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On the Purity of the Art of Logic

Yale University Press

Chapter One

(1) (p. 199) I propose to compile, if God grants it, a kind of treatise on the purity of the art of logic, so that youths who are arguing about any problem at all can be trained and can quickly dispose of it. The little book will contain four parts. In the first part certain general rules will be set out to be used in what follows. The second part will deal briefly and succinctly with certain points about the sophistical art, the third part about the art of training students, and the fourth part about demonstrative art.

(2) The first part will have three subparts: In the first, general rules of inferences will be established. The second will deal with the nature of syncategorematic words. The third will discuss certain matters concerning the suppositions of terms.

The First Part: On General Rules

The First Subpart: On General Rules of Inferences

(3) First therefore I assume a certain distinction, namely this one: One kind of inference is simple, another kind is 'as of now'. A simple inference is one that holds for every time. For example 'A man runs; therefore, an animal runs'. An 'as of now' inference holds for a determinate time and not always. For example 'Every man runs; therefore, Socrates runs'. For that inference does not hold always, but only while Socrates is a man.

RULE 1

(4) The first rule of inferences is this: In every good simple inference, the antecedent cannot be true without the consequent. (p.200) So if in some posited possible case the antecedent could be true without the consequent, then the inference was not a good one. But in an 'as of now' inference the antecedent cannot as of now be true without the consequent-that is, for the time for which the inference holds.

(5) From this rule there follow two other rules. The first is: The impossible does not follow from the contingent in a simple inference. The second is that the contingent does not follow from the necessary. The reason for both of these is that the contingent can be without the impossible, and the necessary without the contingent.

RULE 2

(6) The second main rule is that whatever follows from a consequent follows from the antecedent.

(7) There is another rule too, almost the same as this one: Whatever is antecedent to an antecedent is antecedent to the consequent.

(8) For these two rules [(6)-(7)] always produce a good argument.

(9) Two other rules, which always produce a fallacy of the consequent, are false. They are these: Whatever follows from an antecedent follows from the consequent, and: Whatever is antecedent to a consequent is antecedent to the antecedent.

(10) When an argument proceeds through many intermediate inferences, an inference 'from first to last' holds by means of the rule 'Whatever follows from a consequent follows from the antecedent' [(6)]. You have to take into account that an inference 'from first to last' does not hold except when the same thing that is consequent in the preceding conditional is antecedent in the subsequent conditional. For if the antecedent in the subsequent conditional was other than the consequent was in the preceding conditional, the inference from first to last does not hold. Rather, there is a fallacy of accident, arising from a variation in the middle. For the consequent in the preceding conditional is the middle that links the later conditional with the earlier one. So the same thing that is consequent in the preceding conditional has to be antecedent in the subsequent conditional.

(11) For example: 'If a man exists, an animal exists; if an animal exists, a body exists; if a body exists, a substance exists; therefore, from first to last, if a man exists, a substance exists'. If all these inferences are linked with one another, the inference 'If a man exists, a substance exists' holds 'from first to last'. (p. 201) For the same thing that was consequent in the earlier inference was antecedent in the later inference.

(12) It is clear from this that if someone argues like this: 'If no time exists, it is not day; and if it is not day and some time exists, it is night; and if it is night, some time exists; therefore, from first to last, if no time exists, some time exists', the inference from first to last does not hold. For the consequent in the preceding conditional is not the same as the antecedent is in the subsequent conditional. For the first inference was 'If no time exists, it is not day', so that the consequent in this inference was only 'It is not day'. And in the second inference the antecedent was only 'It is not day and some time exists'. Therefore, the inference from first to last is invalid, because the antecedent in the later inference was not the same as the consequent in the earlier one.

Sophisms

(13) From this rule, the solution to sophisms like these is plain: It is proved that to the extent that something is larger, to that extent it appears smaller. This goes as follows: To the extent that something is larger, to that extent it is seen from farther away; and to the extent that something is seen from farther away, to that extent it appears smaller; therefore, from first to last, to the extent that something is larger, to that extent it appears smaller.

(14) Likewise it is proved that to the extent that someone is uglier, to that extent he is handsomer. This goes as follows: To the extent that you are uglier, to that extent you dress yourself up more; but to the extent that you dress yourself up more, to that extent you are handsomer; therefore, from first to last, to the extent that you are uglier, to that extent you are handsomer.

(15) Likewise it is proved that to the extent you are thirstier, to that extent you are less thirsty. For to the extent you are thirstier, to that extent you drink more; to the extent you drink more, to that extent you are less thirsty; therefore, from first to last, to the extent you are thirstier, to that extent you are less thirsty.

Reply to the Sophisms

(16) The solution to such sophisms is plain. For it does not follow 'from first to last', because the consequent in the preceding conditional is not the same (p. 202) as the antecedent was in the subsequent conditional. For the consequent in the preceding conditional is taken with 'to that extent', and the antecedent in the subsequent conditional is taken with 'to the extent that'. Hence it is not the same proposition.

Additional Rules

(17) From the rule 'Whatever follows from a consequent follows from the antecedent' [(6)] other rules follow. One is that just as in a universal proposition one can descend under the subject to any suppositum of the subject with respect to the predicate, so in any good inference one can descend under the antecedent to any antecedent of that antecedent with respect to the same consequent.

(18) For example, the inference 'If a man runs, an animal runs; therefore, if Socrates runs, an animal runs' is a good one. And 'If every man runs, Socrates runs; therefore, if every animal runs, Socrates runs' is likewise good. In both cases one is arguing by the rule 'Whatever follows from a consequent follows from the antecedent'. For example, because 'A man runs' follows from 'Socrates runs', therefore whatever follows from 'A man runs' follows from 'Socrates runs'. Therefore, if it follows 'A man runs; therefore, an animal runs', then 'If Socrates runs, an animal runs' follows as well.

(19) There is another rule, that in a conditional the antecedent of which is a universal proposition, the subject of the antecedent supposits immobilely with respect to the consequent in such a way that one cannot descend under the subject of the antecedent with respect to the consequent. But in a conditional the antecedent of which is an indefinite or particular proposition, the subject supposits confusedly, distributively, and mobilely with respect to the consequent.

(20) For example, in a conditional the antecedent of which is a universal proposition (like 'If every man runs, Socrates runs'), one cannot descend under the subject of the antecedent. For it does not follow: 'If every man runs, Socrates runs; therefore, if Plato runs, Socrates runs'. Rather, it is a fallacy of the consequent, because it argues by the false rule 'What follows from the antecedent follows from the consequent'. Nevertheless it correctly follows 'If a man runs, an animal runs; (p. 203) therefore, if Socrates runs, an animal runs'. And so in a conditional one can descend under the subject of the antecedent taken without distribution with respect to the consequent. But one cannot descend under the subject taken with distribution.

(21) Once more, from the rule 'Whatever follows from a consequent follows from the antecedent' [(6)], there follow two other rules. One of them is: Whatever follows from a consequent and from its antecedent follows from the antecedent by itself.

(22) The second rule is: Whatever follows from a consequent together with something added follows from the antecedent with the same thing added.

(23) The reason for the first rule is: Every proposition implies itself together with its consequent. For example, it follows: 'Socrates runs; therefore, Socrates runs and a man runs'. Therefore, since the antecedent implies the antecedent and the consequent, and whatever follows from a consequent follows from its antecedent [(6)], therefore it follows that whatever follows from an antecedent and its consequent follows from the antecedent by itself.

(24) The reason for the second rule is: An antecedent together with something added implies the consequent with the same thing added. For it follows: 'Socrates runs and you are sitting; therefore, a man runs and you are sitting'. Therefore, since whatever follows from a consequent follows from the antecedent [(6)], whatever follows from a consequent together with something added has to follow from the antecedent with the same thing added.

Counterexamples

(25) But there are arguments by counterexamples against the rule 'Whatever follows from a consequent follows from the antecedent' [(6)].

(26) For the inference 'I say that you are an ass; therefore, I say that you are an animal' is a good one, and yet something follows from the consequent that does not follow from the antecedent. For it follows: 'I say that you are an animal; therefore, I say the truth'. And yet it does not follow: 'I say that you are an ass; therefore, I say the truth'.

(27) Or it could be proved by this rule that you are an ass. For it follows: 'I say that you are an ass; therefore, I say the truth; therefore, it is true that you are an ass; and consequently you are an ass'. Proof of the inference 'If I say that you are an ass, I say the truth': For it follows: 'If I say that you are an animal, I say the truth; but if I say that you are an ass, I say that you are an animal; therefore, by saying that you are an ass, I say the truth'. Therefore, (p. 204) the consequent is true. The inference is plain, because it argues by the rule 'Whatever follows from a consequent does so from the antecedent too' [(6)].

(28) Again, there is once more an argument against the rule mentioned above [(6)]. For the disjunctive proposition 'Socrates runs or does not run' is a consequent of 'Socrates does not run'. Nevertheless, something follows from the disjunctive proposition that does not follow from 'Socrates does not run'. For from Socrates' running or not running it follows that a man runs, and yet from Socrates' not running it does not follow that a man runs. For it does not follow: 'Socrates does not run; therefore, a man runs'.

(29) Again, 'Socrates runs' is a consequent of 'Socrates runs alone', and yet something follows from Socrates' running that does not follow from Socrates' running alone. For from Socrates' running it follows that a man runs, and yet 'From Socrates' running alone it follows that a man runs' is false.

(30) Again, the proposition 'Some proposition is true' is a consequent of 'Every proposition is true', and yet something follows from the consequent that does not follow from the antecedent. For from some proposition's being true it follows that it is true that you are an ass. And yet 'From every proposition's being true it follows that it is true that you are an ass' is not true. For it follows: 'From every proposition's being true it follows that it is true that you are an ass; therefore, from God's existing's being true it follows that it is true that you are an ass'.

(31) Or it could be proved by this argument that you are an ass. For it follows: 'From every proposition's being true it follows that it is true that you are an ass; but it is true that God exists; therefore, it is true that you are an ass'. This is to argue as follows: 'God exists; therefore, you are an ass; the antecedent is true; therefore, the consequent is as well'. Proof of the inference: 'From its being true that God exists it follows that it is true that you are an ass' is true. Proof: For it follows 'From every proposition's being true it follows that it is true that you are an ass; therefore, from its being true that God exists it follows that it is true that you are an ass. The antecedent is true; therefore, the consequent is as well'.

Replies to the Counterexamples

(32) (p. 205) To the first of these [(26)-(27)], it must be said that 'I say that you are an animal' has to be distinguished according to equivocation, insofar as the dictum 'that you are an animal' can supposit for an utterance8 or for a thing. In the first sense it is signified that I say the utterance 'You are an animal'. In the second sense it is signified that I say the thing signified by that utterance. In the same way, any proposition has to be distinguished in which an act relevant to a mode9 is denoted to take a dictum as its object. For such propositions have to be distinguished insofar as the act can take the dictum as its object either by reason of the dictum or by reason of the thing.

(33) For example, in saying 'He knows that you are a man' there can be two good ways of understanding it: (i) that he knows the utterance 'You are a man' (the layman who does not know Latin knows that), and (ii) that he knows what is really conveyed by the proposition 'You are a man' (he does not know that unless he is a cleric).

Continues...

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Excerpted from On the Purity of the Art of Logic by Walter Burley Copyright © 2000 by Yale University. Excerpted by permission.
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