A System of Logic
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"Logic is not the science of belief, but the science of proof"
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John Stuart Mill did not by any means invent logic. The ability to think one thing because another thing is so is perhaps essential to humans, and had been formally studied at least since Aristotle. What made 'A System of Logic, Ratiocinative and Inductive, Being a Connected View of the Principles of Evidence and the Methods of Scientific Investigation' such an instant success was the (relative) clarity it brought to the subject. Mill defined just five, and only five, ways (known as 'Mill's Methods') of determining whether causes and effects are connected, and so produced a system which became an important source for all the experimental sciences.
This abridgement reduces the original 427000 words down to 3096 (1%), giving an estimated reading time of 20 minutes. It is based on the condensed version first published by Sir John Hammerton in 1919.
John Stuart Mill
Squashed version edited by Glyn Hughes © 2011
I - NAMES AND PROPOSITIONS
LOGIC is not the science of belief, but the science of proof, or evidence; and its province must be restricted to that portion of our knowledge which consists of inferences from truths previously known, whether those antecedent data be general propositions or particular observations and perceptions. It includes the subservient operations of naming, definition and classification.
A proposition may be defined as 'discourse in which something is affirmed or denied of something.' Every proposition consists of three parts - subject, predicate and copula. The predicate is the name denoting that which is affirmed or denied. The subject is the name denoting the person or thing of which something is affirmed or denied. The copula is the sign denoting that there is affirmation or denial.
Thus in the proposition 'the earth is round,' the predicate is the word 'round,' which denotes the quality affirmed or 'predicted'; the subject is the words 'the earth,' of which the quality is predicted; and the copula is the word 'is,' which is a mark of affirmation.
Every act of belief supposes two nameable things; every proposition consists of two names, and affirms or denies one of these names or the other.
Propositions may be affirmative, e.g. 'Caesar is dead,' or negative, e.g. 'Caesar is not dead.' They may be universal, e.g. 'All men are mortal,' or particular, e.g. 'Some men are mortal, or indefinite, e.g. 'Man is mortal,' or singular, e.g. 'Caesar is mortal.'
When we further examine the general nature of the assertions of propositions, we find that in every proposition is either existence, co-existence, sequence, causation, or resemblance. This five-fold division is an exhaustive classification of matters of fact; of all things that can be believed or tendered for belief, of all questions that can be propounded and all answers that can be returned to them.
A distinction must be drawn between what may be called real and verbal propositions, between such propositions as predicate of the subject more than its name connotes, and such propositions as merely express what is connoted by the significance of the subject name. Thus, 'Man is a rational being' is a verbal proposition; while 'Man is liable to malaria' is a real proposition.
A definition is a proposition declaratory of the meaning of a name, and the meaning of a name is its connotation. The meaning of the word may be expressed by replacing it by two or more words which together cover the same connotation, and a perfect definition declares all the facts which a name signifies. A proposition which defines a name by one of its accidents is 'a description,' not a definition.
II - RATIOCINATION
THERE are two main types of reasoning: Induction - inference of a proposition from propositions less general; and Ratiocination, or Syllogism - inference of a proposition from propositions equally general or more general. All valid ratiocination may be arranged in certain forms or figures known as syllogisms. A syllogism consists of three propositions, namely, the proposition to be proved, the 'conclusion,' and two other propositions which prove it - the premises. There must be three, and only three terms - the subject and predicate of the conclusion, called respectively the minor and major terms, and another called the 'middle term,' which must not occur in both premises.
If we analyse the process involved in every syllogism we find that it is based on two principles. The first, which is the principle of affirmative syllogisms, is that things which co-exist with the same thing, co-exist with one another. The second, which is the principle of negative syllogisms, is that a thing that co-exists with another thing with which a third thing does not co-exist, is not co-existent with that third thing.
We have now to inquire whether the syllogistic process, that of reasoning from general to particulars, is or is not a process of inference. When we say:
All men are mortal; The king is a man; Therefore, the king is mortal, do the premises prove the conclusion, is there any real inference? It is evident that if the proposition 'all men are mortal' be true the king must be included in the assertion, and therefore the syllogistic process is superfluous. Regarded correctly, the inference is made in the major premise. We know nothing about all men; but from the observation of many men we infer that all men are mortal.
General propositions, therefore, are merely registers of inferences made and short formulae for making more; and the conclusion is not an inference drawn from the formula but an inference drawn according to the formula. The major premise expresses individual cases. The minor premise is the place of comparison.
A, B, C, my father and my forefathers, and an indefinite number of other persons were mortal. The king resembles all these persons in the attributes connoted by the word man. Therefore, he further resembles them in the attribute mortality.
We thus obtain a universal type of the reasoning process. Certain individuals have a given attribute; an individual or individuals resemble the former in certain other attributes; therefore they resemble them also in the given attribute.
Where the resemblances necessary for inference are obvious to the senses, as in the king's resemblance to mortal persons, no difficult deductive process is necessary; but in many cases the required resemblances can only be indirectly established by a train of inductive and deductive processes.
Thus, suppose the syllogism to be 'All arsenic is poisonous.' In this case probably the minor premise would itself require to be established by a syllogistic process thus: Whatever substance gives certain chemical tests is arsenic; this substance gives these tests; therefore this substance is arsenic. Here, therefore, we have two syllogisms, and the major term of each is an induction. In the deductive sciences the processes of induction and deduction are numerous and complicated. It must be noted that even the most deductive sciences start from inductions, and that even the axioms of mathematics are inductions from the evidence of our senses.
III - INDUCTION
INDUCTION is the operation of the mind by which we infer that what we know to be true in a particular case or cases will be true in all cases which resemble the former in certain assignable respects. The mere summing up of details in a single proposition is not induction, but colligation; induction always involves inference from the known to the unknown, from facts observed to facts unobserved.
The fundamental principle of induction is the proposition that the course of nature is uniform. The test of any induction is its consistency with inductions which have been found invariable in experience. If an induction conflicts with stronger inductions it must give way. It is the part of the logic of induction to find certain and universal inductions, and to use them as criteria.
At the root of the whole theory of induction is the notion of physical cause. To certain phenomena, certain phenomena always do, and, as we believe, always will, succeed. The invariable antecedent is termed the 'cause,' the invariable consequent, the 'effect.' Upon the universality of this truth depends the possibility of reducing the inductive process to rules.
Invariable sequence, however, seldom subsists between a consequent and one single antecedent; the consequent usually follows from the concurrence of several antecedents. In such a case it is usual to style the cause that antecedent which came last into existence, or whose share in the matter is the most conspicuous, or whose share in the matter is most easily prevented or encouraged. But the real cause is the whole of the antecedents, the whole of the contingencies of every description, which being realized, the consequent invariably follows. Yet even invariable sequence is not synonymous with causation. The sequence, besides being invariable, must be unconditional.
WE may define, therefore, the cause of a phenomenon to be the antecedent, or the concurrence of antecedents, upon which it is invariably and unconditionally consequent. To distinguish conditionally uniform sequences from those unconditionally uniform is part of the problem of induction. All phenomena have unconditional antecedents, and these antecedents have prior antecedents, and so on, till we come to one primeval cause or a conjunction of several - the so- called permanent causes.
In the analysis of sequences into conditional and unconditional, the first operation is to ascertain and distinguish antecedents and consequents. The next step is to trace the connexion between antecedents and consequents, and this we can do only by a consideration of some of the antecedents or consequents under other conditions; we must either find an instance in nature suited to our purposes, or by an artifical arrangement of circumstances make one. When we make an artificial arrangement, we are said to experiment; and experimentation has great advantages over observation in that it often enables us to obtain innumerable combinations of circumstances which are not to be found in nature.
There are four experimental principles, or canons, on which causation may be established or partly proven:
FIRST CANON. If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree is the cause (or effect) of the given phenomenon. This is sometimes known as the method of agreement.
SECOND CANON. If an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur, have every circumstance in common save one, and that one occurring only in the former, the circumstance in which alone the two instances differ is the effect or the cause, or a necessary part of the cause, of the phenomenon. This is sometimes known as the method of difference
THIRD CANON. If two or more instances in which the phenomenon occurs have only one circumstance in common, while two or more instances in which it does not occur have nothing in common save the absence of that circumstance, the circumstance in which alone the two sets of instances differ is the effect or cause, or a necessary part of the cause, of the phenomenon.
FOURTH CANON. Subduct from any phenomenon such part as is known by previous inductions to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents.
To these four canons may be added a fifth, the method of concomitant variations. Whatever phenomenon varies in any manner whenever another phenomenon varies in some particular manner is either a cause or an effect of that phenomenon, or is connected with it through some fact of causation. The difficulty of discovering causation is greatly increased by the fact that in many cases there are plurality of causes and intermixture of effects.
Certain effects may be produced by diverse causes; thus heat may be produced by the sun and by friction. How can such causes be found? Here, the first canon fails, for causes, A B C and A D E, both producing effect a, might have A, and only A, in common, and yet not A, but B and D might be the cause of a. Only by an exhaustive analysis of antecedents and a multiplication of instances can plural causes be disproved by the method of agreement. It is necessary in most cases, and best in all cases, to use the method of difference, which is at once decisive, for if two instances, B C and A B C, are found, and the latter gives rise to a, and the former does not, it is at once evident that A is the cause of a.
Many effects are compounded, are the product of several causes. Such a compound may be quite a new product incomparable with its causes, or it may be simply composed of the effect of its several causes.
A compound of the first kind is seen in the chemical products of chemical substances. Thus hydrogen and oxygen may produce a new product, a new bundle of effects known as water. How are the causes in such cases to be unravelled? In most cases such compound effects can be unravelled by experiment, for such compounds can usually be made to reproduce their causes. Thus, water under certain circumstances may be made to reproduce its causes, oxygen and hydrogen. Complex mental effects, however, do not lend themselves to this simple mode of analysis, and we can only discover their causes by the slow process of studying the simple feelings themselves, and ascertaining synthetically, by an examination of their possible combinations, what they are capable of eventually producing.
A Compound of the second kind, produced by the interplay of the regular effects of multiple causes, is always difficult to analyse, since the effects become mixed and mingled, and oppose or augment each other. Here we must fall back on the deductive method, which is the chief method by which we acquire knowledge of the conditions and laws of occurrence of the most complex phenomena.
It consists of three operations: firstly, direct induction; secondly, ratiocination; and, thirdly verification. In the first place, the consequents or laws of individual causes must be ascertained; in the second place the effect of various combinations of such causes must be estimated, and causes selected adequate to produce in combination the compound effect in question; and, in the third place, the causes so selected must be shown to produce the effect, unless frustrated by other known causes.
IV - FALLACIES
THERE are five distinguishable classes of fallacy.
Fallacies of simple inspection, or a priori fallacies, are due to mistaking the idea of a thing for the reality of the thing itself, subjective facts for objective, laws of the percipient mind for laws of the perceived object. A large proportion of the erroneous thinking which exists in the world arises from the assumption that the same order must obtain among the objects in nature which obtains among our ideas of them; that if we always think of two things together, the two ideas must always exist together - that if one thing makes us think of another as preceding or following it, that other must precede it or follow it in actual fact. And conversely, that when we cannot conceive two things together they cannot exist together. Instances of these errors are legion. For instance, it was long held that the Antipodes was impossible because our ideas had difficulty in conceiving persons with their heads in the same direction as our feet.
Observation may lead to fallacies either through non-observation or through mal-observation. Mal-observation always arises from mistaking inference for perception. Perception and inference always go together; but it is necessary to discriminate between parts played by each. The Copernican theory was opposed by many because they thought they saw the sun move; whereas they did not actually see the sun move, but inferred its motion from certain appearances.
Fallacies of generalisation are very numerous, and are due to fundamental misconceptions of the legitimate mode of drawing conclusions from observation and experiment.
A common fallacy of generalisation is that due to induction which proceeds per enumerationem simplicem ['by simple enumeration'], without real comparison of instances, without even ascertainment of the material circumstances in any given instance, and without any attempt to establish causal connexion. The common fallacy of post hoc, ergo propter hoc ['after this, therefore on account of this'] is of this nature.
Another fallacy of generalisation may be called the fallacy of false analogies. An argument from the analogy takes the following form. An object has a property B; another object is found to resemble this object in property A; and, therefore, it probably resembles it in property B. The argument has little value unless there is a real connexion between properties A and B; and if there be a real connexion the argument is no longer a mere argument from analogy.
In some cases an analogy is brought to support an inference when the resemblance fails at the really important point, and an argument of this nature is properly a fallacy of false analogies. For instance, paternal government in a family works well, therefore it is argued that a despotic government in a state will work well; but the success of paternal government depends on the affection of the parent for his children and on the superior wisdom of age; and neither the paternal affection nor the superior wisdom is likely to exist in a political despot.
Metaphors are obviously a kind of analogy and, consequently, must be used for purposes of inference with the greatest caution. The main purpose of a metaphor is to make a proposition clear and vivid, not to prove it.
It remains to be said that the most fertile source of fallacies of generalisation is bad classification, grouping together things which have no common properties, or none permitting any important general propositions to be made with respect to the class.
AMONG the fallacies of ratiocination are to be ranked all cases of vicious syllogism laid down in books. These generally resolve themselves into having more than three terms to the syllogism, either avowedly or in the covert mode of an undistributed middle term, or an illicit process of one of the two extremes.
A common and dangerous fallacy of this class is committed when, in the premises, a proposition is asserted with a qualification, and the qualification lost sight of in the conclusion; or, oftener, when a limitation or condition, though not asserted, is necessary to the truth of the proposition, but is forgotten when that proposition comes to be used as a premise.
Many of these fallacies are due to ambiguity of terms and to the use of terms as synonyms which are not really synonymous. Words used in several senses contribute to the confusion. Another type of this class of fallacy is known as petitio principii ['begging the question'] with its variety, 'reasoning in a circle.' This fallacy consists in the employment of a premise to prove a proposition upon which the premise itself depends. As a rule the fallacy is disguised by variations in language, so that the same thing is called by different names. Thus 'Opium produces sleep because it is a soporific.'
None of the modes of assuming what should be proved are more frequent than what are termed by Bentham 'question-begging appellatives'; names which beg the question under the guise of stating it. The most patent are those which have a laudatory or vituperative character, e.g. materialist, socialist, imperalist.
STILL another fallacy of confusion, known as ignoratio elenchi, consists in mistaking the conclusion which is to be proved, or in intentionally proving an irrelevant conclusion. Thus, a man might endeavour to prove the bellicosity of Germany by an estimate of the guns made by Krupp, or an unphilosophical critic might endeavour to disprove Berkeley's idealism by breaking a window.
John Stuart Mill
The grave of John Stuart and Harriet Taylor Mill
Cimetiere St. Veran, Avignon, Vaucluse, France
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