Abstract
In this paper I will attempt a unified analysis of the various examples of the fallacy of accident given by Aristotle in the Sophistical Refutations. In many cases the examples underdetermine the fallacy and it is not trivial to identify the fallacy committed. To make this identification we have to find some error common to all the examples and to show that this error would still be committed even if those other fallacies that the examples exemplify were not. Aristotle says that there is only one solution “against the argument” as opposed to “against the man”, and it is this solution the paper attempts to find. It is a characteristic mark of my analysis that some arguments that we might normally be inclined to say are fallacious turn out to be valid and that some arguments that we would normally be inclined to say are valid turn out to be fallacious. This is (in part) because what we call validity in modern logic is not the same as the apodicticity that Aristotelian syllogisms require in order to be used in science. The fallacies of accident, uniquely among the fallacies, are failures of apodicticity rather than failures of, in particular, semantic entailment. This makes sense in a tensed and token-based logic such as Aristotle’s. I conclude that the closest analogue to the fallacy of accident that we can point to is a fallacy in modal logic, viz., the fallacy of necessity.
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Notes
Unlike “musical Coriscus”, “rational Coriscus” is a genuine unity. The significance of the kind of unity will hopefully become clearer in the discussion of “the veiled man” type of example in Sect. 4.
Like the doctrine of distribution, the doctrine of supposition is a medieval addendum to Aristotelian philosophy. A term has ‘material supposition’ when it stands for that thing in the mind the term corresponds to, roughly analogous to putting the term in question in quotes. A term has ‘personal supposition’ when it stands for those things in the world that the term refers to. So “man” in personal supposition stands for real men and “a man” stands indefinitely for any one of those men, whereas in material supposition it stands for an idea of man, construed usually as a term in the language of thought.
Probably all fallacies depending on double meaning commit this kind of quantifier-shift fallacy, since for each premise there is a meaning of the ambiguous term for which the premise is true, but there is no meaning for which both premises are true.
Arguably, “is” does not have a sense for Aristotle (the copula is a syncategorematic term that only signifies together with a categorematic term) and ipso facto does not have multiple senses that can be equivocated between.
The alternative readings could be put as “A small number (multiplied by a small number) is a small number” with “A small number” acting as the subject and “multiplied by a small number” acting like an adjective qualifying it, or as “(A small number multiplied by a small number) is a small number” where “A small number multiplied by a small number” is a definite description of the subject. Obviously it is in the latter way that the argument should be taken, and it is in this sense that the statement is typically taken to be false, but as I will show in the sequel if “a small number” is taken as indefinite the proposition is actually true; it is made true by, e.g., “One multiplied by one is one”. Schreiber considers and prefers an alternative explanation that I will not discuss.
Thus, Aristotle is correct to say that individuals, or at least those that are perishable, cannot be defined, but it is quite consistent with this that Coriscus – a man – should have necessarily those predicates that are defined to be the essence of man.
Note that I am not claiming that all de re necessities are grounded on de dicto necessities. Some may be grounded on propria. For instance, I would say that “The number 1 is necessarily a small number” is true even though “1” is not defined as being small, and arguably is not defined at all. The de dicto necessities at issue in singular propositions are those of the species of the singular and not the singular-term itself which, having no definition, cannot be mentioned in a statement of de dicto necessity. Propositions are always to be thought of extensionally; what we have to consider is what that which is referred to is essentially and not what might be true in virtue of the meanings of the terms, which is not to say that the two issues are completely independent, of course.
It is always a one-to-one or many-to-one relation. The situation is complicated here by the fact that “work” can be a mass-noun, and the claim probably makes more sense when it is taken as a mass-noun since “your work” might otherwise be taken as a one-to-many relation. Note that it is assumed here that the indexicality of ‘your’ has been resolved.
I do not think Charles would agree with this inference; I am taking some liberties with Charles’ notation where I would not object, for instance, to the genus term alone being the left-hand side of ‘Φ def’. I do not know why there is this asymmetry where the genus term cannot but the differentia can be the only term on the left-hand side. What is more, Charles (2000, 183) puts “Being an animal Φ nec all men” rather than “Being an animal Φ def all men” even though “animal” is part of the definition of “man”. I think that ‘Φ def’ is not, then, quite the same as de dicto necessity, because I would say that “It is necessary that all men are animals” is true. Charles seems to take genera to belong by de re necessity only and differentia by de dicto necessity, or at least this is how it appears in his example.
Perhaps this is why the relation of a substance to its essence is described as identity.
We could say that although it is essential of a figure that it is a triangle when it is, in fact, a triangle, “A figure is necessarily a triangle” would not qualify as an essential predication in this context. I am not sure whether I am not here revising what ‘essential predication’ means, so I will mostly talk instead of ‘accidents’ in the sense I have given them, but sometimes I will talk of essential predicates and predications as a mode of speech.
Note, though, that given A Φ def B implies A Φ nec B, then
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Having angles equalling two right-angles [Φ def/Φ nec] [all/a] triangle(s)
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Being a triangle Φ nec a figure
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Having angles equalling two right-angles Φ nec a figure
follows from the transitivity of ‘Φ nec’.
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This was basically my first suggestion of what an ‘accident’ was in Sect. 1 in which I said that “a man” was an accident of “Coriscus”. I rejected that view. But if we replace “___ is an accident of…” with “___ is different from…” then we get something true.
In conversion of a particular proposition the undistributed term becomes distributed and the distributed term becomes undistributed.
Thus I disagree with Schreiber (2003, 133) who says that “nonconvertibility of terms is simply the formal symptom of the underlying mistake of thinking an accidental predication to be an essential predication.” But perhaps he takes essential predication here to involve the complete definition, and not just the genus-term or differentia.
Note that just because a statement does not follow by conversion does not mean that it is false; it is not logically impossible that all yellow things are honey or that all two-footed things are men.
It is to be noted in this regard that none of the Coriscus examples fail simply on the grounds that there are tokens of Coriscus that fail to refer and that for this reason propositions predicating anything at all of Coriscus will be false.
It is tempting to say that, given the figure of the syllogism, for both premises to be true as de re statements the extreme terms must be related as genus to species. But it seems that
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A man is necessarily two-footed
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A bird is necessarily two-footed
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A man is necessarily a bird
where the minor and major term share a common genus is a counterexample.
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The ‘respect’ in question is that in which Aristotle claims that contraries cannot belong to a substance “in the same respect.” This respect is, I have claimed elsewhere, a condition on the application of principles of logic to what is said rather than any part of its content. Laws of Non-Contradiction and of Identity are applicable only under certain conditions that are described respectively in the fallacies of secundum quid and accident.
References
Aristotle. 1984. Sophistical Refutations. In The Complete Works of Aristotle ed. J. Barnes, (trans: Pickard-Cambridge, W.A.). Princeton: Princeton University Press.
Buridan, Jean. 2001. Summulae de dialectica. Gyula Klima (trans: Gyula Klima). New Haven and London: Yale University Press.
Charles, David. 2000. Aristotle on meaning and essence. Oxford: Clarendon Press.
Poste, Edward. 1866. Aristotle on fallacies, the sophistici elenchi: with translation and notes. London: MacMillan and Co.
Schreiber, Scott G. 2003. Aristotle on false reasoning. Albany: SUNY Press.
Sellars, Wilfred. 1957. Substance and form in Aristotle. The Journal of Philosophy 54(22): 688–699.
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Botting, D. Fallacies of Accident. Argumentation 26, 267–289 (2012). https://doi.org/10.1007/s10503-011-9255-2
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DOI: https://doi.org/10.1007/s10503-011-9255-2