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IS 'EVERY MAN IS AN ANIMAL' TRUE WHEN NO MAN EXISTS?

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*[[Directory:Logic_Museum/The_Square_of_Opposition |Main]]

* [[Directory:Logic Museum/Nullo homine (1230-50)|Early writing (1230-50)]]

* [[Directory:Logic Museum/ Nullo homine (Modist)|Late thirteenth and early fourteenth modist school (1270-1310)]

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<~~a name~~ = "intro">Introduction

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On this page I am collecting together primary references on the medieval discussion on the question whether 'every man is an animal' is true, when no man exists. The question is closely connected with Terence Parsons' ~~<a href = "~~http://plato.stanford.edu/entries/square">discussion of the O proposition~~</a>~~ in the Stanford Encyclopedia of Philosophy. Parsons claims that 'For most of the history of Aristotelian logic, logicians assumed that negative particular propositions [i.e. Latin propositions of the form quoddam A est B, standardly represented in English as 'some A is not B'] are vacuously true if their subjects are empty'. I am suspicious of this claim. There is pretty firm evidence that no logician before Abelard even considered the special case where the subject term is empty. There is ample evidence that post-scholastic traditional logicians (i.e. from the seventeenth to the late nineteenth century and later) did not hold the view that Parsons mentions. But there is almost no literature in the high scholastic period on the O proposition, and what references we do have are confusing.

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<div id="intro">Introduction

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However, it turns out there is an extensive literature on the question of whether the proposition 'Every man is an animal' is true when no man exists

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(Utrum haec sit vera, homo est animal nullo homine existente), which was a favourite subject of sophism-literature in the late thirteenth century. Alain de Libera (loc. cit), lists 36 texts devoted to this question, which I reproduce below, together with a number of additions of my own. If Parsons' claim is correct, and for most of the history of Aristotelian logic, logicians assumed that negative particular or O propositions are vacuously true if their subjects are empty, it follows they must have thought that universal affirmative propositions are vacuously false if their subjects are empty, since the A and the O propositions are contradictory. So the question hangs upon what the logicians of the high scholastic period thought about 'every man is an animal', when the subject is empty, i.e. no men exist.

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On this page I am collecting together primary references on the medieval discussion on the question whether 'every man is an animal' is true, when no man exists. The question is closely connected with Terence Parsons' [http://plato.stanford.edu/entries/square discussion of the O proposition] in the Stanford Encyclopedia of Philosophy. Parsons claims that 'For most of the history of Aristotelian logic, logicians assumed that negative particular propositions [i.e. Latin propositions of the form quoddam A est B, standardly represented in English as 'some A is not B'] are vacuously true if their subjects are empty'. I am suspicious of this claim. There is pretty firm evidence that no logician before Abelard even considered the special case where the subject term is empty. There is ample evidence that post-scholastic traditional logicians (i.e. from the seventeenth to the late nineteenth century and later) did not hold the view that Parsons mentions. But there is almost no literature in the high scholastic period on the O proposition, and what references we do have are confusing.

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However, it turns out there is an extensive literature on the question of whether the proposition 'Every man is an animal' is true when no man exists (Utrum haec sit vera, homo est animal nullo homine existente), which was a favourite subject of sophism-literature in the late thirteenth century. Alain de Libera (loc. cit), lists 36 texts devoted to this question, which I reproduce below, together with a number of additions of my own. If Parsons' claim is correct, and for most of the history of Aristotelian logic, logicians assumed that negative particular or O propositions are vacuously true if their subjects are empty, it follows they must have thought that universal affirmative propositions are vacuously false if their subjects are empty, since the A and the O propositions are contradictory. So the question hangs upon what the logicians of the high scholastic period thought about 'every man is an animal', when the subject is empty, i.e. no men exist.

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The answer is fairly straightforward, and probably what you would expect: they were deeply divided on the subject. The problem is that certain universal propositions seem to be essentially or necessarily true. How could 'every man is an animal' or 'three and four are seven' possibly be false? It is contrary to the view of all philosophers, according to Francisco Suarez, writing at the very end of the scholastic period. Furthermore, great authorities of the Church such as Augustine and Anselm, had said that such propositions are perpetually and eternally true. Augustine says (IV On the Literal Exposition of Genesis, c. 7) 'Six is a perfect number, not because God completed all things in six days, but rather, conversely, the reason God completed things in six days, was because that number is perfect, which would be perfect even if those things did not exist'. Therefore, such propositions should be true, even when their subjects are empty.

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However, Aristotelian doctrine, strictly interpreted, requires that such propositions be false when their subjects are empty. A proposition is only true, according to Aristotle, when the combination of terms in the proposition (e.g. 'man' with 'animal') corresponds to some existing combination in reality (e.g. man and animal. Now the proposition 'a man is an animal' is true when a man exists, because the predicate 'animal' belongs to the 'essence' of its subject, man. (An essence is a set of attributes which make that substance the kind of thing it is, thus any essential attribute is necessarily found in the substance to which it belongs). But Aristotle also holds that when the existence of anything ceases, its essence perishes also (ablata existentia, perit essentia). So, by implication, the composition of things in that essence (man and animal) ceases to be a real composition when the man perishes. But when every man perishes, every combination of man and animal also perishes, therefore a proposition in which a predicate is essentially predicated of a thing is not necessarily or forever true. Aristotelian doctrine seems to imply something which is false and contrary to all philosophical opinion.

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However, Aristotelian doctrine, strictly interpreted, requires that such propositions be false when their subjects are empty. A proposition is only true, according to Aristotle, when the combination of terms in the proposition (e.g. 'man' with 'animal') corresponds to some existing combination in reality (e.g. man and animal. Now the proposition 'a man is an animal' is true when a man exists, because the predicate 'animal' belongs to the 'essence' of its subject, man. (An essence is a set of attributes which make that substance the kind of thing it is, thus any essential attribute is necessarily found in the substance to which it belongs). But Aristotle also holds that when the existence of anything ceases, its essence perishes also (ablata existentia, perit essentia).

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So, by implication, the composition of things in that essence (man and animal) ceases to be a real composition when the man perishes. But when every man perishes, every combination of man and animal also perishes, therefore a proposition in which a predicate is essentially predicated of a thing is not necessarily or forever true. Aristotelian doctrine seems to imply something which is false and contrary to all philosophical opinion.

<blockquote>Quia si, ablata existentia, perit essentia, ergo propositiones illae in quibus praedicata essentialia de re praedicantur non sunt necessariae neque perpetuae veritatis; consequens autem est falsum et contra omnium philosophorum sententiam. [Suarez]</blockquote>

Opinions were divided on the subject, and the arguments on each side are diverse and interesting. The were some very curious views on the subject. Siger of Brabant thought the proposition would be false if there were no men, but as men necessarily exist, the proposition is necessarily true. (He thought that every man must have parents, from whom the essence of man is handed down through the ages, therefore men must always have existed – a false and heretical view, which was condemned in 1277). A number of philosophers, including Scotus, argued that by a syllogism based on opposite propositions, every animal is a substance, some man is not a substance, we derive 'some man is not an animal'. But Aristotle says (Prior Analytics II, 64b7-10) that the conclusion of such a proposition is not possible. Ergo its contradictory, namely 'every man is an animal' is necessary. Boethius of Dacia points out the obvious fallacy in this argument.

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Another argument was that the universal proposition is ambiguous between signifying a categorical proposition, in which one existing thing is predicated of another existing thing, and a conditional proposition of the form 'if x is A, x is B'. With no men existing, the former is false, but the latter is true. We find this view as early as the 1250's, defended by William of Sherwood. It is roundly denounced by William of Ockham. We find it again in Vincent Ferrar, and again in Francisico Suarez, and substantially the same view is held by Maritain and other neo-scholastic logicians. Another view, unsurprisingly held by Scotus, is that essence has a separate being, esse essentiae, and that in some sense it does not perish when all the individuals that possess it have perished.

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The list of primary references is below. I have located many of these, and they will start to appear in the Logic Museum in the coming months (August-November 2007). There is very little secondary literature on the subject, but it is all the more interesting for that.

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Philosophers and dates

Richard the Sophister (fl c 1230-40)

Ockham

3,209

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