...Complementary and aditional definitions of PURE LOGIC...! William Thomson, Immanuel Kant and Richard Frederick Clarke...!http://anagrammatt2.blogspot.ca/2014/09/my-re-edition-re-print-aquired.html
[A] ARCHBISHOP William Thomson
I will use a reference to the "particular" definition
or usage given by the late ARCHBISHOP of CANTERBURY,
William Thomson, of pure logic, in his Book of Logic.
I happen to have a reprint of his Book! Probably not
buried from World Libraries and re-prints on amazon.com,
but buried most likely from Universities Academia!
The Books title is:
An outline of the necessary LAWS OF THOUGHT: A treatise
on Pure and Applied Logic. By William Thomson, D.D.
5. Pure Logic (which is later in the order of discovery
than applied, inasmuch as it is formed by abstracting
from that more general science) takes no account of
modes in which we collect the materials of thought, such
as Perception, Belief, Memory, Suggestion, Association
of Ideas; although these are all in one sense laws of
thought.* Presupposing the possesion of the materials,
it only refers them to their proper head or principle,
as conceptions, as subjects or predicates, as judgements,
or as arguments. It enounces the laws we must observe in
thinking, but does not explain the subsidiary processes,
some or all of which must take place to allow us to think.
Again, in pure logic, the different processes of the mind
are regarded in their perfect and complete state; whilst
in applied, the imperfect faculties of man, the limited
opportunities of observation, the necessity of deciding
upon a question when the materials of a judgement are still
insufficient, impose many limitations on the perfection
of our knowledge.
11. Pure Logic is a science of the form, or of the formal
laws of thinking, and not of the matter. The terms form
and matter, in their philosophic use, will require some
A statue may be considered as consisting of two parts, the
marble out of which it is hewn, which is its matter or
stuff, and the form which the artist communicates. The
latter is esential to the statue, but not the former,
since the work might be the same, though the material
different; but if the form were wanting we could not even
call the work a statue. This notion of a material
susceptible of a certain form, the accesion of which shall
give it a new nature and name, may be regarded as matter,
and geometrical figures as the form imprssed in it. The
voice is the matter of speech, and articulation the form.
But as it is the form which proximately and obviously makes
the thing what it is (although there can be no form whitout
matter), the word form to be interchanged with essence and
I completely understand your doubts on my usage of the
terminology of PURE LOGIC!
But what has meaning and usage in chemistry, minerals,
language, can be completely defined using a combined
Thus I simplify the issue, by merely saying pure is not
only the specific pure H2O formula for water, but can
also mean the necessary (complete) water contents the
human body needs, as MINERAL WATER, from a mountain
spring, plus a bit of chlorine, the brain needs, etc...!
Or as you find the origin of pure bauxite from where you
can make Aluminum. Or the pure form of gold found in rock
in Nature, which is pure, but can be further purified to
a specific form of Gold. But that came from a complete
general form in nature!
Pure logic is the complete realm of the necessary rules
for thought: the realm of positive good logic, and the
realm of negative bad logic! And so on!
Anyway, I am allowed to define or make a self definition
as pertaining the redaction of my Books and studies! In
this lies my originality!
For example in thought we can show a pure perfect idea,
or a merely logic idea!
Light is white, which is logic! But in complete pure logic,
we know light is not only white, it is even out of the
range of human eyesight perception!
[B] The Critique of Pure Reason, by Immanuel Kant
I. Of the difference between Pure and Empirical Knowledge
That all our knowledge begins with experience there can be no doubt. For how is it possible that the faculty of cognition should be awakened into exercise otherwise than by means of objects which affect our senses, and partly of themselves produce representations, partly rouse our powers of understanding into activity, to compare, to connect, or to separate these, and so to convert the raw material of our sensuous impressions into a knowledge of objects, which is called experience? In respect of time, therefore, no knowledge of ours is antecedent to experience, but begins with it.
But, though all our knowledge begins with experience, it by no means follows that all arises out of experience. For, on the contrary, it is quite possible that our empirical knowledge is a compound of that which we receive through impressions, and that which the faculty of cognition supplies from itself (sensuous impressions giving merely the occasion), an addition which we cannot distinguish from the original element given by sense, till long practice has made us attentive to, and skilful in separating it. It is, therefore, a question which requires close investigation, and not to be answered at first sight, whether there exists a knowledge altogether independent of experience, and even of all sensuous impressions. Knowledge of this kind is called a priori, in contradistinction to empirical knowledge, which has its sources a posteriori, that is, in experience.
But the expression, “a priori,” is not as yet definite enough adequately to indicate the whole meaning of the question above stated. For, in speaking of knowledge which has its sources in experience, we are wont to say, that this or that may be known a priori, because we do not derive this knowledge immediately from experience, but from a general rule, which, however, we have itself borrowed from experience. Thus, if a man undermined his house, we say, “he might know a priori that it would have fallen;” that is, he needed not to have waited for the experience that it did actually fall. But still, a priori, he could not know even this much. For, that bodies are heavy, and, consequently, that they fall when their supports are taken away, must have been known to him previously, by means of experience.
By the term “knowledge a priori,” therefore, we shall in the sequel understand, not such as is independent of this or that kind of experience, but such as is absolutely so of all experience. Opposed to this is empirical knowledge, or that which is possible only a posteriori, that is, through experience. Knowledge a priori is either pure or impure. Pure knowledge a priori is that with which no empirical element is mixed up. For example, the proposition, “Every change has a cause,” is a proposition a priori, but impure, because change is a conception which can only be derived from experience.
II. The Human Intellect, even in an Unphilosophical State, is in Possession of Certain Cognitions “a priori”.
The question now is as to a criterion, by which we may securely distinguish a pure from an empirical cognition. Experience no doubt teaches us that this or that object is constituted in such and such a manner, but not that it could not possibly exist otherwise. Now, in the first place, if we have a proposition which contains the idea of necessity in its very conception, if, moreover, it is not derived from any other proposition, unless from one equally involving the idea of necessity, it is absolutely priori. Secondly, an empirical judgement never exhibits strict and absolute, but only assumed and comparative universality (by induction); therefore, the most we can say is—so far as we have hitherto observed, there is no exception to this or that rule. If, on the other hand, a judgement carries with it strict and absolute universality, that is, admits of no possible exception, it is not derived from experience, but is valid absolutely a priori.
Empirical universality is, therefore, only an arbitrary extension of validity, from that which may be predicated of a proposition valid in most cases, to that which is asserted of a proposition which holds good in all; as, for example, in the affirmation, “All bodies are heavy.” When, on the contrary, strict universality characterizes a judgement, it necessarily indicates another peculiar source of knowledge, namely, a faculty of cognition a priori. Necessity and strict universality, therefore, are infallible tests for distinguishing pure from empirical knowledge, and are inseparably connected with each other. But as in the use of these criteria the empirical limitation is sometimes more easily detected than the contingency of the judgement, or the unlimited universality which we attach to a judgement is often a more convincing proof than its necessity, it may be advisable to use the criteria separately, each being by itself infallible.
Now, that in the sphere of human cognition we have judgements which are necessary, and in the strictest sense universal, consequently pure a priori, it will be an easy matter to show. If we desire an example from the sciences, we need only take any proposition in mathematics. If we cast our eyes upon the commonest operations of the understanding, the proposition, “Every change must have a cause,” will amply serve our purpose. In the latter case, indeed, the conception of a cause so plainly involves the conception of a necessity of connection with an effect, and of a strict universality of the law, that the very notion of a cause would entirely disappear, were we to derive it, like Hume, from a frequent association of what happens with that which precedes; and the habit thence originating of connecting representations—the necessity inherent in the judgement being therefore merely subjective. Besides, without seeking for such examples of principles existing a priori in cognition, we might easily show that such principles are the indispensable basis of the possibility of experience itself, and consequently prove their existence a priori. For whence could our experience itself acquire certainty, if all the rules on which it depends were themselves empirical, and consequently fortuitous? No one, therefore, can admit the validity of the use of such rules as first principles. But, for the present, we may content ourselves with having established the fact, that we do possess and exercise a faculty of pure a priori cognition; and, secondly, with having pointed out the proper tests of such cognition, namely, universality and necessity.
Not only in judgements, however, but even in conceptions, is an a priori origin manifest. For example, if we take away by degrees from our conceptions of a body all that can be referred to mere sensuous experience—colour, hardness or softness, weight, even impenetrability—the body will then vanish; but the space which it occupied still remains, and this it is utterly impossible to annihilate in thought. Again, if we take away, in like manner, from our empirical conception of any object, corporeal or incorporeal, all properties which mere experience has taught us to connect with it, still we cannot think away those through which we cogitate it as substance, or adhering to substance, although our conception of substance is more determined than that of an object. Compelled, therefore, by that necessity with which the conception of substance forces itself upon us, we must confess that it has its seat in our faculty of cognition a priori.
III. Philosophy stands in need of a Science which shall Determine the Possibility, Principles, and Extent of Human Knowledge “a priori”
Of far more importance than all that has been above said, is the consideration that certain of our cognitions rise completely above the sphere of all possible experience, and by means of conceptions, to which there exists in the whole extent of experience no corresponding object, seem to extend the range of our judgements beyond its bounds. And just in this transcendental or supersensible sphere, where experience affords us neither instruction nor guidance, lie the investigations of reason, which, on account of their importance, we consider far preferable to, and as having a far more elevated aim than, all that the understanding can achieve within the sphere of sensuous phenomena. So high a value do we set upon these investigations, that even at the risk of error, we persist in following them out, and permit neither doubt nor disregard nor indifference to restrain us from the pursuit. These unavoidable problems of mere pure reason are God, freedom (of will), and immortality. The science which, with all its preliminaries, has for its especial object the solution of these problems is named metaphysics—a science which is at the very outset dogmatical, that is, it confidently takes upon itself the execution of this task without any previous investigation of the ability or inability of reason for such an undertaking.
Now the safe ground of experience being thus abandoned, it seems nevertheless natural that we should hesitate to erect a building with the cognitions we possess, without knowing whence they come, and on the strength of principles, the origin of which is undiscovered. Instead of thus trying to build without a foundation, it is rather to be expected that we should long ago have put the question, how the understanding can arrive at these a priori cognitions, and what is the extent, validity, and worth which they may possess? We say, “This is natural enough,” meaning by the word natural, that which is consistent with a just and reasonable way of thinking; but if we understand by the term, that which usually happens, nothing indeed could be more natural and more comprehensible than that this investigation should be left long unattempted. For one part of our pure knowledge, the science of mathematics, has been long firmly established, and thus leads us to form flattering expectations with regard to others, though these may be of quite a different nature. Besides, when we get beyond the bounds of experience, we are of course safe from opposition in that quarter; and the charm of widening the range of our knowledge is so great that, unless we are brought to a standstill by some evident contradiction, we hurry on undoubtingly in our course. This, however, may be avoided, if we are sufficiently cautious in the construction of our fictions, which are not the less fictions on that account.
Mathematical science affords us a brilliant example, how far, independently of all experience, we may carry our a priori knowledge. It is true that the mathematician occupies himself with objects and cognitions only in so far as they can be represented by means of intuition. But this circumstance is easily overlooked, because the said intuition can itself be given a priori, and therefore is hardly to be distinguished from a mere pure conception. Deceived by such a proof of the power of reason, we can perceive no limits to the extension of our knowledge. The light dove cleaving in free flight the thin air, whose resistance it feels, might imagine that her movements would be far more free and rapid in airless space, just in the same way did Plato, abandoning the world of sense because of the narrow limits it sets to the understanding, venture upon the wings of ideas beyond it, into the void space of pure intellect. He did not reflect that he made no real progress by all his efforts; for he met with no resistance which might serve him for a support, as it were, whereon to rest, and on which he might apply his powers, in order to let the intellect acquire momentum for its progress. It is, indeed, the common fate of human reason in speculation, to finish the imposing edifice of thought as rapidly as possible, and then for the first time to begin to examine whether the foundation is a solid one or no. Arrived at this point, all sorts of excuses are sought after, in order to console us for its want of stability, or rather, indeed, to enable us to dispense altogether with so late and dangerous an investigation. But what frees us during the process of building from all apprehension or suspicion, and flatters us into the belief of its solidity, is this. A great part, perhaps the greatest part, of the business of our reason consists in the analysation of the conceptions which we already possess of objects. By this means we gain a multitude of cognitions, which although really nothing more than elucidations or explanations of that which (though in a confused manner) was already thought in our conceptions, are, at least in respect of their form, prized as new introspections; whilst, so far as regards their matter or content, we have really made no addition to our conceptions, but only disinvolved them. But as this process does furnish a real priori knowledge, which has a sure progress and useful results, reason, deceived by this, slips in, without being itself aware of it, assertions of a quite different kind; in which, to given conceptions it adds others, a priori indeed, but entirely foreign to them, without our knowing how it arrives at these, and, indeed, without such a question ever suggesting itself. I shall therefore at once proceed to examine the difference between these two modes of knowledge.
So far I can extend the definition of pure logic, to at least three usages and definitions:
 Pure complete logic, is not only the purity of a chemical element of the periodical table, but the pure natural form of a element as found in nature, which is not as pure as to its main element, but complete as to what else is found with it.
 Pure complete logic, is all logic, including non-logic or illogic.
 Pure logic, as un-biassed, true and factual logic. Has no need to invent or make up stories.
 And the Immanuel Kant, pure logic, of what is pure a priori knowledge and what is not pure a priori knowledge.
I am sure there exists more usages of pure and applicable to pure logic! But if there aren’t these four listed ones, are well sufficient.
George F. Thomson