Abstract
Peter Abelard is nowadays credited as the first philosopher to recognize the problem of existential import. I argue that he does not recognize our modern problem, and that his own take on the logical issues that are said to give rise to the problem is much more interesting and subtle than has usually been acknowledged, depending on claims in the philosophy of language that are worthy of investigation in their own right—in the end, vindicating Abelard’s claims about the traditional Square of Opposition.
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Notes
- 1.
- 2.
Sic quoque in categoricis propositionibus ea tantum propria contradictio ac recte diuidens cuilibet affirmationi uidetur quae negatione praeposita totam eius sententiam destruit, ut eius quae est: Omnis homo est homo ea quae est: Non omnis homo est homo, non ea quae est: Quidam homo non est homo; haec enim fortasse simul erit falsa cum ea. Re enim hominis prorsus non existente neque ea uera est quae ait: Omnis homo est homo nec ea quae proponit: Quidam homo non est homo…
All translations are mine. For the works cited and their abbreviations, see the Bibliography.
- 3.
See Seuren [2010] for an attempt to salvage “traditional” logic along Abelardian lines.
- 4.
Abelard also notes that contrapositive conversion may fail in assertoric sentences when one of the negated terms is empty: “The same error in conversion [by contraposition] happens for the same reason in simple sentences as it does in modal sentences, namely because terms that contain all things are part of the mixture. For instance, if I were to say ‘Every non-human is non-rose’ when roses have been destroyed, ‘non-rose’ contains all things, and so the converse [contrapositive of ‘Every non-human is non-rose’, namely ‘Some rose is human’], doesn’t preserve the truth-value…” (in Per. 400.239–401.243, cited in Binini [2018]). Yet here too Abelard is not pointing to a general logical problem but to a specific failure of conversion due to a specific cause.
- 5.
A minor wrinkle: (2*) says more than a mere existential commitment to a nonempty subject-term warrants; it also declares that the S that exists is also P. It would be equally falsified by an empty predicate-term, or even the failure of any S to be P. Simplification on the complex formula does yield (∃x)(Sx), as noted below, but doesn’t address the wrinkle.
- 6.
See Abelard, in Top. 271.32–273.3 for a description of the view of William of Champeaux (noster praeceptor), and for his characterization: “According to his theory, individual sentences have two senses: (i) dialectical, which is broader and in a certain way better, according to simple inherence; (ii) grammatical, which is more determinate, according to the connection of things.”
- 7.
As opposed to ‘impersonal’ verbs, as in sentences such as “It is raining.”
- 8.
Non est autem illud praetermittendum quod uerba in enuntiationibus posita modo proprie, modo per accidens praedicari dicuntur; proprie autem praedicantur hoc modo: Petrus est, Petrus currit; hic enim gemina ui funguntur, cum non solum copulandi officium tenent, sed etiam rei praedicatae significationem habent. Per accidens autem et non proprie praedicari dicitur, cum ipsum praedicato ad eius tantum copulationem apponitur, ita: Petrus est homo.
- 9.
Et sciendum, quod personalia uerba quae praedicari possunt, cuiuscumque significationis sint, omnia sese copulare possunt, ut, si dicatur: Socrates est, Socrates legit, esse et legere per se ipsa praedicantur, et gemina ui funguntur, quia et uim praedicati habent et copulantis, ut simul et praedicentur et se ipsa copulent. Sic enim dicitur currit quasi diceretur est currens.
- 10.
See also De int. 6 17a25–26. Note the problem with ‘quantifying in’ here: to say that something is such-and-so is to say of something that it is such-and-so (a notational variant), which is not the same as saying of some thing that it is such-and-so; the latter is an explicit ontological commitment not entailed by the former, at least not in Abelard’s eyes, as we shall see shortly.
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- 12.
Cum autem proprie dicitur, rem etiam praedicatam continet atque aliquam rerum existentium indeterminate attribuit, ueluti eum dicitur: Petrus est, hoc est Petrus est aliqua de existentibus rebus.
- 13.
At uero est uerbum, quod omnia in essentia continet, primo loco praedicatum ens coniungit, cum dicitur: Ego sum ac si dicerem: Ego sum aliquid de exsistentibus.
- 14.
Two points. First, the substantive verb has some company; Abelard thinks that the nuncupative verb [nuncupor] has many of the same unusual features. Second, note that only the substantive verb is predicated incidentally, since it is the only verb that can be used as an auxiliary; we can say “Socrates is reading” but we cannot say “Socrates runs reading” and even have a well-formed sentence, much less a sensible one. Abelard holds that modal verbs and other periphrastic forms require the substantive verb, forming complex verbal compounds, so they are not counterexamples: see Jacobi [1980] and Martin [2001].
- 15.
Unde mihi, si profiteri audeam, illud rationabilius uidetur ut rationi sufficere ualeamus, ut scilicet, quemadmodum oppositionem in adiecto secundum compositionem* magis quam secundum appositionem sumimus, ita accidentalem praedicationem accipiamus, ac cum dicitur est homo uel est opinabile uel est album pro uno uerbo esse hominem uel esse album uel esse opinabile intelligamus. [* = Reading compositionem for oppositionem, as suggested in Wilks [1993] 90 n.16.]
- 16.
Si uero eam sententiam et hic quoque uelimus tenere quam in Tertio Postpraedicamentorum posuimus, quando scilicet uerbum cum adiuncto praedicato unum componere uerbum diximus, oportet accidentalis quoque praedicationis coniunctionem secundum compositionem accipere…
- 17.
- 18.
Neque enim hic interpositum quoque rem praedicatam continet, quippe iam homo superflue supponeretur, sed tantum quod subiungitur praedicatum copulat; nec si iam aliquid praeter hominem in ipso esset attributum, in eodem loco hominem copularet subiunctum.
- 19.
As noted earlier, one apparent vice is that if the substantive verb is combined with a predicate-term to form a single semantic unit, it seems that neither rules of conversion nor of the syllogism, which are usually taken to refer to the subject-term and the predicate-term independent of the copula, will work any longer. Abelard has to hold that the welding of the component pieces of three-piece predication into a single verb always permits certain kinds of logical decomposition, so that from “Every S is P” we can infer “Some P is S” (for instance).
- 20.
At uero mihi omnis illa uerbi praedicatio per accidens atque impropria uidetur, quando ipsum, ut dictum est, tertium adiacens interponitur, cum non rem, ut dictum est, praedicatam contineat, sed solius copulae officium habeat, ut in ea quoque qua dicitur: Petrus est homo uel albus. Nec quidem quantum ad eius interpretationem pertinet, ex eo quod dicitur: Petrus est homo, inferri potest Petrus est, sed fortasse quantum ad praedicationem hominis, quod existentis rei tantum nomen est.
- 21.
Cum enim dicimus Homero defuncto Homerus est poeta, si significatarum significationem dictionum pensemus atque Homeri nomen hominis ut poeta sumamus, uerum est et simpliciter Homerum esse, ex eo scilicet quod poetae proprietatem habere dicitur, atque propria fuit locutio.
- 22.
Sic quoque et Chimaera est opinabilis in eo figuratiua atque impropria locutio dicitur, quod aliud uerba quam uideatur in uoce, proponant in sensu; non enim chimaerae, quae non est, aliqua proprietas per opinabile datur sed magis animae alicuius opinio de ipsa attribuitur, ac si ita diceremus: Anima alicuius opinionem habet de chimaera.
- 23.
Kretzmann [1980] 506: “Abelard’s fundamental objection to this maneuver seems to be that it is only a maneuver.”
- 24.
Cum aliquid posuit, ipsum tam existentium nomen quam non-existentium accepit secundum quod dictum est hircoceruus aliquid significare.
- 25.
Unde potius concedendum est Aliquid esse aliquid quod ipsum est in ui orationis accipi; et aliquid, ubicumque ponitur, nomen est omnium tam exsistentium quam non-exsistentium, sicut et quando dicitur aliquid esse id quod non est, ut Chimaera est homo uel Chimaera est chimaera.
- 26.
Abelard uses ‘something’ like a schematic letter. In the sentence “Homer is something (namely a poet),” the term ‘something’ stands in for whatever Homer is—in this case a poet, but it might as well have been any other word. Likewise, ‘saying that something is something’ is Aristotle’s general characterization of what it is to make a statement, which of course might be true (when we say of something that it is something it is) or false (when we say of something that it is what it is not), no matter what word we put in for the various occurrences of ‘something’.
- 27.
Oportet itaque Socratis nomen tam in affirmatione quam in negatione in eadem significatione accipi, in designatione scilicet eius qui periit tamquam existentis…
- 28.
Ebbesen [1979] discusses how later medieval philosophers dealt with this problem sentence.
- 29.
For Abelard’s presentism see King [2004] IV.2.2 100–103.
- 30.
Sicut enim chimaera proprie non-homo dicitur, hoc est unum ex his quae non sunt homines, cur non etiam opinabilis diceretur, idest unum ex his de quibus opinio habetur, quippe eadem exstitit ad non-existentia nominum suorum impositio quae ad existentia suorum. Sicut enim dictum est in impositione hominis Dicatur ista res homo, sic etiam dictum est in huiusmodi re non existente: Dicatur ista res opinabilis.
- 31.
How to interpret this suggestion, and which mereological relation it might involve, have long been matters of dispute. Modern logicians ever since Russell have faulted Aristotle for conflating class-membership (∈) with class-inclusion (⊆); Leśniewski takes the part/whole relationship literally and builds a logic around it, an approach that continues to command adherents today (see for instance Vlasits [2019]); the literature on the subject is extensive. Contemporary logic ignores Aristotle altogether, instead representing quantifier-terms as sentential operators binding variables that occur within expressions determined by translation-rules.
- 32.
In hoc enim totum et omne discrepant quod omne ad species, id est ad inferiora, totum uero ad partes, scilicet constituentes, ponitur. Et utrumque quidem quantitatis signum esse potest, illud quidem quantitatis uniuersalis rei secundum comprehensionem singularum specierum, hoc uero indiuidui compositi secundum constitutionem componentium partium… Omnis autem multorum est singillatim comprehensiuum et eadem singillatim colligit quae uox ipsa cui apponitur, signumque uniuersalitatis secundum comprehensionem omnium singulorum inferiorum dicitur. Nam uniuersalis rei quantitas in diffusione sua per inferiora consistit. —There are parallels in the use of plural general terms, ‘every horse’ and ‘horses’ for example; see dial. 64.31–65.7 and in Cat. 170.34–171.10.
- 33.
Fortasse autem facilius nos absolueremus, si omnis signum cum adiuncto nomine tamquam compositam dictionem acciperemus—non tam quidem auctoritatem quam rationem sectantes. Veluti cum dicitur omnis homo, per omnis homo tamquam per compositum nomen de singulis hominibus ageremus in ea quae uniuersalis propositio diceretur, quod de omnibus nullo excluso proponeretur aliquid, particularis uero uel singularis, quod de aliquo indeterminate uel determinate proponeret.
- 34.
As before with his proposal that in three-piece predication the substantive verb is welded together with the predicate-phrase to form a single semantic unit, Abelard will have to explain how the rules of conversion can decompose such semantic units, as in the case of (say) “Every S is P” and “Some P is S.” His answer is that conversion is designed to ‘decompose’ the semantic composition of a sentence and transform it into an equivalent, which is very different from the function the sentence was designed to accomplish in the first place, namely saying of something that it is something.
- 35.
And not just the subject-position! There is no reason to think that such a composite term could not appear as a predicate noun-phrase, in three-piece predication. Abelard recognizes and endorses this consequence, and permits both subject and predicate to be quantified. “Socrates is every animal” is false if there is some animal other than Socrates; “Every man is some animal” is straightforwardly true, since each man is the animal he is. Abelard offers a sketch of double-quantificational logic, with its own Square of Opposition and the like.
- 36.
See Yi [2021] §3.3.3 for a detailed discussion of Abelard’s account of how the Square of Opposition works in relation to other medieval philosophers as a matter of formal logic.
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King, P. (2023). Abelard on Existential Inference. In: Hochschild, J.P., Nevitt, T.C., Wood, A., Borbély, G. (eds) Metaphysics Through Semantics: The Philosophical Recovery of the Medieval Mind. International Archives of the History of Ideas Archives internationales d'histoire des idées, vol 242. Springer, Cham. https://doi.org/10.1007/978-3-031-15026-5_2
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