Abstract
Peter of Ailly was another member of the tradition starting with Ockham Buridan heavily influenced Peter as well, particularly in his writings on logic and language. His works became very influential in the early sixteenth century. The selections presented here are from his Insolubilia treatise. The Insolubilia is primarily a work on logical paradoxes and semantic puzzles, but in the beginning of it he presents a general semantics of language as a preamble to his treatment of the so-called insolubles. Like Ockham, he argues for a mental language which is meant to be free from paradoxes and puzzles. All insolubles, hence, arise in spoken and written languages, for Peter.
Text from: Spade, Paul V. trans. 1980. Peter of Ailly: Concepts and Insolubles. Dordrecht: Reidel.
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- 1.
It seemed so to Ockham.
- 2.
See Aristotle, De interpretatione, 4, 16b26-27. Boethius ’ Latin translation has: “Now an expression is a significative utterance one of the parts of which is significative when separated.” Note that Peter strengthens the claim so that each of the parts must be separately significant.
- 3.
Gregory of Rimini.
- 4.
of whatever kind: I.e., both categoricals and hypotheticals.
- 5.
I.e., they would be only numerically distinct.
- 6.
Since God, who exists necessarily, cannot be a whiteness. The point would not hold if “qualitas” were read for “entitas” in the examples. For it is possible for God to create only a single quality, one that is not a whiteness.
- 7.
I.e., in the intellect. This is not strictly implied by what Peter and Gregory have said, and moreover does not seem required for the argument. See, e.g., the last sentence of the paragraph, which does not appeal to this claim. See also pars. 104, 105, 110 and 123.
- 8.
One might object that the relation among the parts of the one is not the same as the relation among the parts of the other, since they differ in word order . This objection is raised in pars. 105–106 and answered in pars. 107–110.
- 9.
The point is that there seems to be no difference between, on the one hand, having the three concepts “Socrates,” “is,” and “mortal” and, on the other hand, having the mental sentence “Socrates is mortal.” One might object that there is indeed a difference, since in the case of the mental sentence, the three concepts are arranged in a sequence. But this is just what Gregory means to deny. There is no way to make out the supposed difference between having unordered, isolated concepts and having mental sentences composed of those concepts in a certain order and arrangement. See pars. 105–110. Neither should one argue that the difference between having the three concepts and having the mental sentence comes from some superadded act of composition or division performed by the intellect, as in the theory of the intellect as “composing and dividing.” For, according to that theory, the intellect’s act of “composing” (its affirmative judging) plays the role of the copula , linking subject with predicate.
- 10.
This is a good example of a common form of argument in late mediaeval authors (e.g., Ockham). Since there is no reason to prefer one alternative to the other, the two must be treated alike; hence, one must either grant them both or grant neither.
- 11.
That is, the concepts “whiteness” and “entity” will each serve as both the subject and the predicate of the mental sentence, so that the spoken sentences “Every whiteness is an entity,” which signifies a truth, and “Every entity is a whiteness,” which signifies a falsehood, will be subordinated to the same mental sentence, or at best to mental sentences that differ only numerically. Hence that mental sentence will be both true and impossible. Note that, properly speaking, spoken and written sentences are not true or false, but rather signify what is true or false. Nevertheless. Peter sanctions the less proper way of speaking, according to which spoken and written sentences may also be said to be true or false.
- 12.
The suggested difference here is one of word-order . Since the soul is a spiritual entity, however, word-order cannot be established by a spatial arrangement of the terms, as it can in written language, and so must be a matter of the temporal order of their production in the mind, just as word-order in spoken language is a matter of the temporal order of production in speech.
- 13.
Gregory is perhaps thinking of mental sentences that are affirmed in an instantaneous “flash of insight.” Furthermore, the kind of thinking that takes place in time, where first subjects and then predicates pass before the mind, is probably a case of thinking in mental language improperly so called, thinking in Latin or English. Just as speech is a temporal process, so is such improper thinking. But it is not this kind of mental sentence that is at stake in the discussion.
- 14.
I.e., the result is the same no matter what the order of construction is. But it is the result alone that concerns us. This argument seems weak. If thinking is a temporal process, rather than the result or product of such a process, then the order of production does make a difference, just as it does in a musical composition.
- 15.
I.e., Gregory of Rimini’s.
- 16.
I.e., Averroes.
- 17.
There are two reasons given here for calling a mental sentence “complex” even though, properly speaking, it is not: (a) because it is equivalent in signifying to spoken and written sentences that really are put together out of subject, copula and predicate; (b) because it signifies a composition (or, in the case of negative sentences, a division) in reality. Gregory takes either reason to be sufficient. But see Peter’s view in pars. 129 and 131.
- 18.
Par. 99.
- 19.
I.e., that some hypothetical, mental sentence is put together out of several partial acts of knowing. A “hypothetical” sentence is a molecular sentence with two or more atomic constituents. “Hypothetical” does not here mean “conditional,” although conditionals are one kind of hypothetical sentence.
- 20.
Mediaevals were notoriously lax about distinguishing conditionals, which are sentences, from inferences, which are arguments.
- 21.
Thus, at best Gregory’s view will hold only for mental categoricals. See par. 119.
- 22.
Sentences with a “hypothetical extreme” are sentences with complex subjects or predicates, such as “Socrates and Plato run,” “Socrates runs or sits,” etc. Peter suggests that these may be analyzed into real hypotheticals composed of categorical sentences without hypothetical extremes.
- 23.
I.e., Gregory’s arguments appear to apply correctly to simply categorical sentences, even though they fail for hypotheticals.
- 24.
“Confused and distributive” and “merely confused” are usually taken as modes of personal supposition . But “to represent” is to signify. The suggested argument, then, seems to propose dividing signification into kinds parallel to the modes of personal supposition . This is unusual. Most authors held that the signification of a term is context independent; it was its supposition that varied with context. Ockham, in his Commentary on the De interpretatione, perhaps has in mind a doctrine similar to the one Peter suggests here.
- 25.
This seems too quick. If signification is distinguished into kinds, as suggested in par. 121, then it might very well be said that the two concepts “whiteness” in the sentences differ in species and also the two concepts “entity”. If that is so, the difficulty vanishes.
- 26.
In the case of the third reason (par. 104), this seems to be false. If one accepts the theory in par. 121, then subject and predicate can be distinguished on the basis of the kind of signification they have. The argument in par. 103, however, appears to stand.
- 27.
I.e., an infima species in some category of accident, a species that is not also a genus.
- 28.
For the sense of this phrase, see the argument later in the paragraph, that the consequent is “against reason.”
- 29.
I.e., the same intellect.
- 30.
Delight and cognition, then, come in degrees. (This is hard to make out in the case of cognition.) The claim here is that if there exists in an intellect the quality of delight to degree m, and a second quality of delight to degree n is added in the same intellect, the result is not two instances of specifically the same quality of delight, existing in the same intellect and differing only in degree, but rather a single quality of delight to degree m+n.
- 31.
The example involved qualities that admit of degrees. Not all accidents are like this, however, and in particular the mental qualities that are concepts do not appear to admit of degrees. It may seem, therefore, that Peter is too quick with his denial of sufficient difference. But the example is probably misleading. The universal claim rests only on the quite general thesis that two accidents in the same infima species cannot inhere in the same substrate simultaneously. Just as two numerically distinct instances of a given color (of the same hue, brightness and saturation) can exist at the same time only in two numerically distinct bodies, so too two concepts that differ only in number can exist at the same time only in two numerically distinct intellects.
- 32.
Namely, the inference in par. 123, that if the conclusion in par. 119 were false, it would follow etc.
- 33.
Peter here puts the view he is attacking into the mouth of an imaginary opponent in a disputation.
- 34.
I.e., grammatical subjects, not “subjects” in the sense of subjects of accidents, as in par. 123.
- 35.
I.e., the subject of the first mental sentence and the subject of the second one do not naturally tend to combine, as for instance the qualities of delight tend to combine additively in the example in par. 123. It is not clear, however, why Peter thinks the subjects of the two mental sentences must be numerically distinct to begin with, unless it is because one cannot think two mental sentences at the same time. What Peter needs (and lacks) is an argument to show that numerically the same concept cannot be bound into the subject position of two distinct mental sentences at once.
- 36.
The point is not that no mental expression is put together in this way. Peter denied that in his first conclusion (par. 113). Rather, the point is that since not all are put together in this way, and yet all are called “complex,” there must be some other reason for calling them all “complex.” That other reason is given in par. 135.
- 37.
Hence, even if in fact all (created) mental sentences (or, for that matter, all created mental expressions—see par. 125) were complex in the way described—and Peter denies that they are, par. 119—still that would not be a necessary fact. It is possible to have mental sentences that are not complex. Such mental sentences would still be called “complex,” and so the argument in par. 126 would apply.
- 38.
I.e., it signifies the sum total of what the constituent absolute categorematic terms of its nominal definition signify.
- 39.
I.e., enough whiteness that it can be called by the name “white.”
- 40.
God’s knowledge is identical with God himself, who is absolutely simply according to the tradition. And yet we can call “complex” God’s act of knowing that every man is an animal. Therefore, it must be for some reason other than a real composition that mental sentences are called “complex.”
- 41.
This was one of the reasons sanctioned by Gregory of Rimini. See par. 111.
- 42.
I.e., if it is called. “complex” for that reason.
- 43.
“Can be signified” would have been preferable.
- 44.
The utterances or inscriptions at stake here are those “subordinated” to the mental expressions. They signify those expressions, to which they are subordinated, only “nonultimately.”
- 45.
Since the subordination relation is purely conventional.
- 46.
This was the second reason sanctioned by Gregory of Rimini. See par. 111.
- 47.
The definition of “man.”
- 48.
I.e., Gregory of Rimini’s. See par. 111. The kind of composition or division Gregory has in mind is that which answers to a sentence, not to a definition. The composition or division is expressed by the affirmative or negative copula . Note, however, that Gregory’s conclusion is stated only for sentences.
- 49.
The proposed reason for calling mental expressions “complex” is not general enough.
- 50.
Since God is absolutely simple, and is identical with his existence.
- 51.
There are no chimeras from which existence could be “divided.”
- 52.
Rather, Book VI. See Averroes, Aristotelis metaphysicorum, fol. 1520-E, on Aristotle’s Metaphysics, VI, 4, 1027bl6-22.
- 53.
See par. 111.
- 54.
Note that this conclusion avoids the problem raised in par. 130. Ockham allows something like this as one possible approach in his Commentary on the De interpretatione.
- 55.
This is not quite so. Spoken and written expressions would also be so equivalent. But they have been ruled out as reasons for calling mental expressions “complex.” See par. 129.
- 56.
A mental expression is “equivalent in signifying” to several distinct acts of knowing only in the sense that it signifies the sum total of what they do. But Peter adopts a different notion of the signification of mental sentences. That notion is of “how” a sentence signifies, not of “what” it signifies.
- 57.
E.g., proper names . Not just “singular” in the sense opposed to “plural.”
- 58.
Thus, e.g., the term “Socrates” signifies some part of what the quantitative-whole term “man” signifies.
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Read, S. (2017). Peter d’Ailly. In: Cameron, M., Hill, B., Stainton, R. (eds) Sourcebook in the History of Philosophy of Language. Springer Graduate Texts in Philosophy, vol 2. Springer, Cham. https://doi.org/10.1007/978-3-319-26908-5_18
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