For clear thinking and reliable conclusions logic is the thing. Emotion, rhetoric, even ideology may be useful in the political struggle, but when we want to get at the truth of a matter, rather than to win an argument or an election, what we need is logic. Logic provides the standard by which thinking, and behaviour governed by thinking, have finally to be judged.
This approach has great attractions, but it also presents difficulties. They begin to appear when we ask: Which logic? Different authorities use the term in different senses, so that what is logical in one system may be illogical in another, and one respectable work speaks of logic having no agreed definition. It goes on to advance a definition of its own, but “the pure theory of involution”  is probably not what is in the minds of most who use the term.
When it is suggested that logic be used to test a political proposal, or to expose or counter ideology, the logic advocated cannot well be the bottomless subtleties of Hegel, or the complexities of Boole’s logical algebra, or the system for which Frege found himself obliged to invent a special script. To be of general use it has to be a set of rules by which people without special training can test the validity of their own thinking and of the arguments they encounter. In this connection, and indeed almost universally except between specialists, anybody speaking of logic means traditional or Aristotelian logic, and not the whole of that but the part of it which can be confidently relied upon. They do not mean to include, for example, Aristotle’s theory of syllogisms with problematic premisses, which seems to have been almost totally wrong.  This use of the term, although limited, does not go directly against the authorities, for they mostly agree that their science finds its origins in the work of Aristotle.
Logic serves as a criterion of validity, but if validity were nothing more than the ability to satisfy the requirements of logic neither would carry more importance than the rules of chess. Logic and validity enjoy the respect they do because, accident and contingency apart, we expect thinking which logic has certified as valid to eventuate in action producing the desired result, whether this be a closer approximation to absolute truth or more bananas. The function of logic is to formulate universal relationships, so that when our thinking has been brought into conformity with these we can take it out into the world in the confidence that it will “fit” and our action be successful.
If we were to take logic to mean only Aristotle’s ideas and the system now based upon them, this would mean that people unacquainted with these could be successful only at random; obviously this is not so. Logicians recognise that people made inferences, and criticised those of others, long before the time of Aristotle;  we can add that they also maintained themselves, creating civilisations, and, further, that people unaware of his laws are making and criticising inferences, maintaining themselves and operating a society, all around us today. Evidently there is some criterion of validity, some logic, available to people who have not met that of Aristotle. There may be more than one of these, and in fact there are two; their main features appear when we take the basis of Aristotelian or formal logic and ask whether it rests upon any presuppositions.
Aristotle himself declared: “The firmest of all first principles is that it is impossible for the same thing to belong and not to belong to the same thing at the same time in the same respect.”  This has come to be known as the Law of Contradiction
(Harold WaLsby pointed out that it would be better known as the law of non-contradiction); it has since been expressed in the form: Nothing can be both x and non-x, (and appears in current textbooks in still other versions) and upon it has been erected, over the centuries, the towering structure of formal logic.
Although this law serves as the foundation of formal logic it is not basic in the sense of resting, itself, upon no presuppositions. With all respect to Aristotle it is not in that sense a first principle. In specifying a precise universal distinction it assumes a pre-existing imprecise one.
This imprecise type of universal classification rests in its turn upon something still less sophisticated, namely a process of distinction that is carried only as far as may be convenient, not attempting universality.
All action and all thinking involve distinction; we cannot act or think without acting upon, or thinking about, this rather than that. But in order to act or think it is not necessary to universalise the distinction made; I can think about this rather than that without asking whether everything else is either a this or a that, and the this now in my hand I may treat, for another purpose, as a that, perhaps using a tool as a weapon. Here distinctions are pressed only so far as may be expedient on the occasion and the logic, the mental pattern available to the subject as a guide, partakes of this adventitious quality, being little more than recollections of past experiences, not to any extent analysed or systematically related to each other. Implied by overt behaviour but rarely stated as a proposition, it is an approach unsuited to expression in the strictness of a formula, but we get close to it with: x is not non-x.
A great many people use no logic other than this, treating each case on its merits, doing whatever may be convenient on the occasion. Others sometimes act by more rigorous rules, but we all conduct a great part of our lives by expediency, for the trivial actions that occupy so much of our time – moving about, picking things up and shifting them from here to there – admit of no other criterion. If the chosen procedure does not work, or works in a way that increases dissatisfaction, this shows it to be inexpedient and hence, by this system, illogical and invalid. Argument and rational consistency are irrelevant, for expediency has no theory; it can only be practised.
The logic of expediency has the virtues of being available to everybody and widely applicable, but it also has disadvantages; possessing no firm structure it can offer little guidance, often delivering its judgement only after the event.
Expedience concerns itself only with the xs and non-xs to hand, but once this first distinction has been made, everything encountered goes into one category or the other. What appeared to be a feature merely of the xs and non-xs so far examined turns out to be a universal principle, giving the formula: x is in principle distinct from non-x.
Principle is an ambiguous term, but here the two meanings come together, for x and non-x embrace not only material things but also thoughts, actions and values, everything objective to the thinking subject, ideational as well as material. Here we have the first attempts at universal and systematic elsssification: good and bad; yin and yang, mundane and supra-mundane; natural and artificial; hot and cold; animate and inanimate; earth, water, fire and air; right and wrong; sacred and secular… The list is endless, each culture having its own variations.
Here we have also the beginnings of hierarchy. So long as anything can be treated, according to expediency, as anything else, society and the world remain a shifting incoherence. But principles are firm; when they, or the institutions embodying them, come into contact, they behave like two plates pressed edge to edge, one riding up over the other.
So long as principles are left, so to speak, to fight it out among themselves, relations between them remain unprincipled. Full development of principle requires that relations between principles be set out, and not in any general way, permitting further conflicts, but precisely. Where one principle holds another may not intrude. Or, in the Aristotelian formula: Nothing can be both x and non-x.
Distinctions of principle are firm but not clear-cut. Furthering effective action on the whole, in one way they inhibit it. They overlap, creating confusion as it were at the edges. Creatures living in the sea are fish, we must all obey the law, be loyal and tell the truth. But whales, dolphins and porpoises are mammals, a legal maxim has it that the law does not bother about trifles (de minimis non carat lex), and the requirements of loyalty and truthfulness sometimes conflict. Beyond a commitment to principle lies another step: critical scrutiny of the principles accepted, the attempt to discover rules which shall specify not only in principle but precisely what is good and what bad, the pursuit of a truth with no admixture of untruth, an x which rigorously excludes all non-x. Here, for the first time in the series, thinking turns back on itself, examining not merely the x and non-x objective to the subject but also the activity of that subject itself.
The logic of expedience governs the wide range of behaviour that can be judged by no criterion other than fitness directly for purpose. The logic of principle comes into operation when we seek consistency and order, and Aristotelian logic when attention focuses upon precision. In moving from expediency to principle the distinction between x and non-x acquired firmness, and with the further step to Aristotelian logic it attains rigour. This logic appears in social activity most notably as the hard sciences.
With the assertion that nothing can be both x and non-x, Aristotelian logic completely separates these two, leaving them with nothing in common. But to say they have nothing in common is to name something they have in common, namely nothing. Or, to put it another way, when each of them is separate from the other they have their separation in common. This only appears upon analysis; at first sight, externally, they are separate. The feature they have in common is internal: x and non-x are internally related.
Expediency deals only with what affects the agent and principle (directly, at least), only with generalities, but Aristotelian logic claims full universality, asserting it to be impossible that the same thing, whatever it may be, should both belong and not belong to the same thing, whatever that may be. Or, more briefly, nothing can be both x and non-x. The attempt to demonstrate or realise this universality encounters phenomena in which x and non-x are indissolubly united. A rock is a rock is a rock and remains so through wide variations of conditions; the statement that this x is not non-x possesses a high degree of truth. A lung behaves differently. Any definition that ignores its ability to oxygenate blood must be incomplete, but this ability depends upon the lung’s being connected, within a living organism, to a functioning heart. Here logic has to go beyond the careful discriminations of precision to the recognition of a connection between x and non-x more significant than mere external contact, the internal relatedness that gives living things their special qualities.
The only feature possessed by either x or non-x is that of not being the other. Each of them is the negative of the other and nothing more. Each of them is everything that the other is; they are identical. But each of them is also what the other is not, so that while identical they are yet opposed: x is and is not non-x.
Each logic has encountered limits which could only be overcome by transition to another, and the logic of internal relationships is no exception. Essential for useful thinking about living matter it is of limited value in social affairs, for here x and non-x are not merely related, even internally, but sometimes interdependent in such a way that if one disappears the other goes with it. The parts of a living creature continue to exist (though deprived of their most important features) after it dies, but there can be no natives without foreigners, no atheists without religion, no rulers without subjects. The members of each of these pairs depend upon each other for their identity, they have their identity in common. But although identical they are also opposed, as often appears in wars between nations,, attacks upon religion, and rebellions. The members of these pairs are constituted by their opposition, deriving their identity from it.
The forceful assertion of x in opposition to non-x enforces also the identity between them, the imposition of foreign rule producing nationalist revolts, atheism when dominant becoming a religion, and the elimination of rulers resulting in something called a democratic dictatorship of the proletariat and the attempt to impose by force a system claiming to provide freedom and plenty for all.
Being identical, x and non-x are not two but one, and equally so if they are opposed, for there again neither is anything apart from the other. Their identity in opposition resolves into: everything is x, nothing non-x. The reason for all the difficulties encountered has now become clear: it was the presence of those damned non-xs; their elimination will bring the final solution.
Capitalism, government, law, police, oppression, war, exploitation, dictatorship, industry and all the other forces imposing restrictions upon humanity have together produced a society in which they are no longer needed. In order to enjoy the freedom and plenty won by the struggles of the ages human beings have only to cast off these outworn fetters. Here we fmd the logic of repudiation, often appearing in the repudiation of logic along with all other restrictions.
When everything is x, nothing non-x, x itself disappears, for there is nothing for it to be distinguished from.Without non-x there can be no x. Unrestricted freedom cannot be realised, for although it includes freedom to live the liberated life, to relax, to dance in the streets and wander in the fields, to sing, to love, to play with children and be happy, it also includes freedom to murder, torture, exploit and oppress. Freedom without qualification is freedom to do anything, even to suppress freedom. The proponents of universal freedom fmd themselves obliged to accept the qualification that it shall not be exercised in ways that restrict the freedom of others and this simple phrase, when examined, is found to constitute acceptance of all the limitations we have encountered in moving through the series of the logics. For the freedom which these others seek to exercise is the freedom to think and act in accordance with one or another of these logics, accepting the limitations it imposes for the sake of the advantages it offers. This series of logics, taken as a whole with all its inter-relationships, is nothing less than the specification of freedom.
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SEXISM, racism, speciesism; every up-to-date reformer opposes them all. IC scorns such pettiness, striding boldly forward to attack orders-of-existence-ism: Never mind the Titanic; what happened to the iceberg?
 Kneale W. & M. 1962 The Development of Logic Oxford: Clarendon Press 740.742
 Ibid 87
 Ibid 1
 Ibid 46
from Ideological Commentary 42, November 1989.