every triangle has three sides, arises from a mere analysis of the notion of a triangle; as that every island is surrounded by water, arises from a mere analysis of the notion of an island. This necessity is derived solely from the laws of formal thinking.

Of synthetical judgments, every statement of a physical fact is in contingent matter; at least if

the opposite term be used in its highest sense.$test of However rigidly certain phenomena may be djal

deduced from the assumption of a general law of nature, the law itself remains nothing more than an observed fact, of which we can give no other explanation, than that it was the will of the Creator to constitute things in a certain manner. For example: that a body in motion, attracted by a force varying inversely as the square of the distance, will describe an ellipse having the centre of attraction in one of the foci,-this is matter of demonstration: but that the earth is such a body, acted upon by forces of this description, is matter of fact, of which we can only say that it is so, and that it might have been otherwise. The original premise being thus contingent, all deductions from it are materially contingent likewise.

The same is the case with all psychological judgments, so far as they merely state the fact that our minds are constituted in this or that manner. But there is one remarkable difference

between this contingency, and that which is presented by physical phenomena. The laws of the latter impose no restraint on my powers of thought: relatively to me, they are simply universally observed facts. There is therefore no impediment to my uniting in a judgment any two notions once formed; though the corresponding objects cannot, consistently with existing laws of nature, be united in fact. I may thus conceive a mountain moving, or a stone floating on the water; though my experience has always presented to me the mountain as standing, and the stone as sinking. But as regards Psychology: the powers of my mind cannot be presented to consciousness, but under one determinate manifestation. The only variety is found in the objects on which they operate. I am thus limited in my power of forming notions at all, in all cases where I am, by mental restrictions, prevented from experiencing the corresponding intuition. I have thus a negative idea only of the nature of an intelligent being constituted in a different manner from myself; though I have no difficulty in supposing that many such exist. I can suppose, for instance, that there may exist beings whose knowledge of material objects is not gained through the medium of bodily senses, or whose understanding has a direct power of intuition; but to conceive such a being is beyond my power; conception being limited to the field of positive intuitions. In another point of view,