George Walford: The Logic of Logics


Some ways of thinking are more logical than others and this suggests the presence, somewhere in the background, of pure logic, a set of clear, precise and rigid laws which, if only we comply with them, will ensure that our thinking moves as if along rails to the correct conclusion. We seldom in practice welcome attempts to think with strict logic; anybody trying to bring rigorous thinking into ordinary conversation commonly gets put down with accusations of nitpicking and logic-chopping, rather than thanked for their contribution, and in serious discussion things are seldom very different. But it is reassuring to know that this final standard is there should we need it.

Unfortunately, when we turn to grasp this definitive logic it proves surprisingly elusive. Turning to ‘Logic’ in a dictionary of philosophy produces not a single set of definite rules but an involved discussion of different sorts of logic, each with its conditions and limitations. If there really is any final logic it is evidently a recondite exercise for specialists, not something we can all, if we choose, apply in practical life.

Yet clearly something regulates our thinking, it does not move completely at random. We seldom all reach the same conclusion, but great numbers of us often reach similar ones, and this indicates the presence of rules of thinking honoured in the observance. Not final rules, nor yet universal ones, but rules and systems of rules – logics – which we follow even though we do not all follow the same ones.

Two people engaged in serious discussion often find it hard to speak directly to each other’s arguments. They find themselves talking past each other; each comes to feel the other has failed to meet the points made and has even, in some indefinable way, cheated. The discussion sometimes descends into recrimination, ranging from restrained questioning of the good sense of the honourable Member to a blunt ‘Nonsense!’ and beyond. Sometimes charges of dishonesty arise, but more often each participant finds the thinking of the other illogical. People engaged in discussion tend to assume that everybody facing the same circumstances must, if thinking logically, come up with the same response. They assume that there is, and can be, only one valid way of thinking, only one valid logic.

Although some who readily accuse their opponents of lacking logic would find it hard to say at all clearly what they mean by the term, ‘logic’ usually indicates the system of rules for thinking derived from laws first formulated by Aristotle. Any recognition of other logics nearly always restricts their validity to some rarefied sphere of advanced mathematics or high-flying modern philosophy. In matters of general interest ‘logic’ almost invariably means the classical or Aristotelian logic.

From ancient times specialists have worked to develop this, and it now forms an extensive, complex system, any adequate discussion of it far beyond a small journal mainly devoted to other subjects. Yet it still rests upon the three laws formulated so long ago by its founder:

1. The law of identity: X is X.
2. The law of contradiction: Nothing can be both X and non-X.
3. The law of the excluded middle: Everything is either X or non-X.

Of these the law of contradiction (which would be better known as the law of non-contradiction) has priority.

If this system enjoys, as it claims to do, universal validity (nothing can be both X and non-X), then any thinking which diverges from it, taking an X to be also a non-X, merits condemnation. A great deal can be said about this, but for present purposes it will be sufficient to point out that Aristotelian thinking deals only with what is; it excludes time, change, development, and with them evolution. If, without qualification, every X is X and nothing both X and non-X, then a nose is totally and simply a nose, not in any sense or to any degree anything else; it can never develop into a trunk. A leg can never become a wing, or a toe a hoof. Every species is totally and simply itself, not in any sense or to any degree also another, and new species can never develop out of existing ones.

These different logical presuppositions, the one that X is (at least potentially) also non-X, the other that it is a simple, hard-edged identity, go far to explain the differing valuations placed upon biological studies. For the one side they follow a definite (though non-Aristotelian) system of thinking, while to the other they are (because non-Aristotelian) loose and inaccurate, not fully deserving to rank as sciences.

Aristotelian logic has demonstrated its validity over the millenia. The logic implied by evolutionary thinking has demonstrated its validity by bringing within the scope of systematic theory wide ranges of phenomena which Aristotelian excludes. As Hegel puts it: ‘the battle of reason is the struggle to break up the rigidity to which the understanding has reduced everything.’ In order to extend logical thinking to its maximum we have to accept both of them, and this means accepting that each of them has limitations, that Aristotle’s X is a non-evolutionary X and that of evolutionary logic an evolutionary one. Each of them has validity in certain connections, and if there are two valid logics there may be more.


Aristotelian logic emerged late in human history, and even today the greater part of life goes on without reference to it. For the most part we do treat an X as nothing more than that, but only because this offers the greater convenience; we do not accept it as a binding rule. We know that children become adults, that clothes wear out, that food quickly becomes rotten. These things, and many besides, are in process of becoming something other than they are and we treat them accordingly, educating children for adult life, expecting clothes to need replacement and either eating food soon after purchase or freezing it for future use. We treat these Xs as if they were, at least potentially, also non-Xs, and on the whole this works, producing the intended results. It does not indicate, however, that we are using evolutionary logic, for that operates according to principles the textbooks strive to formulate, although not always with complete success, while in daily life we do for the most part simply what we find convenient at the moment, without reference to any more definite principle.

Putting this panhuman practice into terms of X and non-X gives: X and non-X, although often distinct in practice, are not distinguished in principle. Both logically and chronologically, in the history of society and in individual life, this is the primary logic, imposing virtually no limitation, leaving its adherents free to deal with each situation they encounter in the easiest, pleasantest or most convenient way.


Although we all, at times, follow this primary logic, many of us sometimes follow another which comes into operation mainly in social affairs. Leaving us to act, in merely personal matters, by the primary logic, this second one tends to establish, in each affair where we interact with other people, two groupings (‘classes’ would carry too strong an implication of rigidity) commonly arranged as a hierarchy, one valued above the other. Thus actions may be brave or cowardly, loyal or treacherous, guilty or innocent, while people may be polite or offensive, books instructive or frivolous. Religious practice and social organisation, in particular, follow this logic with their sacred / secular, heaven / hell, God / devil, and ruler / ruled, employers / employed and native / foreign groupings.

More demanding than the primary logic, this requires us to allow these divisions to guide our actions even when it may be inconvenient to do so, regularly favouring fellow-citizens against foreigners, valuing sacred things above secular, and respecting rulers more than the ruled. Subscription to it tends to produce consistent or principled behaviour, giving: X is in principle distinct from non-X.


Something has already been said of the Aristotelian (formal, traditional, classical) and evolutionary logics, while dialectical, and its poor relation dialectical materialism, have been developed elsewhere. Still other logics – informal, philosophical, mathematical, symbolic and deontic – appear in the textbooks. The point has perhaps been sufficiently made, that there is no such thing as one fundamental logic, unquestionably valid, against which all propositions may be tested for validity. The logic we accept depends upon the type of world we assume ourselves to inhabit, it is the pattern of thinking appropriate to one or another ideology.


CHRISTIAN SOLDIERS: We have long been assured that capitalism promoted Christianity as a slave religion to help keep the workers quiet. This may apply to the New Testament, but the Old – also promoted under capitalism – is a different matter. ‘Nobody ever called Joshua submissive – except to God – when he fit the battle of Jericho’ [1], and other biblical heroes were fighting men taking charge of their own destinies. American negroes have drawn strength from the old stories and, looking back before the period covered by the book under review, Cromwell’s warriors, too, found in the Bible encouragement to struggle rather than submit. [1] Patrick Allitt reviewing African-American Religion in the Twentieth Century by Baer and Singer. U of Tennessee Press.


HELPING THE HOLOCAUST: IC 61 included (p.22) a note on Christopher Browning’s study of the (German) Reserve Police Battalion 101, active in the Holocaust in Poland. Although reporting that this unit consisted of very ordinary middle-aged conscripts, not Nazi fanatics, and that those of them who refused to take part in the slaughter suffered no severe punishment, this still failed to make its point at all clearly. Alan Bullock did better in his review:

The detailed interrogation of 210 out of the original 500 members of the battalion provided… a unique record of the Final Solution, seen through the eyes of those who were not its victims but its agents, not of those who gave the orders but of those who carried them out. Without the collaboration of many thousands of such helpers, the Holocaust could never have taken place. [2]

The members of that amorphous body comprising people of all nations, for which it is difficult to find any more specific title than ‘the general body of the people,’ are not helpless victims forced to obey their rulers. They are moral agents who tolerate those rulers, and support them in effect though often not of set purpose. They are, and have been from the beginnings, the source of social power. Without their help the rulers can do little, and indeed ‘the rulers,’ democratic or Nazi, running the Welfare State or the death camps, are those who enjoy their support. [2] TLS 5 Feb 93, emphasis added.


T. H. WHITE comes up with a suggestion for preventing war more practical than some, having no damned nonsense about justice: after each war, let the victors execute all officers on the losing side above the rank of colonel. Unfortunately, as he notes, even this seems unlikely to work: ‘The kings of Irish mythology were compelled by their station to march in the forefront of the battle, which occasioned a frightful mortality among them, yet there never seems to have been a lack of kings or battles in the history of the Green Isle.’ (T. H. White The Book of Merlyn)


‘One should never discount the possibility that a person might actually mean what he is saying.’ (Rudolf Peierls)

from Ideological Commentary 62, November 1993.