Chapter II.
Reasoning.

22. Reasoning is the mental act or process of deriving judgments, called conclusions, from other judgments, called premises.

The principle underlying all valid reasoning is that the conclusion is implicitly contained in the premises; therefore whoever grants the truth of the premises thereby really grants the truth of the conclusion. For instance, in this reasoning, "Every good son is pleased to see his mother honored; but Christ is a good Son; therefore He is pleased to see His Mother honored," whoever grants the first two propositions must grant the third, since it is contained in them.

Reasoning is styled pure, if the judgments are analytic judgments; empiric, if they are synthetic, and mixed if one premise is analytic and the other synthetic. Reasoning expressed in words is called argumentation.

ARTICLE I. THE CATEGORICAL SYLLOGISM.

23. All argumentation may be reduced to the categorical syllogism. A syllogism is an argument consisting of three propositions so connected that from the first two the third follows. If all the propositions are categorical, the syllogism is categorical. It will be remembered that a proposition is called categorical if it affirms or denies absolutely the agreement of a subject with a predicate. (No. 21.) " All virtues are desirable; but sobriety is a virtue; therefore sobriety is desirable," is a categorical syllogism. This conclusion, "Sobriety is desirable," is implicitly contained in the first or major premise, "All virtue is desirable"; and the second or minor premise, " Sobriety is a virtue," points out the fact that it is therein contained. Such reasoning is, therefore, perfectly valid.

§ 1. Constructing Syllogisms.

24. To prove a thesis by a syllogism we begin by finding a proposition which really involves the truth of the thesis, and in a second proposition we state that it does so. Thus, if I am to prove that every one must honor his father and mother, I may start with the premise, " Every one must do what God commands"; I add the minor premise, "But God commands to honor father and mother." Hence I legitimately draw the conclusion, "Therefore every one must honor his father and mother."

25. We must next examine in what ways premises may contain conclusions. If the major is a universal proposition, it may contain the conclusion in four different ways:

1. The proposition being universal, the subject is distributed or taken in its widest extension; thus, "Every stone is matter," means that the predicate 'matter' applies to everything that is a 'stone.' If, therefore, the minor states that something, say 'marble,' is a stone, the conclusion will follow that marble is matter. Thus the major affirms that a predicate belongs to a whole class; the minor affirms that a certain thing is of that class; the conclusion affirms that the same predicate belongs to that certain thing.

2. Similarly, if the major is negative, as, "A stone is not a spirit," and the minor declares that "Marble is a stone of some kind," the conclusion will be that "Marble is not a spirit." That is: the major denies a predicate of a whole class; the minor affirms that a certain being is of that class; the conclusion denies that same predicate of that same being.

3. A third form reasons thus: The major denies a predicate of a whole class; the minor affirms that a certain being has that predicate; the conclusion denies that said being is of said class; for if it were of that class, it would not have that predicate. Thus, "A stone is not a spirit; but an Angel is a spirit; therefore an Angel is not a stone."

4. In the three cases just explained the minor is affirmative. A fourth form of syllogism arises if the major affirms somc predicate of a whole class, and the minor denies that certain being has that predicate; the conclusion will then be that said being does not belong to said class, since all the individuals of that class have been affirmed to possess that predicate. "Every stone is matter; an Angel is not matter; therefore an Angel is not a stone."

In these four forms the major is a universal proposition, and the reasoning is founded upon the wide extension of the subject. The major need not be universal in the fifth form, which derives its validity from the full comprehension of the predicate.

5. The fifth form reasons thus: The major affirms that a being has a certain predicate, i.e., that it has all the notes comprehended in that predicate; the minor affirms that a certain note is comprehended in that predicate; the conclusion affirms that said being has said note. Thus, "This stone is matter; but all matter is extended; therefore this stone is extended." By changing the order of the premises, this fifth form is reducible to the first.

26. The first and second of these five forms are the most obvious modes of argumentation and the most constantly used. The reasoning so familiar in Mathematics, A = B, B = C, A = C, is an application of the first form. The argument, if expressed in full, would read thus: "Any two things equal to a third thing are equal to each other; but A and C are equal to a third, B; therefore they are equal to each other." Similarly, from the second form we have the following reasoning: "Two things, one of which is equal to a third thing and the other unequal, are not equal to each other; but A is equal to B, and C is not equal to B; therefore A is not equal to C.

27. In these two special modes of reasoning the major propositions are usually suppressed, because they are so obvious; and the arguments assume an abridged form, so constantly in use and so practically useful, that we must explain it with special care. In fact, many logicians reduce all syllogisms to these two abridged forms, which they call the affirmative and the negative syllogism.

28. The affirmative syllogism, i.e., that in which both the premises are affirmative, is based on the principle that two things equal to a third are equal to each other: A = B, B = C; therefore A = C.

The negative syllogism, i.e., that in which one premise is negative, is based on the principle that two things, one of which is equal and the other unequal to a third, are unequal to each other: A = B; B is not equal to C; therefore A is not equal to C.

29. The purpose of comparing A with B, and B with C, in the premises is to bring A and C together in the conclusion, as equal or unequal to each other. A and C are to be brought together; they are therefore called the extreme terms, and B, which brings them together, is the middle term. The subject of the conclusion is styled the minor extreme; its predicate, the major extreme. The premise containing the major extreme is the major premise, and that containing the minor extreme is the minor premise; still, practically the first expressed is usually called the major, and the second the minor premise. All the propositions together are the matter of the syllogism; the proper connection between them is its form or sequence, a term not to be confounded with consequent or conclusion.

30. A syllogism is valid when both the matter and the form are without a flaw. The following is materially true, formally false: "All virtue is good; intemperance is not a virtue; therefore intemperance is not good." The following is materially false, formally true: "Gloomy things are hateful; but virtue is a gloomy thing; therefore virtue is hateful."{1}

§ 2. Criticising Syllogisms.

31. In the mathematical formula, A = B, B = C, .'. A = C, there is no danger of error; but when we substitute ideas for the letters, there is need of great care to avoid mistakes. Thus, suppose that for A I substitute "silver," for B "a certain metal," for C "yellow," and instead of the formulas, A = B, B = C, .'. A = C I write: "Silver is a certain metal; but a certain metal is yellow; therefore silver is yellow," the conclusion is not legitimate; for 'a certain metal' is taken in two different significations, and consequently 'silver' and 'yellow' - are not compared to one thing, but to different things. To avoid and to discover errors in syllogistic reasoning, the following eight rules must be applied:

1. The terms are only three, to this attend;
2. Nor let the consequent a term extend.
3. Conclusions ne'er the middle term admit;
4. At least one premise must distribute it.
5. Two negatives no consequent can show,
6. From affirmations no negations flow.
7. A universal premise you'll provide,
8. And let conclusions take the weaker side.

32. Rule 1. The terms are only three, to this attend. There must be three terms, representing three ideas, and only three terms and ideas; this is the most important rule of all: it virtually contains most of the other rules. We evidently need three terms, that two things may be compared with a third; and, as each term must occur twice, there is no room for a fourth term. This rule is often violated by using one of the terms in two different meanings, especially the middle term; as:

Chewing is a bad habit;
But chewing is necessary to man;
Therefore a bad habit is necessary to man.

Rule 2. Nor let the consequent a term extend. Let no term have a wider meaning in the conclusion than in the premises; else there would really be more in the conclusion than is contained in the premises; as:

You are not what I am;
I am a man;
Therefore you are not a man.

'A man' is distributed in the consequent; for it stands for 'any man at all,' 'you are not any man at all'; but 'man' is particular in the minor; it means 'a certain man,' 'some man.'

Rule 3. Conclusions ne'er the middle term admit. This rule is evident, as the conclusion has nothing to do but to compare the extremes. We could not argue:

Lincoln was President;
Lincoln was of Illinois;
Therefore Lincoln was President of Illinois.

Rule 4. At least one premise must distribute it. The middle term must be used in its widest meaning in at least one of the premises. If the middle term were taken twice in a particular meaning, it might denote different objects; as:

Some monks were very learned;
Luther was a monk;
Therefore Luther was very learned.

Notice that a singular term is taken in its widest meaning, as 'Cicero,' 'Columbus,' 'the Eternal City,' etc.; e.g., "Columbus discovered America; but Columbus was disgraced; therefore the discoverer of America was disgraced."

Rule 5. Two negatives no consequent can show. From the fact that two things are not equal to a third, it does not follow that they are equal to each other, nor that they are unequal.

Rule 6. From affirmations no negations flow. If the two premises are affirmative, they declare that two things are equal to a third; whence it follows that they are equal, not unequal, to each other.

Rule 7. A universal premise you'll provide. If both premises are particular, no conclusion will follow. For their subjects are particular (No. 20), and if both are affirmative, their predicates are particular (No. 20); thus all their terms are particular, and the middle term is not distributed as it should be by Rule 4. If one is negative, its predicate is distributed (No. 20), but that is not enough; we need then two universal terms, one for the middle term and one for the predicate of the conclusion. For that conclusion will be negative (Rule 8), and therefore must have a universal predicate (No. 20). We cannot reason thus:

Some Inquisitors were cruel;
Some good men were Inquisitors;
Therefore some good men were cruel.

Rule 8. And let conclusions take the weaker side. The meaning is that, if one of the premises is negative, the conclusion is negative; if one is particular, the conclusion is particular. The first assertion is evident: it regards the negative syllogism explained above (No. 28). As to the second, if one premise is particular, two cases may occur: If both are affirmative, they can contain only one distributed term, since one subject and both predicates are parrticular. The distributed term must, of course, be their middle term, for the middle term must be at least once distributed; and therefore the subject of the conclusion must particular. 2. If one premise is negative, there may be two distributed terms in the premises, viz., the suhject of the universal proposition, and the predicate of the negative -- one of these is needed for the middle term, and one for the predicate of the negative conclusion; thus the subject of conclusion will again be particular.^{2}

33. These same rules apply to all syllogisms having categorical premises, even though the premises be compound propositions. The rules may seem at first sight to be violated, but they will be found, on careful inspection, to be observed in all correct reasoning of this kind. Attend especially to that part of the compound premises in which the stress of the argument lies. Thus, when we say, "God alone is eternal; but Angels are not God; therefore they are not eternal;" the term 'eternal' is distributed in the conclusion, while it seems to be the predicate of an affirmative proposition in the major premise. But the major is compound, and contains a negative part, "Whatever is not God is not eternal." Hence the rule is not violated.

ARTICLE II. THE HYPOTHETICAL SYLLOGISM.

34. A hypothetical syllogism is one whose major is a hypothetical proposition (No. 21); and such it always is when the syllogism is not categorical. We have seen that there are three kinds of hypothetical propositions: the conditional; the disjunctive, and the conjunctive. Hence there are three species of hypothetical syllogisms.

35. I. Conditional syllogisms derive their force from an affirmed connection between a condition and a consequent; so that, if a certain condition is verified, a certain consequent must be admitted. Therefore, if the consequent does not exist, the condition is thereby known not to be verified. Hence this argument may validly conclude in two ways:

4. "Monopolists are rich;
Some rich men are proud;
Therefore monopolists are proud."

5. "Many men are rich:
Many men oppress the poor;
Therefore the rich oppress the poor."

6. "The free-traders wish to reduce the tariff:
Mr. C. wishes to reduce the tariff:
Therefore Mr. C. is a free-trader."

36. II. The disjunctive syllogism has a disjunctive major premise; e.g., "Either the father, or the mother, or the child is the natural head of the family." It is supposed that the disjunction is complete, i.e., that no fourth alternative is possible. From this major we may reason in three ways:

1. The minor may deny one member of the disjunction, and the conclusion affirm the other members disjunctively.

"But the child is not the natural head of the family;
Therefore either the father or the mother is such."

2. The minor may affirm one of the members, the conclusion deny the other members copulatively:

"But the father is the natural head;
Therefore neither the mother nor the child is such."

37. III. The conjunctive syllogism has a conjunctive major premise; as: "No one can love God and hate his neighbor." From this premise we can reason validly by affirming one of the incompatible predicates in the minor, and denying the other in the conclusion: "But the Martyrs loved God; therefore they did not hate their neighbor," or "But Nero hated his neighbor, therefore he did not love God."

ARTICLE III. OTHER SPECIES OF DEMONSTRATIVE ARGUMENTS.

38. 1. The Enthymeme, as now usually understood,{3} is an elliptical syllogism, one of the premises being understood (en thumô, in the mind); e.g., "The world displays a wonderful adaptation of means to an end; therefore it is the work of an intelligent Maker." The major is understood, viz., "Whatever displays a wonderful adaptation of means to an end is the work of an intelligent maker." To criticise the validity of an enthymeme we have only to supply the omitted premise, and then apply the ordinary rules of the syllogism.

39. 2. The sorites (sôros, a heap) is an abridged series of syllogisms; it is an argument consisting of more than three propositions so connected that the predicate of the first becomes the subject of the second, the predicate of the second the subject of the third, etc., till the conclusion joins the subject of the first with the predicate of the last premise. Man is accountable; whoever is accountable is free; whoever is free is intelligent; whoever is intelligent cannot be mere matter; therefore man cannot be mere matter."

40. To test such reasoning, it should be resolved into connected syllogisms, thus:

"Whoever is accountable is free; but man is accountable; therefore man is free."

"Whoever Is free is intelligent hut man is free; therefore man is intelligent."

"Whoever is intelligent cannot be mere matter; but man is intelligent; therefore man cannot be mere matter."

41. 3. The dilemma (dis lêmma, a twofold assumption) is an argument which offers an adversary the choice between two or more alternatives, from each of which a conclusion is drawn against his position. The alternatives are called the horns of the dilemma. Such was the reasoning of one whom a Protestant parent was preventing from becoming a Catholic. He answered: "Either Protestantism or Catholicity is right. If Protestantism is right, every one must be guided by his own judgment in religious matters, and you should not prevent me from judging for myself. If Catholicity is right, you ought not only not to prevent me, but even to follow my example."

42. To be conclusive, the dilemma must leave no escape from the alternatives presented; thus, the dilemma just quoted would not be conclusive against a Pagan; for he would deny the major. Besides, the partial inferences must follow strictly from their respective premises; else the argument may often be retorted. A young man, striving to dissuade his sister from devoting herself to the exclusive pursuit of holiness argued thus: "Either you have still a long or but a short life before you: if a long life, you will forego countless pleasures; if a short life, you cannot get far on the path of holiness." She retorted: "If a short life, I shall forego few pleasures, if a long one, I can get far on the path of holiness."

43. 4. When proofs of the premises or of one of them are inserted in a syllogism, the argument is called an epichirema (epi cheir, at hand, ready for use), which is rather an oratorical form of the syllogism than a distinct species of reasoning; e.g., "Education should promote morality; but it fails to do so when severed from religious teachings, since morality derives all its force from religious convictions; therefore education should be religious."

44. 5. Induction requires careful consideration, on account of its constant application to the Physical Sciences. It follows a process the reverse of the syllogistic; for it argues not from universals to particulars, but from particulars to universals. It may be defined as an argument in which we conclude that what is found by experience to hold true of single objects of a class holds true of the whole class. Induction may be complete or incomplete.

45. Complete induction examines every single object of a class, and then enunciates universally that all the class has certain properties; for instance, after exploring every zone of the earth, we may conclude, "All the zones of the earth's surface are capable of supporting human life." Complete induction rests for its validity on this syllogism: "Whatever is true of every individual of a class is true of the whole class; but a certain proposition is true of every individual of a class; therefore it may be predicated of the whole class."

46. Incomplete induction, the ordinary process of physical studies, does not examine every single object of a class, but a sufficient number of such objects, and under sufficiently varied circumstances, to make it certain that the property or action observed cannot be owing to any accidental cause, but must be due to the very nature of the objects, and therefore must always accompany them, even in such cases as have not been examined. As long as any doubt remains whether, perhaps, the peculiarity constantly observed may not be owing to some accidental circumstances, induction cannot give truly scientific certainty; but when all such doubt is excluded, the argument is conclusive. It rests then upon this clear syllogistic reasoning "Whatever property or action flows from the very nature of objects must always accompany those objects; but a certain property or action is known by a sufficient variety of experiments to flow from the very nature of certain objects; therefore it must always accompany them." For instance, heavy bodies when left unsupported have been found in most varied circumstances to fall to the earth, and therefore we judge without fear of error that this tendency must be due to their very nature, and we formulate the natural law: "Heavy bodies when unsupported fall to the earth."

47. The only danger is that scientists, in their eagerness to formulate general laws, will not always examine a sufficient variety of cases to exclude all doubt as to the real cause of the phenomena observed. Thus, Laplace laid it down as a natural law that all the parts of the solar system revolve from west to east; while it is now known that some of the solar planets and their satellites perform motions in the opposite direction.

48. It is evident that no conclusion is valid, except in as far as it is contained in the premises from which it is derived. Therefore the fact that an assertion is found to hold in ninety-nine cases is no certain proof that it will hold true in the hundredth case, since this hundredth case is not contained in the cases observed. Incomplete induction, therefore, cannot by itself, without resting on a syllogism, furnish a scientific proof. But we have scientific proofs of many things. Hence it is evident that Materialists and Positivists (i.e., those pretended philosophers who admit nothing but matter and sensible phenomena) are entirely mistaken when they teach that the mind has no knowledge of any universal propositions whatever, except as far as it has observed and generalized individual facts; that all reasoning, therefore, is only the generalizing of facts, or that all the elements of our knowledge are only inductive, without any universal proposition on which their certainty rests. Some of these philosophers maintain that we do not even know that a circle must be round, but only that it is always known to be so on this earth, while elsewhere it may, for all we know, be square. But the proposition, "A circle is round," is self-evident, independently of observation and induction. A system is known to be false if it leads logically to absurd consequences, as their system does.

ARTICLE IV. PROBABLE REASONING.

49. In all the forms of argumentation so far explained, the process is every way reliable and the conclusion certain; such reasoning is called demonstrative; to distinguish it from probable reasoning, which fails to remove all prudent fear of error.

A syllogism one or both of whose premises are only probable will, of course, yield only a probable conclusion; it is called dialectic, i. e., open to discussion (dialegomai, I discuss). We shall here consider two important species of probable arguments, Analogy and Hypothesis, both of frequent application, chiefly in the Physical Sciences.

50. I. Analogy (analogos, parallel reasoning) is an argument by which we conclude that a certain line of reasoning will hold in one case because it is known to hold in a similar case. Thus, because we see that the actions of brutes are to a great extent similar to those of men, and in men they are prompted by certain feelings, we conclude, with very strong probability, that in brutes also they are prompted by similar feelings.

51. The principles underlying analogical reasonings are such as these: "Similar causes are apt to produce similar effects," "Similar properties suggest similar essences," "Things similarly constructed appear to be governed by similar laws," etc. Sometimes the probability thus obtained is very strong; at other times the argument is deceptive, because, though alike in many other ways, the two cases may differ on the very point in question. Such are many of the analogies urged in support of the Evolution of Species. "The vile grub is evolved into a beautiful butterfly; why may not a hawk be developed into an eagle?" asks the popular scientist. But from the egg of the butterfly comes the vile grub again, and the species remains ever the same. Varieties of type within the same species of animals are numberless, but no single case of an evolution from one species into another has ever been scientifically established.

52. The argument of analogy is more useful to the orator than to the philosopher. It supplies the former with the topics of Similitude and Example. It suggests much effective reasoning a majori, a minori, and a pari. In scientific investigations analogy is often suggestive of solutions, which may afterwards be proved demonstratively to be correct; till they are so proved, they are called hypotheses.

53. II. An hypothesis (hupothesis, a supposition) is a proposition provisionally assumed as if true, because it accounts plausibly for many facts. For instance, it was formerly supposed that light consisted of particles emitted by luminous bodies; the present hypothesis explains the phenomena of light more plausibly by the vibrations or undulations of ether. When an hypothesis is so far confirmed by experience that it leaves no reasonable doubt as to its correctness, it ceases to be an hypothesis and becomes a thesis.

That an hypothesis may be probable and truly scientific, it is necessary: 1. That it explain a considerable portion of the facts in question. 2. That it do not certainly contradict any well-established truth; for, as two contradictories cannot both be true, whatever hypothesis contravenes a well-established truth is thereby known to be false. Numerous important discoveries have been made, especially in the Physical Sciences, by means of ingenious hypotheses. On the other hand, science has often been much retarded by false hypotheses, which led investigations into wrong directions. To point out such false assumptions is to render most important services to the cause of progress. For one Copernican theory retarded a while till supported by stronger proofs, numerous wild vagaries have been discountenanced by the Roman tribunals, and the energies of the learned diverted from wasting themselves in the pursuit of idle fancies.

ARTICLE V. INDIRECT REASONING.

54. Reasoning, whether demonstrative or probable, is styled indirect when, instead of proving the thesis, it simply aims at clearing away objections against it, or at establishing some other proposition from which the truth of the thesis may be inferred. Indirect reasoning may assume various forms:

1. The self-contradiction, or reductio ad absurdum, is a form of argument showing that the denial of the theses leads to absurd consequences; thus we argue the necessity of admitting certainty from the fact that the denial of all certainty leads a man to stultify himself.

2. The negative argument points out the absence of all proof from an opponent's assertions. "Mere assertions go for nothing," "Quod gratis asseritur gratis negatur," are received axioms of discussion.

3. The instance or example adduces a test case in which the assertion or the reasoning of an opponent is shown to be at fault. Thus, if one asserted that all history is unreliable, we might instance our Declaration of Independence as an undeniable fact of history.

4. An argumentum ad hominem draws from an opponent's principles, true or false, a conclusion against him; e. g., when a Fatalist philosopher was about to flog his slave for the crime of theft, the latter argued that he could not be justly punished for a crime which he was fated to commit.

5. A retort turns an adversary's argument or some portion of it against himself; as when the same philosopher answered that he likewise was fated to flog the slave.

6. We evade an argument when, without discussing his proofs, we call on an adversary to explain what he is unwilling or unable to explain; thus many a specious theorizer is silenced by summoning him to explain the consequences of his theories.

7. The argument ad ignorantiam shows that an opponent is unable to prove his point or answer our objections.

8. The argument ad invidiam makes an adversary's thesis or his proofs odious or ridiculous.

55. In answering objections we should attend with special care to distinguish what is true from what is false in the arguments of our opponents.

Most objections contain some element of truth; for falsity, as such, is not plausible: it is the truth blended with falsity that gives plausibility to an objection. To separate the one from the other, by drawing clear lines of demarcation, is the keenest test of logical skill, and the direct road to complete victory. To facilitate for the student this task of neatly distinguishing the true from the false, we shall now point out the chief forms which fallacious arguments are apt to assume.

ARTICLE VI. SOPHISMS OR FALLACIES.

56. A sophism or fallacy is an argument which, under the specious appearance of truth, leads to a false conclusion. The deception is caused either by some ambiguity in the expression, or by some confusion in the thoughts expressed.

57. I. The fallacies arising from ambiguity in the expression are chiefly two:

1. The equivocation, or ambiguous middle, uses a middle term in two different meanings; e. g., "The soul is immortal; but a brute animal has a soul; therefore a brute animal has something immortal." We answer by distinguishing the two meanings of the word 'soul.' In the major it denotes the human soul, in the minor the principle of life in any animal: there are four terms.

2. The fallacy of composition and division confounds what holds of things separate with what holds of them united; e.g., " It is absolutely impossible that the dead should live" is true in the sense that they cannot live and be dead at the same time, i.e., in the sense of composition but it is not true in the sense of division. Those now dead can, by the power of God, be made to live again.

58. II. Fallacies result from confusion of thought in six ways, chiefly:

1. The fallacy of the accident confounds an essential with an accidental property; e.g., "We buy raw meat, and we eat what we buy; therefore we eat raw meat." What we eat has the same essence as what we buy, but not the same accident of rawness.

2. What is true in the proper sense of the word, 'simpliciter,' is often confounded with what is true in a qualified sense or under a certain respect (secundum quid); e.g., "A sea-captain who willingly throws his cargo overboard ought to indemnify the owner; but A did so; hence A ought to indemnify the owner." The major would be true, if the captain were absolutely willing to destroy the cargo entrusted to him; but not if he is willing in a way only, i.e., as a necessary means to save vessel and crew.

3. An irrelevant conclusion, ignoratio elenchi, or missing the point, proves what is not in question, refutes what is not objected; as when Evolutionists prove elaborately that the body of man resembles in various ways the bodies of brutes -- a fact which no sensible man denies.

4. The petitio principii, or begging the question, consists in taking for granted the point which is to be proved; when this very point is used as a premise in the reasoning, the fallacy is called a vicious circle.

5. The fallacy of the false consequence, often called a non-sequitur, or want of sequence, is used when a conclusion is drawn which is not contained in the premises; e. g., "There exists a wonderful gradation in the perfection of plants and animals; therefore the more perfect are evolved from the less perfect."

6. The undue assumption, or false cause, non causa pro causa, assumes as a cause what is not a cause; as when the Reformation is assumed to be the cause of scientific progress. This fallacy often arises from the fact that mere priority in time is mistaken for causality; post hoc; ergo propter hoc.{4}

ARTICLE VII. METHOD IN REASONING.

59. Order is a proper arrangement of parts for any purpose whatever, theoretical or practical; method is a suitable arrangement of parts with a view to a practical end. In reasoning, the end is the acquisition or the communication of knowledge.

60. All reasoning must begin with undoubted premises, which themselves need not to be supported by reasoning: no science is expected to prove its first principles. Thus, Geometry starts out with a number of axioms, from which the whole science is derived by logical reasoning. Such axioms are not blindly or arbitrarily taken for granted; but they are self-evident, they need no proof. Thus, too, in Philosophy the first principles are self-evident and need no proof.

61. As the mind must, of course, apprehend the premises before it draws conclusions from them, we say that in the logical order, i.e., in the order of thought, the premises are always prior to the conclusions. But in the ontological order, i.e., in the order of being, a truth stated in the premises may be really posterior to the truth expressed in the conclusion. Such is the case whenever we reason from an effect to its cause, say from a beautiful picture to the skill of the painter; for the effect is posterior to the cause, is dependent on the cause.

62. Reasoning thus from effect to cause is reasoning a posteriori, and, vice versa, reasoning from cause to effect is called a priori, since causes are ontologically prior to their effects.

63. It will be noticed that the terms a priori and a posteriori have not exactly the same meaning when applied to reasoning and when applied to judgments. A judgment a priori, as explained above (No. 17), is one formed independently of experience, while a reasoning a priori is one proceeding from cause to its effect.

64. While in a priori and a posteriori reasonings we consider relations between two things, one of which is ontologically prior to the other, in analytical and synthetical reasonings we consider only one thing, studying the relations between the whole being and its parts, between a substance and its qualities. If we are first acquainted with the whole being and from the study of it strive to discover its parts, we are said to analyze the subject (analuô, I take apart): we then proceed analytically. But if we know the parts first, and put them together to find the whole, we proceed synthetically (sunthesis, a putting together). The chemist analyzes a mineral to discover its simple ingredients; the apothecary combines simples into compounds. The synthetic geometrician puts together lines and angles to find the properties of surfaces and solids; while the analytical geometrician finds the particular mathematical relations implied in a general formula.

65. The metaphysician considers an idea as a whole, and the notes of it as its parts. For instance, knowing that an oak is a tree, he examines the notes involved in the concept 'tree,' and finds analytically that an oak is a substance, material, vegetable, etc. On the other hand, seeing that the human body is a substance, extended, living, sensitive, he concludes synthetically that it is of an animal nature. Now, it is obvious that the idea analyzed is less extended than the notes; e.g., 'tree' is less extensive than 'substance,' for every tree is a substance, but not every substance is a tree. Therefore, when we reason analytically, we proceed from the particular to the universal, and vice versa we reason synthetically from the universal to the particular.

66. A science may use either analysis or synthesis, or now the one and then the other. Thus, in this treatise on Dialectics, while first explaining ideas, next the union of ideas into judgments, then the combination of judgments into arguments, we have used synthesis; and, in analyzing the nature of reasoning to discover the rules that must guide it, we have used analysis. This latter process is, in most studies, better suited for the investigation of truth, synthesis for the imparting of truth to others.

67. While treating of scientific methods, it is proper to speak of the distinctions existing between various sciences. These are distinguished according to their objects; thus, Astronomy is evidently distinct from Botany, because it treats of a different class of objects. When sciences treat of the same object, as do Geology, Geometry, and Geography, all of which study the earth, they view that object differently; and the view they take of their objects is called their formal object, the object itself being called the material object. Sciences are therefore more correctly said to be specified by their formal objects. It naturally follows that a science is esteemed as more or less noble in proportion as its formal object is more or less worthy of man. Theology is therefore the noblest of all, since it views all its objects as they are known by the highest light, viz., by the supernatural light of Divine Revelation. Philosophy is the noblest of the merely human sciences, since its formal object is what is most intellectual in all things, viz., their very essences and their relations to the highest good.

68. The true teachings of any science can never come into conflict with the true teachings of any other science; for truth objectively considered is something absolute, not merely relative; it is that which is. In the case of an apparent conflict between two sciences, it will always be found that one of the conflicting teachings is not demonstrated nor capable of demonstration.

ARTICLE VIII. EXERCISE IN REASONING.

69. The most useful exercise in philosophic studies is the manner of discussion called The Circle. We shall here explain at some length: One pupil is appointed to defend on a given day, during about half an hour, any thesis that has been explained in the class; two others are appointed to object; and the whole discussion is to be conducted in strict syllogistic form. The discussion is opened by the first objector, who challenges the defender to prove the thesis. The latter begins by explaining the exact meaning of the thesis; he next gives the proof in a formal syllogism, adding, if necessary, the proof of the major or the minor, or both. The objector then attacks the thesis or its demonstration: he offers a syllogism the conclusion of which is contradictory to the thesis or to the validity of the proof. The defender repeats the objection in the very words of the opponent; next, he replies separately to each of its propositions.

Let us suppose that the third thesis of Critical Logic -- the theory of universal scepticism is self-contradictory (No. 94) -- is the subject of discussion. The defender, at the summons of the first objector, explains and proves the thesis. Then the first objector: "That is not self-contradictory which does not affirm and deny the same thing; but the theory of universal scepticism does not affirm and deny the same thing; therefore it is not self-contradictory." The defender repeats the objection word for word, and then adds: "The major, 'That is not self-contradictory which does not affirm and deny the same thing,' I grant. The minor, 'The theory of universal scepticism does not affirm and deny the same thing,' I deny." Objector: "I prove the minor: that does not affirm and deny the same thing which affirms nothing whatever; but the theory of universal scepticism affirms nothing whatever; therefore it does not affirm and deny the same thing." The defender repeats the syllogism, and adds: "The major, 'That does not affirm and deny the same thing which affirms nothing whatever,' I grant. The minor, 'The theory of universal scepticism affirms nothing whatever,' I deny." Objector: "I prove my new minor: the theory which doubts of everything affirms nothing whatever; but the theory of universal scepticism doubts of everything; therefore it affirms nothing whatever." Defender, after repeating the syllogism, adds: "The major, 'The theory which doubts of everything affirms nothing whatever,' let that pass. The minor, 'The theory of universal scepticism doubts of everything,' I deny." Objector: "I prove the last minor: universal scepticism is defined as the theory which doubts of everything; therefore universal scepticism doubts of everything." Defender repeats the enthymeme, and adds: "The antecedent, 'Universal scepticism is defined as the theory which doubts of everything,' I distinguish: as the theory which pretends to doubt of everything, I grant; as the theory which really doubts of everything, I deny; and therefore I deny the consequent."

Objector. "But the sceptic really doubts of everything; therefore the distinction is of no avail." Defender repeats, and adds: "The antecedent, 'The sceptic really doubts of everything,' I deny." Objector: "May I ask your reason for deny it?" Defender: "I deny it because no man can really doubt of everything; even his own existence; the fact that he is reasoning, speaking, etc." Objector: "But the sceptic sincerely affirms that he doubts of everything." Defender: "Then he affirms something, and thereby contradicts himself."

The Second Objector: "That should not be maintained as a thesis which cannot be validly proved; but it cannot be validly proved that universal scepticism is an absurd theory; therefore it should not be maintained as a thesis." The defender repeats, then adds: "The major, 'That should not be maintained as a thesis which cannot be validly proved,' I will let that pass for the present. The minor, 'It cannot be validly proved that universal scepticism is an absurd theory,' I deny, and therefore I deny the conclusion." Objector: "I prove the minor: that proof is not valid which takes for granted what cannot be proved; but the proof of this thesis does so; therefore it is not valid." Defender repeats, and adds: "'That proof is not valid which takes for granted what cannot be proved,' I distinguish that major: if that which is taken for granted needs proof, I grant; if it needs no proof, I deny. As to the minor: 'But the proof of this thesis takes for granted what cannot be proved,' I distinguish this the same way: it takes for granted what is evident, and therefore needs no proof, I grant; it takes for granted that which needs proof, I deny. And therefore I deny the conclusion, etc., etc."

{1} Exercises like the following will be found to be of great advantage: Construct syllogisms proving the following theses: The Saints deserve to be honored, No man is to be hated by his fellow-man, Theft should be punished, Good books are valuable treasures, Bad books are injurious, Riches are not lasting possessions, The study of mustc should be encouraged, Jealousy cannot please God. No time is useless.

{2} Exercise. Criticise the following syllogisms

"The beings conjured up by spiritists are spirits;
But the souls of the dead are spirits;
Therefore the beings conjured up by spiritists are the souls of the dead."

2. "Blessed are the poor in spirit;
The Apostles are blessed
Therefore the Apostles are poor in spirit."

3. "Scientists deal with physical laws;
But Huxley and Darwin are scientists;
Therefore they deal with nothing but physical laws."

{3} The word was differently derived and explained by Aristotle.

{4} Exercise. Point out the fallacies contained in the following arguments:

1. "Liberty is desirable; but the laws restrict liberty; therefore the laws restrict what is desirable."

2. "The liberty of the press is a blessing; but blessings should not be restricted; therefore the liberty of the press should not be restricted."

3. "The Inquisition was the cause of much cruelty; but the Popes approved the Inquisition ; therefore the Popes approved the cause of much cruelty."

4. "The Spanish Inquisitors were often cruel; but St. Peter Arbues was a Spanish Inquisitor; therefore the Saints are often cruel."

5. "Galileo was condemned by a Roman tribunal; therefore the Pope is not infallible."

6. "The Supreme Court of the United States is a fallible tribunal; therefore its decisions are not to be regarded."