Reformed Logic / A System Based on Berkeley's Philosophy with an Entirely New Method of Dialectic

'No idle person can be a successful writer of history; therefore Hume, Macaulay, Hallam and Grote must have been industrious.'

'Lithium is an element; for it is an alkali-producing substance, which is a metal, which is an element.'—Fallacy of no-application.

'Rational beings are accountable for their actions; brutes not being rational, are therefore exempt from responsibility.'

'Whatever tends to withdraw the mind from pursuits of a low nature deserves to be promoted; classical learning does this, since it gives us a taste for intellectual enjoyments; therefore it deserves to be promoted.'

'Bacon was a great lawyer and statesman; and as he was also a philosopher, we may infer that any philosopher may be a great lawyer and statesman.'—The theorem infers the general inherence of philosophy with eminence in law and politics, from the single instance of Bacon: it is evidently a fallacy of doubtful precedent.

'Snowdon is the highest mountain in England and Wales. Snowdon is not so high as Ben Nevis. Therefore the highest mountain in England and Wales is not so high as Ben Nevis.'

This means: 'the highest mountain in England and Wales is called Snowdon, and it is not so high as Ben Nevis.' The apparent conclusion merely repeats a part of the information given already. There is no case. The following is a theorem of the same kind—

'Lithium is the lightest metal known. Lithium is the metal indicated by one bright line in the spectrum. Therefore the lightest metal known is the metal indicated by a spectrum of one bright line.'

'If ye were Abraham's children, ye would do the works of Abraham.'

'Since all metals are elements, the most rare of all the metals must be the most rare of all the elements.'—There is a suppressed precedent to the effect that the most rare individual of a species must be the most rare of its genus, which may or may not be true.

'All vice is odious; but avarice is a vice; for it makes men slaves; therefore avarice is odious.'

'Bucephalus is a horse; a horse is a quadruped; a quadruped is an animal; an animal is a substance; therefore Bucephalus is a substance.'

This is what logicians call a Sorites. There may be a chain of valid arguments, in which the conclusion of one is precedent or case of the next; but the propositions just quoted do not make an argument, being merely a string of classifications. If we know what Bucephalus and substance mean, we know by perception that Bucephalus is a substance.

'Every being is then happy when it acquires the proper perfection of its nature; and consequently all vital beings are capable of receiving felicity that are capable of arriving at the perfection of their nature.'

This is perilously near tautology; it can be saved only by assuming that 'every being capable of happiness' is a more extensive class than 'all vital beings capable of arriving at the perfection of their nature.'

'The soul's debility is not owing to her lapse into matter; for as this lapse is voluntary, the soul must have sinned prior to her descent.'

Cogito ergo sum.—

That we exist is the most certain fact we know: it cannot be strengthened by any argumentation. If we can doubt that we are, we can with better reason doubt that we think.

Here is Hamilton's example of a disjunctive syllogism, which he considered a valid argument—'The hope of immortality is either a rational expectation or an illusion; but the hope of immortality is a rational expectation; therefore the hope of immortality is not an illusion.' It is a flagrant tautologism.

'If man be not a morally responsible being, he must want either the power of recognising moral good (as an intelligent agent), or the power of willing it (as a free agent); but man wants neither of these powers; therefore man is a morally responsible being.'

Adopted by Hamilton from Krug and given as valid. It is first a fallacy of contrast, and if amended in this respect it would still be a fallacy of tautology.

'If Aeschines joined in the public rejoicings, he is inconsistent; if he did not, he is unpatriotic; but he either joined, or not, therefore he is either inconsistent or unpatriotic.'—An excellent specimen of logicians' logic: on a par with this—If it is fine weather, I go; if it rains, I stay; it must either rain or be fine, therefore I must either go or stay.

'If the world were eternal, the most useful arts, such as painting, &c. would be of unknown antiquity: and on the same supposition there would be records long prior to the Mosaic; and likewise the sea and land in all parts of the globe might be expected to maintain the same relative situations now as formerly: but none of these is the fact: therefore the world is not eternal.'

'If the world existed from eternity, there would be records prior to the Mosaic; and if it were produced by chance, it would not bear marks of design: there are no records prior to the Mosaic, and the world does bear marks of design: therefore it neither existed from eternity, nor is it the work of chance.'

Two theorems are here mixed together, both fallacies of contrast—

'If this man were wise, he would not speak irreverently of Scripture in jest; and if he were good he would not do so in earnest; but he does it, either in jest or earnest; therefore he is either not wise or not good.'

As it stands this is quite circular, but it might be rendered valid by generalisation:—

'If virtue were a habit worth acquiring, it must ensure either power, or wealth, or honour, or pleasure; but virtue ensures none of these; therefore virtue is not a habit worth attaining.' Fallacy of contrast—

'If men are not likely to be influenced in the performance of a known duty by taking an oath to perform it, the oaths commonly administered are superfluous; if they are likely to be so influenced, everyone should be made to take an oath to behave rightly throughout his life; but one or other must be the case; therefore either the oaths commonly administered are superfluous, or everyone should be made to take an oath to behave rightly throughout his life.'—This will be more intelligible if contracted thus: If oaths fail to influence they are superfluous; if they influence they should be obligatory; but they either influence or do not; therefore they are either superfluous or should be obligatory. There is no argument; the alternative conclusions merely repeat the alternative precedents.

'If virtue is voluntary, vice is voluntary; but virtue is voluntary; therefore so is vice.' (Arist. Eth. Bk. III. quoted by Whately.) This is a circular way of saying that we believe it to be a fact that vice is voluntary. The argumentative form is probably supposed to give the assertion greater weight than it would have if expressed as a perceptual judgment.

This is valid argument, according to Hamilton—'If man were suited to live out of society, he would either be a god or a beast; but man is neither a god nor a beast; therefore he is not suited to live out of society.'—It has faults of contrast and tautology.

'If iron is impure, it is brittle; but this iron is impure; therefore it is brittle.'—A valid dogmatic argument.

'If the weather is fine, we shall go into the country; now the weather is fine, therefore we shall go into the country.'—We never get beyond the simple judgment that our going into the country is associated with fine weather.

The following is valid:—'As often as the weather is fine, my brother has a habit of going into the country; if the weather be fine to-morrow I infer that he will go into the country.' Here a particular hypothetical case is illustrated by reference to a general habit.

'As often as the weather is fine my brother goes into the country; if it be not fine to-morrow I conclude that he will not go into the country.'—A fallacy of contrast: we are not informed in the antecedents what the brother does on wet days.

'If there are sharpers in the company we ought not to gamble; but there are no sharpers in the company; therefore we ought to gamble.'

'Logic as it was cultivated by the schoolmen proved a fruitless study; therefore logic as it is cultivated at the present day must be a fruitless study likewise.'—We must take the conclusion as valid, until we know in what respects modern logic is superior to scholastic logic.

'Few treatises of science convey important truths, without any admixture of error, in a perspicuous and interesting form: therefore though a treatise would deserve much attention which should possess such excellence, it is plain that few treatises of science do deserve much attention.'

This means no more than that treatises of a certain excellence would deserve attention, and that there are few of them. There is no argument.

'Some objects of great beauty answer no other purpose but to gratify the sight: many flowers have great beauty; and many of them accordingly answer no other purpose than to gratify the sight.'

'None but Whites are civilised; the ancient Germans were Whites; therefore they were civilised.'

'Wilkes was a favourite with the populace; he who is a favourite with the populace must understand how to manage them; he who understands how to manage them must be well acquainted with their character; he who is well acquainted with their character must hold them in contempt; therefore Wilkes must have held the populace in contempt.'

'Something has existed from eternity. For since something now is, it is manifest that something always was. Otherwise the things that now are must have risen out of nothing, absolutely and without cause. Which is a plain contradiction in terms. For to say a thing is produced, and yet that there is no cause at all of that production, is to say that something is effected when it is effected by nothing, that is, at the same time when it is not effected at all. Whatever exists has a cause of its existence, either in the necessity of its own nature, and then it must have been of itself eternal: or in the will of some other being, and then that other being must, at least in the order of nature and causality, have existed before it.'

In this theorem we have a case—'Something is'; and a conclusion—'Something has existed from eternity.' The reasoner seeks a credible or conceivable precedent by which to connect that conclusion with the case.

We are offered a choice of two theorems. The first is untenable, for we have never had the experience that is given as precedent; it is also tautological, as the 'something' of the case is the 'whatever' of the precedent.

It is not inconceivable that something should be self-existent, but we know nothing as to its being eternal. We are not familiar enough with self-existent things and eternal things to warrant us in asserting dogmatically that where the first quality is, there also must be the second.

The next theorem is that everything must be caused, and that causation involves a regressum ad infinitum. On this principle there must have been things for an eternity backwards. According to the theory of causation given in section xxvii, a true beginning is reached when we discover the motive, design and power that produced an effect. It is not necessary to ask next what caused that motive, design and power. The infinite regress is applicable only to material sequence, in which there is no proper beginning or end. The author of the above argument seems to be trying to combine the notion of causation by will with that of infinite regress. But his language is too obscure to make it certain what he means exactly.

The three following theorems—in a diluted form—occur in an otherwise excellent work on the politics and social life of the ancient Greeks.

'The Athenians who opposed the union of Greece and Macedonia were old men, and the result was mischievous; other similar instances are found in history; therefore the government of old men is always mischievous.'—A fallacy of false generality. Everybody knows that some old men have been wise governors. Cicero, from his experience, drew the opposite conclusion—that the only safe rulers were old men.

'All old political leaders are mischievous; Gladstone is old; therefore he is to be considered politically mischievous.'—Even were the precedent not false the argument is superfluous, for the effect of Gladstone's politics is now matter of fact or history.

'Gladstone is politically mischievous; he advocates Home Rule for Ireland; therefore Irish Home Rule must be mischievous.'—A fallacy of division: a political leader might on the whole be mischievous, but his measures need not on that account be each and every one mischievous.

If dialectic were taught generally and on a rational method, a responsible author would avoid bad reasoning of this sort as carefully as he avoids bad grammar, vulgar imagery, or faulty arithmetic.