Abstract
It seems not, [a] because one can have perfect knowledge of a conclusion from principles that are proper and immediate5 and thus without any knowledge of first principles6; therefore [all principles need not be foreknown]. Also, [b] because special sciences7 do not know the existence of first principles beforehand and nonetheless they have perfect knowledge of their conclusions; therefore knowledge of [the truth of] first principles is not required.
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Notes and Commentary
F2: On Foreknowledges of Principles
Second Disputation: Galileo’s labeling this the “second disputation” is an indication that another disputation had preceded it. The title of the missing disputation is unknown, since Carbone reorganized Vallius’s notes and did not preserve the titles of the disputations into which the treatise was originally divided. From a study of Vallius-Carbone’s version one can surmise that the first disputation was entitled “How many foreknowledges and foreknowns are there?” It is probable that Galileo wrote out the disputation and that the folios of the codex containing it were subsequently lost. Less likely is the possibility that Galileo did not appropriate it and began his treatment directly with the second disputation. The entire content of this second disputation, like that of the other three in this treatise, has counterparts in Vallius-Carbone. When composing it Galileo apparently appropriated about 25 To of the material available in his source; for this type of information and relevant word counts, see Lat. Ed. Xxxiv–xxxv.
for every principle: that is, for every premise or statement that enters into the demonstration or bears on its conclusion, either directly or indirectly.
“Is it [true]“: Lat. an sit, literally ”Is it?“ As applied to a principle this is equivalent to asking whether the principle is true and known to be such — an instance of complex truth; see D2.1.2–3.
known beforehand: that is, foreknown, or known efore the demonstration can be understood and assent given to its conclusion.
proper and immediate: that is, principles that are proper to a particular subject matter and that elicit immediate assent. An example would be definitions, such as that of a triangle; see D2.5.
first principles: axioms or common principles that underlie all reasoning, examples of which are given in paragraph [4]. Sometimes “first principles” refers to proper principles, but in this context the emphasis is on general or common principles; see D2.5.4–5.
special sciences: Lat. scientiae particulares, sciences concerned with particular subject matters, also known as “partial sciences” and thus opposed to “total sciences,” those broader in scope; see F3.1.1 n. 8, and F3.2.1 n. 4. In this context, as can be seen from the reply in paragraph [6], the special sciences are opposed to metaphysics, the science of being in general.
in some way: Lat. aliquo modo, not absolutely or simply but in a qualified way. Various possible qualifications, such as being foreknown actually, habitually, or virtually, are discussed in F2.3.
proximate and immediate: the same sense as “proper and immediate” in paragraph [1]; see n. 5 above.
“that on account...more so itself“: an expression occurring at 72a29 that is difficult to translate but is usually rendered into Latin as propter quod unumquodque tale et illud magis; it also occurs in Aristotle’s Metaphysics at 993b24. The sense of the axiom, much used in scholastic reasoning, is this: if water is made hot by fire, then the fire must possess heat to a higher degree than the water. Galileo uses the axiom again in D2.6.10.
induction, division, and hypothetical syllogism: this expression occurs again at F2.4.4 and, in truncated form, at F3.2.3. The principle it is invoked to support is, in effect, the opening sentence of the Posterior Analytics on which the entire treatise on foreknowledge is based, namely, “All teaching and all learning through discourse arise from previous knowledge” (71a1). In the remaining sentences of his first paragraph, Aristotle goes on to offer a complete “induction” that is based on a “division” of the ways in which all learned disciplines are acquired. He mentions “syllogism” in this context, but not “hypothetical syllogism.” Perhaps the expression is to be understood in this way: to grasp the truth of this principle, all one need to do is divide knowledge acquired by teaching into its various kinds (division), examine the different cases to show how some other knowledge is presupposed in each kind (induction), and then argue hypothetically, if this is true of each and every kind, it must be true of all (hypothetical syllogism). See D3.1 n. 38, Sec. 4.6 of Galileo’s Logic of Discovery and Proof.
nominal definitions: Lat. quid nominis, or meaning of the term, as opposed to quid rei, or meaning of the thing. The first is usually called a nominal definition, the second a real definition.
in text 2: medieval and Renaissance commentators on Aristotle divided his exposition into sections, frequently of paragraph length, which they numbered for purposes of ready reference. Here the reference is to the section marked off approximately by the Bekker numbers 7Ia12–17.
existence: Lat. an sit; see F2.1 n. 3.
complex principles: Lat. principia complexa, meaning propositions composed of subject and predicate that serve as principles of knowing, as opposed to entities that serve as principles of being for other entities (e.g., elements in relation to compounds) and in this sense are simple. Complex principles are known by complex truth, simple principles by simple truth; see D2.1.2. For the difference between principles of knowing and principles of being, see F2.4.2–4.
texts 13, 14, and 15: that is, Metaphysics Z.4, 1030a3–b5.
texts 5 and 14: text 5 corresponds to the entire second chapter of the book, 71b10–72b4, in which Aristotle sets out the requirements for knowing any subject scientifically; text 14, to the latter part of the fifth chapter, 74a33–b4, where he explains what it means to know universally and without qualification.
Averroes, Philoponus, and Themistius: commentators on the text of Aristotle. For biographical and bibliographical details on these authors and their works, see the alphabetical listing by author in the Biographical and Bibliographical Register at the end of the volume.
make no mention: the question, as stated, is withdrawn in the last sentence of this paragraph, where it is claimed that Aristotle does make mention of this foreknowledge in texts 5 and 14, in chapters 2 and 5 respectively. Perhaps its sense is that Aristotle makes no mention of it in chapter 1, where he expressly enumerates only two foreknowledges, existence and meaning (71a11–14), as stated in the second reply to the query.
this foreknowledge: that is, the meaning of terms in principles, not the meaning of the subject; see F3.6 n. 2 and F3.6.4 n. 12.
inventive science: alternatively, investigative science or dialectics, which employs topical reasoning whose methodological procedures are set forth in the Topics. It is characteristic of such science to proceed from common opinion, that is, from principles that are accepted by all and thus do no require special foreknowledge to be understood. See Sec. 2.8 of Galileo’s Logic of Discovery and Proof.
directing or acting foreknowledge: Lat. praecognitio dirigens...agens, technical terms that are explained in the missing “first disputation” of this treatise and are here presupposed; they occur again at F3.6.3 and F4.1.12–13. The distinction is attributed to Averroes. As Vallius explains it, directing foreknowledge assists one in knowing but does not make one know, whereas acting foreknowledge actually produces new knowledge. Vallius-Carbone liken directing foreknowledge to a conditio sine qua non and acting foreknowledge to an efficient cause in the learning process. (For a fuller explanation, see Sec. 4.1 of Galileo’s Logic of Discovery and Proof.) The most universal principles involved in demonstration do not require this assistance nor are they efficient causes in a proper sense; thus they do not require either type of foreknowledge.
actually or habitually: to have foreknowledge actually would be to have explicit knowledge of a principle, whereas to have it habitually would be to be able to reason with it without being explicitly aware of it. Thus the sense of the question is this: in working a problem in arithmetic does one have to have explicit knowledge of an axiom such as “equals added to equals the results are equal,” or does the ability to use the axiom suffice?
texts 5 and 16: for text 5, see F2.2.3 n. 5; text 16 is at 74b13–26.
efficient cause of the science: in the sense of being the efficient cause of the conclusion; see D2.6.14. For a fuller explanation of the types of causality involved in demonstration and in science, see D1.1.2.
cause and effect are correlatives: that is, a cause is a cause strictly speaking only when it is actually producing an effect, and thus the one, either cause or effect, cannot be known without the other; further use of this line of reasoning is made in Galileo’s treatment of the demonstrative regress, D3.3.7–8.
enter {actually }... foreknown actually: in appropriating this conclusion Galileo inadvertently left out the first “actually” and thus obscured its meaning. If an axiom states an impossibility, for example, and this is one of the premises on which the demonstration is based, then the axiom must be foreknown actually for the conclusion to be understood.
imperfect demonstration: on the various types of demonstration, including demonstration to the impossible, see D1.1.1 and D3.1. The reason why demonstration to the impossible is said to be imperfect is that it argues from false premises rather than from premises that are true and certain (D3.1.4); yet it is true demonstration (D2.1.5) in that it leads to a necessary conclusion.
virtually: neither actually nor habitually, but in a way intermediate between the two. This distinction was invoked by the Dominican commentator on St. Thomas, Cardinal Cajetan, to explain how causes, and demonstrations based on them, could be applied in theology to explain the divine attributes. It was further used by commentators on the PosteriorAnalytics to solve problems relating to premises and the ways in which they can be said to be first, prior, and immediate; see D2.2.7 and D2.4.4.
order of being...order of knowing: in other words, though axioms may not serve as principles in the order of being they may nonetheless serve as principles in the order of knowing; this distinction is elaborated in the following question, particularly in F2.4.2–4.
to convince the obstinate: the statement here is cryptic, but the meaning seems to be that reduction to the impossible is a type of ad hominem argument that can be used to convince one of the absurdity of one’s position, in which case it becomes a reduction to the absurd (reductio ad absurdum).
so evident: Lat. ita nota, to be taken in the sense of the principles being per se nota or self-evident and thus not requiring proof through antecedents that are more known. See Sec. 4.7 of Galileo’s Logic of Discovery and Proof.
cannot be proved by any reasoning: Lat. nulla ratione probari possint, that they cannot be established by any type of discourse.
text 15: in ch. 6, 74b5–13.
supposed: Lat. supponuntur, a technical term used by Aristotle to indicate that principles in a demonstration function as “suppositions,” i.e., as a type of immediate proposition. Unlike axioms, the other type of immediate proposition, suppositions do not have to be foreknown; usually they are accepted by those to whom the demonstration is being proposed and on this account do not have to be proved. See D2.3.7; also Sec. 4.2 of Galileo’s Logic of Discovery and Proof.
the metaphysician: in its expositive role, metaphysics is the science of being qua being, concerned with explicating the universal properties of being as such. As the supreme science it also takes on a critical role, justifying and defending principles (including first principles) against those who would reject them or attempt to deny them. See Sec. 3.3b of Galileo’s Logic of Discovery and Proof.
moderns: Lat. recentiores, possibly referring to contemporary but unnamed Neoplatonists. Galileo’s source here speaks of “Avicenna and others,” where the “others” refers to Plato, Plotinus, Themistius, and Simplicius (for details, see Lat. Ed. 129).
as a physicist: that is, as a natural philosopher, equivalent in that day to a natural scientist. A number of principles in Aristotle’s Physics have counterparts in his Metaphysics, whence the ground for the objection.
existence follows essence in common: a statement with Neoplatonic overtones. Essence and existence are the two basic principles of all being, and in creatures, according to Aquinas, they are really distinct from each other. For a being to exist it must first have an essence; thus there is a certain priority in the principles themselves, with essence preceding existence in the ontological order.
the metaphysician: that is, the person who studies being in common, the subject of metaphysics; see n. 5 above.
a priori: from cause to effect, from something prior in the order of being to something posterior in the same order.
{a posteriori}: omitted by Galileo here and supplied for sense; the opposite of a priori, i.e., from effect to cause, from something posterior in the order of being to something prior in the same order. (This reading emends that found in the Latin Edition, p. 6, whose critical apparatus for line 21 indicates that Galileo omitted a priori at this point and wrote nisi instead. If Galileo did so the text would read, in translation: “principles in the order of being cannot be demonstrated {a priori} through principles in the order of knowing.” Although this conveys the correct sense, in view of the presence of the nisi it is more faithful to the text to add the a posteriori after the nisi than to delete the nisi and substitute a priori instead.)
protomatter: Lat. materia prima, Gr. hylé proté, the primordial indeterminate substrate that is a component of all material being and is conserved in all changes, substantial as well as accidental, in the universe. Aristotle argues for the existence of such a substrate in Physics I.7 (189b30–191a22) from an analysis of transmutation or substantial change. See also D3.2.3.
first mover: Lat. motor primum, the eternal and immovable mover required, according to Aristotle in Physics VIII.6 (258b10–260a19), to explain all movement or change in the universe. This and the previous example are invoked by Zabarella and Balduino in their commentaries on the Posterior Analytics; see Lat. Ed. 130. See also D3.2.3.
usually not proved but manifested: Lat. non solere probari sed ostendi, not demonstrated but simply shown to the person who does not see them by the process described in F2.1.4 n. 11; see Sec. 4.6b of Galileo’s Logic of Discovery and Proof.
first and immediate principles: already mentioned in F2.1 and explained at length in D2.2 and D2.3.
subalternating science: a science that is higher than another (called the subalternated science) in the sense of being more abstract and more certain. For Aristotle mathematics stands in this relation to physics and so can supply principles for “mixed sciences” such as astronomy, optics, and mechanics, the ancient counterparts of mathematical physics. See Secs. 3.3c and 3.4 of Galileo’s Logic of Discovery and Proof.
dialectics: the branch of logic concerned with probable reasoning, whose canons are set forth by Aristotle in the Topics; see Sec. 3.6 of Galileo’s Logic of Discovery and Proof.
sought: Lat. quaesita, in the sense that principles are the end of the reasoning process when one argues from effect to cause, whereas they are the beginning of the reasoning process when one argues from cause to effect.
F3: On Foreknowledges of Subjects
{of the Subject}: this expression is missing in Galileo’s manuscript; Galileo left a space for it but then failed to return and fill the space in, thus omitting it inadvertently from the title of the disputation.
Aristotle: the reference is to the first chapter of the first book of Aristotle’s Posterior Analytics, where Aristotle maintains that to have demonstrative knowledge of the unit, one must first know what the term “unit” means and whether or not a unit in this understanding exists (71a16–17). The question thus relates to previous knowledge, i.e., to foreknowledge, as this is required to demonstrate properties of some subject such as a unit.
“is”: Lat. esse in the first occurrence, and an sit in the second. Literally esse means “to be,” and sometimes it is used as a synonym for “being,” but it is employed in scholastic Latin in a more technical sense to indicate existence, following the usage of St. Thomas Aquinas. Similarly an sit literally means “Is it,” “Whether it be,” or “Whether it exists,” but it is also used as a synonym for existence. Thus the question reads: What does Aristotle mean by existence when he says that the existence of the subject must be foreknown?
subject: the subject of a demonstration whose conclusion is usually expressed in the form S is P, where S stands for the subject and P stands for the predicate or property attributed to it.
subject: subject can be taken for the subject of a demonstration, as above, or it can be taken for the subject of a science. In the latter meaning it is sometimes used interchangeably with object, in the sense that the subject of a science is also the object of its investigations.
properties: predicates in the sense of proper attributes. Thus it is a property of a triangle that the sum of its interior angles is equal to two right angles.
metaphysics: the highest of the speculative sciences, treating of being in the most general sense (ens commune), as opposed to quantified being (ens quantum), studied in mathematics, and changeable being (ens mobile), studied in natural science. See Sec. 3.3b of Galileo’s Logic of Discovery and Proof.
particular sciences: those with special subject matters, such as astronomy, treating of the heavens, or meteorology, treating of phenomena in the earth’s atmosphere.
the “is” of existence: Lat. esse existentiae, usually taken as a synonym for existence. It is opposed to esse essentiae, usually taken as a synonym for essence.
actual or potential: these terms are explained in the examples that follow. Actual existence means existence here and now, whereas potential existence means merely the ability to exist or to come into being. A live human being has actual existence; a fertilized human egg has actual existence as an egg but only potential existence as a human being.
authorities: the reference here is to authors (auctores) who have treated this problem — generally Greek, Arab, or Latin commentators on the Posterior Analytics. Many of them are identified by name in what follows, along with references to the loci where they discuss Aristotle’s text.
for acquiring a science at the start: that is, at the time when a science is first being developed by those who initiate it, its discoverers. The problem is slightly different for those who later acquire a science from those who first discovered it and so may be said to learn it from them. See Sec. 3.1 of Galileo’s Logic of Discovery and Proof.
in the development of a science: Lat. in progressu scientiae. In Galileo’s terminology, progressus as applied to a science has a special technical sense explained in Sec. 4.9c of Galileo’s Logic of Discovery and Proof. Here he is simply referring to what is required for the growth of any science, whether this comes about in those who initiate it or in those who learn from them (cf. D3.3.10 nn. 18–19).
second “is”: i.e., the “is” of existence, as opposed to the “is” of essence.
certain authors: these are not identified by Galileo. Vallius-Carbone name them as Marc Antonio Zimara, Girolamo Balduino, Apollinaris, and Giles of Rome.
the “is” of the essence: Lat. esse essentiae, i.e., the essence of the subject, or its quiddity, usually formulated in its definition. Thus, to demonstrate properties of a triangle one must first know the essence of a triangle, that is, what a triangle is, namely, a three-sided plane figure.
essence before...existence: this statement presupposes the Thomistic real distinction between essence and existence in creatures. In Aquinas’s teaching existence is an act conferred on a creature by the Creator that complements and perfects its essence by putting it among actual existents. See F2.4.1 n. 8.
determinate quiddity: that is, precise definition.
of others: these are not identified by Galileo or by Vallius-Carbone, but Vallius mentions Domingo de Soto as one such author in VL2: 164.
many moderns: Lat. multorum recentiorum, possibly a reference to authors still living and on this account not mentioned by name.
actual “is” of the existence: Lat. esse existentiae actuale, i.e., existence in the real world, not merely in the mind, and not potentially but in full actuality.
at all times: Lat. semper. The word semper occurs twice in this sentence; the first occurrence was apparently missed by Galileo in adapting his text from the source from which he worked, since it is inserted in the text interlinearly. This question has significant implications for the development of Galileo’s science of motion, particularly for his treatment of uniformly accelerated motion. The sense of the query is this: do the things of which we seek scientific knowledge have to be real and existent at the very time our scientific knowledge exists? For example: can there be a science of roses in winter, when all roses are dead; can there be a science of snow in mid-summer, when it is too hot for snow actually to exist? See D2.1.9.
the “is” of the {essence}: Lat. esse essentiae; Galileo wrote esse existentiae here, obviously a copying error and so corrected for sense.
the “is” of the {essence}: see the previous comment.
there cannot be any demonstration: usually the middle term of a demonstration states the definition of the subject; if the definition of the subject, i.e., the “is” of its essence, is not known, no middle term will be available and thus there cannot be a demonstration. See n. 16 above.
in real sciences: Lat. in scientiis realibus, i.e., in sciences concerned with real, extramental beings, such as those in the world of nature. Real sciences are here implicitly differentiated from rational sciences, those concerned with beings of reason, which have existence in the mind only and not in the world of nature. Logical entities are commonly regarded as beings of reason. See Sec. 2.3 of Galileo’s Logic of Discovery and Proof; also n. 34 below.
at least...impediments: this expression was omitted by Galileo in his first draft of the passage, and then inserted at its proper place in the margin of the manuscript. For the importance of the marginal insert as evidence of the derivative nature of Galileo’s composition, see Galileo and His Sources, 41–42. The point of the qualification, as explained by Carbone in his version of the passage (Additamenta, 46vb-47ra), is that one need not know of the actual existence of the subject of demonstration for all times and places and under all conditions whatever. It is sufficient to know, for example, that roses actually exist in the summer in the earth’s northern hemisphere, provided that there is no blight in the region that would kill them; under these suppositions it is possible to have a science of roses, even though no roses may actually be existent here and now. Galileo was interested throughout his life in impedimenta, i.e., accidental causes that interfere with the phenomena of nature, and devoted much of his experimental activity to eliminating them. A good part of his study of naturally accelerated motion, described on the Third Day of his Two New Sciences, was in fact directed at identifying impedimenta such as friction and air resistance that would cause the actual fall of bodies to deviate from the uniform acceleration imparted to heavy bodies by nature. On the supposition of such impediments being removed, one could have a true science of naturally accelerated motion and demonstrate properties of it as a subject. See Sec. 4.2c of Galileo’s Logic of Discovery and Proof.
human sciences: i.e., sciences as possessed by human beings, and thus to be distinguished from those known only to angels or to God. See Secs. 2.7a and 3.1 of Galileo’s Logic of Discovery and Proof; also n. 45 below.
an [“is”] of actual existence: Lat. esse actualis existentiae; in writing this Galileo omitted the esse, here inserted for sense.
the first of all [scientific questions]: according to Aristotle in the beginning of Book 2 of the PosteriorAnalytics (89b23–25), there are only four scientific questions that can be asked about any subject. These were usually given in Latin by the scholastics as follows: an sit (Is it?); quid sit (What is it?); qualis sit (What kind is it?); and propter quid (Why is it of this kind?). Thus the question an sit is the first of all scientific questions.
This is apparent... eternity of motion: see F2.34.3 and D3.2.3. Here are enumerated exceptions to the general principle established in the second conclusion, paragraph [9] above. Although the total subject of the science must be foreknown to exist actually in a general way, this requirement does not entail that everything included under the total subject (spoken of in the following question as a “partial subject”) need be foreknown in detail. For example, to have a science of motion or change, one would have to know the principles that are required for motion or change in general, without having to be aware that a special type of change, known as “substantial change,” requires protomatter or materia prima as its proper subject. Similarly, one might be aware that all change requires an agent, without knowing in detail that a special agent, or “prime mover,” might be necessary to explain the eternal movement of the heavenly bodies. Or again: one would need to foreknow that local movement, or change of place, actually exists in nature in order to have a science of motion, but one would not have to know that there is such a thing as naturally accelerated motion at the outset of the science; indeed, one might prove the existence of the latter type of motion, under certain conditions, as the science later develops. Much of Galileo’s discussion throughout the Third and Fourth Days of the Two New Sciences seems directed at elucidating this point.
of demonstration in its proper sense: i.e., demonstration of the reasoned fact, as opposed to demonstration of the fact, the type discussed in the previous note. For fuller details see Secs. 4.4b and 4.9a of Galileo’s Logic of Discovery and Proof.
rational sciences, if there be such: in D2.1.8 Galileo gives the reason for the qualification “if there be such,” namely, that science must be concerned with real beings that are true in an ontological sense. On this account Vallius-Carbone (and Vallius himself), while occasionally referring to logic as a science, prefer to characterize it simply as an instrumental habit; see Sec. 2.4a of Galileo’s Logic of Discovery and Proof.
its “is” as an object: Lat. esse obiectivum, i.e., objective existence, or existence solely as an object of consideration by a knowing power such as the intellect, and not existence in a real or extramental sense.
sciences abstract from existence: an objection based on the abstractive theory of the sciences deriving from Boethius and Aquinas. In this view the concepts on which a science is based are abstracted from individual, sensible existents, and in the process are universalized; thus they consider the essences or universal features of things, not their singular or particular instantiations, and in this sense do not consider the existence of this or that individual. For an explanation of the knowledge process on which this theory is based, see Sec. 2.3 of Galileo’s Logic of Discovery and Proof.
sciences are not concerned with contingent matters: this is a variation of the objection in paragraph [12], and the reply is the same except that essences or universal features of things are replaced by species, which are not contingent in the way in which individual existents are. On the difference between necessary and contingent matters, see Sec. 3.5a of Galileo’s Logic of Discovery and Proof.
on the supposition of there being a universe: Lat. supposito universo, that is, if there is to be a universe made up of many species at any particular time, then those species are necessary under that supposition. This is an instance of suppositional reasoning, frequently employed by Galileo; see Sec. 4.2 of Galileo’s Logic of Discovery and Proof.
science does not consider individuals: yet another variation of the objection given in paragraphs [12] and [13], and the reply is again the same, except that nature now becomes the universalizing principle. Medieval writers such as Jean Buridan regarded an argument of this type as one made ex suppositione naturae, i.e., on the supposition of nature — an observation which ties this reply to that of the previous argument.
[...]: the ellipsis indicated here is a blank space of about half a line that occurs in the manuscript at this point. Galileo apparently had difficulty abbreviating the argument in his source and so left a space to be filled in later. His lacuna here occupies six lines in ValliusCarbone, which translate as follows: “Since therefore species are conserved in individuals, there must be some individual in which they exist. Thus the universal nature is foreknown, not in the abstract but in some singular individual, though not one determinately assigned, and that is in no way repugnant to the sciences” [Lat. Ed. 140].
removing the impediment of the divine will: note here that God’s efficacious will, which could annihilate the universe at any time, is regarded as an impedimentum to the work of the natural philosopher; thus even this impediment has to be removed by an appropriate supposition if one is to reason as a natural scientist.
angels: the objection is raised to differentiate human sciences, paragraph [9] above, from those that may be acquired by spiritual creatures. Human beings obtain their knowledge of natural kinds through a process of abstraction from individual existents perceived in sense experience, and thus actual existents are necessary for their acquisition of a science, as noted in paragraph [3]. Angels, on the other hand, obtain knowledge through infused species and without sense impressions; therefore they are not limited as are humans in this regard. Again see Secs. 2.7a and 3.1 of Galileo’s Logic of Discovery and Proof for fuller background.
human sciences: i.e., sciences acquired by men, not those possible for angels; see nn. 28 and 45.
properties can be present: the objection makes the point that potential presence, as opposed to actual presence, is sufficient for knowledge of the property, and therefore potential existence might also be sufficient for knowledge of the subject - a restatement of the argument proposed as the second opinion in paragraph [5] above. The reply, rather than rejecting this opinion outright, acknowledges some element of truth in it.
mathematics...goodness: this Aristotelian maxim was quoted frequently by Galileo in his various writings. Some authors used it in a pejorative sense to calumniate mathematicians and their work - examples would be Alessandro Piccolomini and Benedictus Pererius, the latter a Jesuit who taught at the Collegio Romano before Vallius. Following Vallius’s notes, Galileo employs the maxim but turns it to good use to show that mathematics is a human science concerned with existence, as explained in the following note.
human science: that is, a science derived from sense experience. It is also a real science, and not merely a rational science like logic concerned with an esse obiectivum, as indicated in paragraph [11], n. 34. This being the case, it presupposes the actual extramental existence of quantified beings in order to establish its subject, even though it abstracts from such existence when demonstrating their properties.
adequate subject: Lat. obiectum adaequatum, an instance where subject and object are taken to be equivalent; see F3.1.1 n. 5. Many different kinds of subject/object were mentioned and distinguished in Jesuit commentaries on Aristotle’s works, viz., principal subject, adequate subject, total subject, partial subject [see Sec. 4.3a of Galileo’s Logic of Discovery and Proof]. The adequate subject of a science is a subject that is equivalent to, or may be equated to, all of the objects that are considered in a science; thus nature can be said to be the adequate subject of physics or natural science.
total subject: Lat. subiectum totale, one roughly equivalent to the adequate subject of the science but stressing the proper formality under which the science considers it. In the case of physics, this was taken by the Jesuits to be the natural body, which includes all bodies studied in natural science [Sec. 4.3a of Galileo’s Logic of Discovery and Proof].
total object: Lat. obiectum totale, used interchangeably with total subject.
partial science: Lat. scientia partialis, the portion of a science that considers a partial subject; for example, if the atmosphere is only a part of the sublunary region, the science that treats this part of terrestrial nature, meteorology, is a partial science with respect to the science that treats all of the elementary bodies (for Aristotle, the De caelo et mundo), which therefore can be regarded as a total science. Partial and total are thus correlatives. The science of the elements is a partial science with respect to the total science of physics, and the science of earth (as one of the four Aristotelian elements) is a partial science with respect to the total science of the elements. See the following two notes.
total science: Lat. scientia totalis - see the previous note. In a more proper sense, when discussing the specification of the speculative sciences, Vallius-Carbone argue that here are only three such total sciences, namely, physics, mathematics, and metaphysics. The basis of this division is explained in Sec. 3.3b of Galileo’s Logic of Discovery and Proof.
a partial science...of its subject: a partial science has a partial subject or object, and the possibility exists that it can demonstrate the existence of its partial subject. For example, although earth and water and air give evidence of their extramental existence, it is not completely clear that fire exists as an element, and thus it would be necessary to prove the existence of fire if one were to have a science of this element (cf. D3.2.3). This question apparently had important ramifications for Galileo in the later development of his science. For example, the second of the “two new sciences” he proposed to develop in his masterwork of 1638 was the science of local motion; its total subject would therefore be this type of motion, motion according to place (motus localis), and as he proposed it, it would be composed of three partial subjects that could count as its species: uniform motion, naturally accelerated motion, and a combination of these two, projectile motion. For each of these partial subjects, in turn, it would be necessary to offer experimental or a posteriori proofs of their extramental existence.
the [question] “What is it” of its subject: Lat. quid sit sui subiecti, the definition or the quiddity of the subject; see F3.1.4 n. 16 and F3.1.8 n. 25. In the second book of the Posterior Analytics Aristotle argues that no science can demonstrate the definition of its subject, but that nonetheless it can manifest that definition in a demonstrative way by showing the relationships that obtain among its causal components; see chapter 10, 93b37–94a9.
manifested: Lat. ostendi; see F2.1.4 n. 11, F2.4.4 n. 14.
in a higher science: Lat. in [scientia] superiori, that is, in a subalternating science as explained in F2.4.5 n. 16. For fuller details, again see Secs. 3.3c and 3.4 of Galileo’s Logic of Discovery and Proof.
are correlatives: Lat. sunt relativa, basically the same argument as applied to cause and effect, F2.3.1; see also D3.3.7–8.
of the principal subject: Lat. subiecti principalis, the preeminent part of the total subject; in his notes on Aristotle’s De caelo et mundo Galileo identifies the heavens (caelum) as the principal subject (obiectum principalitatis) of that treatise, GG1: 16. See Sec. 4.3a of Galileo’s Logic of Discovery and Proof.
here: Galileo failed to identify the particular text of Aristotle on which the argument in part [c] of paragraph [1] is based. A clue is given in Vallius-Carbone, however, who point to the sixth book of the Metaphysics, ch. 1 (1025b17–18), as the source of the difficulty [CA49ra; Lat. Ed. 146].
quiddity: Lat. quid sit, essence or definition, here again opposed to an sit, existence; see F3.1.4 nn. 16–18.
this text: i.e., that identified in n. 12 above.
habitus: habit in the sense of second nature; a scientific habitus perfects the intellect, enabling it to function in an effortless way with its subject matter in much the same way as the virtue of justice perfects the will of a just man and enables him similarly to act justly in his dealings with others. This notion lies behind Vallius-Carbone’s distinction between actual science and habitual science, as explained in Sec. 3.2 of Galileo’s Logic of Discovery and Proof.
a higher science: a reference to the comparison and subalternation of the speculative sciences, explained in Sec. 3.3c of Galileo’s Logic of Discovery and Proof.
Galileo enumerates this as the “Fourth Question” but actually it is the third of the disputation. From a study of his handwriting and the contents of F3.2 and F3.4 one can establish with near certainty that he did not skip a question here but merely made a mistake in numbering the questions; for details, see Lat. Ed. 146 (16.17–20), 147 (17.1–2). Since much the same terminology is employed here as in F3.2, the reader should consult the notes for that question to supplement those given below.
Some: Lat. Aliqui, not identified by Galileo. Vallius-Carbone note that their objections derive from Averroes, who held the opposite opinion but listed these and other arguments in order to refute them.
Others: Lat. Alii, again not named by Galileo but identified by Vallius-Carbone as Averroes, Grosseteste, and Zimara. Other proponents are specified by Lorinus; see Lat. Ed. 148–149.
habitus of a higher science: see F3.2.10 nn.15–16.
to pass from one genus to another: Lat. de genere in genus transcendere. The prohibition here is usually referred to as that against metabasis or “passing over” from one genus to another, voiced by Aristotle in A.7 of the Posterior Analytics (75a37–39), where he states that one cannot use arithmetic to demonstrate a theorem in geometry. In this particular case arithmetic, whose subject is discrete quantity, is regarded as being concerned with a higher genus than geometry, whose subject is continuous quantity. Following this expression there is an addition of six words in Galileo’s composition; these are omitted here as representing an incomplete thought and so not translatable — for details, see Lat. Ed. 149.
the actuality of the subject: Lat. actus ipsius subiecti, an application of St. Thomas’s teaching on potency and act as the basic components of all being. In this view essence is related to existence as potency is to act; thus existence is the ultimate actuality of the subject, presupposing its quiddity as the potency it actuates. See F2.4.1 n. 8, F3.1.4 n. 17.
[pointless]: Lat. vana, omitted inadvertently by Galileo in this sentence but appearing correctly in the following sentence.
to investigate the parts of its definition: explaining how this investigation is to be carried out takes up a large part of the second book of the Posterior Analytics. A definition may be viewed as composed of two parts, the genus and the differentia, and this would be known among scholastics as a metaphysical definition, or alternatively it may be viewed as composed of four parts, Aristotle’s four causes (formal, material, efficient, and final), in which case it would be called a physical definition.
first text: that is, Metaphysics E.1, 1025b3–18.
all causes...theformal cause: a further explication of the parts of a definition as noted in n. 8 above. Although all four causes pertain to the definition or quiddity in a broad sense, the formal cause is preeminent among them and thus serves best to characterize the quiddity. The statement is corroborated in D2.2.4, where Galileo points out that demonstrations of the reasoned fact are more perfect the more they proceed from formal causes, which are more intrinsic to the thing.
real definition: Lat. quid rei, definition of the thing, as opposed to the quid nominis or definition of the term, also called the nominal definition; see F2.2 n. 1, F3.1.4 n. 18, F3.2.1 n. 7.
explain...apodictically: Lat. reddere propter quid, that is, give a demonstration propterquid of the subject’s existence. Usually “demonstration propter quid” is translated “demonstration of the reasoned fact,” as opposed to “demonstration quia,” which is translated “demonstration of the fact.” The fact of the subject’s existence is not at question here; the problem is the “why” of its existence and how the real definition can supply this.
{existence}: In writing the title of his question Galileo unaccountably left out the word for existence; that it was intended is clear from the first sentence of paragraph [3] in his text.
a posteriori only: Galileo’s first conclusion in this paragraph, that a science can show real definitions of its partial subjects, is unproblematic in view of his conclusions in F3.4; his second conclusion relating to the total subject is more controversial in view of the related discussion in F3.2. He thus qualifies the second conclusion by stating that the demonstration manifesting the real definition of the total subject can only be a posteriori. Vallius-Carbone explicate this by adding how this can be done: “through some effects that are more known.” An example might be the definition of nature given by Aristotle in Physics II.1, 192b21–23, based on its effects as described in 192b9–21.
as we have explained above: i.e., in F3.4.8.
existence in common: Lat. existentia in communi, the way in which existence is considered by the metaphysician, explained in F3.4.8.
one must beg the question: Lat. petere principium necesse est. Note here that this is the first mention of a petitio principii in Galileo’s appropriated questions — important because it was probably a concern over begging the question in his Theorems on the Center of Gravity of Solids that prompted his interest in Vallius’s lecture notes. Other occurrences of the expression are at D2.3.5, D3.1.5–6, D3.1.15, and D3.3.2.
in the minor premise: i.e., in the second premise stating that every man is a rational animal. Precisely how this begs the question is not clear from Galileo’s exposition, since he will give exactly the same syllogism, with the same minor premise, in paragraph [5]. ValliusCarbone make the point more explicitly: the minor premise as here stated is understood to mean that every man exists as a rational animal, taking the “is” of the premise to mean “exists”; therefore it begs what was to be proved in the conclusion, namely, that every man exists. See n. 11 below.
apodictic proof: that is, proof in the sense of that formulated in a most powerful demonstration. How most powerful demonstration can be said to provide propter quid proof of existence is explained at length in D3.1.
of which it is the actuality: Lat. cuius est actus; see F3.4.4 n. 5.
the word “is”...meaning of existence: this second formulation of the syllogism, though expressed with the same premises as that in paragraph [3], is meant only to explicate the content of the preceding enthymeme and not to make any existence claim in the minor premise. Thus the “is” is to be understood only as a logical copula, not as an ontological affirmation.
To the objections: a superfluous addition made by Galileo and not found in his source. The difficulty raised in paragraph [2] is answered in the same paragraph, that in paragraph [3] in paragraph [5].
What does Aristotle mean: that is, at the beginning of the Posterior Analytics, 71a12–14, in a passage included in text 2 according to Galileo’s enumeration of text numbers; see F2.2.1 n. 2.
quiddity that is said [of the subject]: Lat. quid est quod dicitur. The Latin of the version of James the Venetian Greek is a cryptic but faithful rendering of the Greek text. It reads as follows: Dupliciter autem necessarium est praecognoscere; alia namque quia sunt, prius necesse est opinari, alia vero, quid est quod dicitur intelligere oportet... Difficult to translate, this passage was generally taken to mean that two things must be known about the subjects of demonstration, “that” they are (quia sunt) and “what” it is that is said of them (quid est quod dicitur). Some commentators took the quid of the latter expression to refer to the quid rei or real definition, others to the quid nominis or nominal definition; see F2.2 n. 1, F3.2.1 n. 7.
Cajetan: the only recent expositor mentioned by Galileo; Vallius-Carbone identify Soto and Zabarella as others who held this position.
many moderns: to Themistius and Philoponus Vallius-Carbone add Giles of Rome, Paul of Venice, and Apollinaris; Lorinus attributes the position to contemporary Averroists, recentiores Averroistae.
in some demonstrations: Galileo here cites emonstrations a posteriori as exceptions that do not require foreknowledge of real definitions; in his Logica Vallius points to mathematical demonstrations as those wherein foreknowledge of real definitions “is not required in any way” [VL2: 141].
quiddity presupposes existence: a familiar refrain in this treatise; see F2.4.1 n. 8, F3.1.4 n. 17, F3.4.4 n. 5.
“that which the thing was to be”: Lat. quid quod erat esse rei, a literal translation of Aristotle’s to ti en einai (Metaphysics 988a34, 1013a29, 1037a22) attributable to William of Moerbeke, though with the first two words interchanged. The expression was múch used by St. Thomas, usually to signify the formal cause “through which is known what the substance of a thing is” (In I Meta., lect. 11; see also In V Meta., lect 2; In VII Meta., lect. 11).
“the quiddity that was”: Lat. quid quod erat, an abbreviation of the fuller expression found in the previous note.
[and]: omitted by Galileo and required for sense.
“directing. ”.. “acting”: see the comment above at F2.2.5 n. 8 and the fuller discussion in Sec. 4.1 of Galileo’s Logic of Discovery and Proof.
to experts: Lat. sapientibus, an expression based on the scholastic distinction between principles evident to all (per se nota omnibus) and those evident only to experts (per se nota sapientibus), that is, those who have a competent grasp of a particular subject matter.
“How many things should be foreknown“: Lat. Quot sint praecognita, the title of a question pertaining to the first disputation on foreknowledge, missing from Galileo’s treatment. Galileo’s entire treatise, as its title indicates, is concerned not only with foreknowledges (praecognitiones) but also with things that must be foreknown (praecognita). The praecognita would seem to be three in number, corresponding to the objects of consideration in the three disputations into which the treatise is divided, namely, principles, subjects, and properties. Precisely as foreknown, they alternatively may be viewed as praecognitiones, as Galileo implies in the titles of his three disputations. Following Aristotle’s usage, however, the praecognitiones may be differentiated from the praecognita, since in text 2 Aristotle seems to state that the praecognitiones are only two in number, whereas the praecognita are the three just mentioned. The two foreknowledges to which Aristotle refers there can be gathered from the passage given in Latin in n.2 above and introduced by the expression (Dupliciter...praecognoscere); these are the quia sun t, concerned with questions of existence, and the quid est quod dicitur, concerned with questions of meaning. When one understands this, Galileo observes, one will be able to answer the objections that might be brought against the conclusions of this question. For a fuller treatment, see Sec. 4.1a of Galileo’s Logic of Discovery and Proof, which discusses kinds of foreknowledges, and Sec. 4.1b, which discusses kinds of foreknowns.
F4: On Foreknowledges of Properties and Conclusions
of the property: Lat. passionis, i.e., of the attribute that is predicated of the subject in the conclusion, called on this account a proper attribute or simply a property.
of the conclusion: strictly speaking the foreknowledge of the conclusion is already contained in the foreknowledges of the subject and of the property that is predicated of it, and thus it is redundant to treat it as a separate type of foreknowledge. As Galileo indicates in his explanatory remark, however, he is doing so as a matter of convenience. Actually it enables him to make a few notations about the time-sequence involved between knowing the premises and knowing the conclusion in a syllogistic argument, as detailed in F4.2. Indirectly, therefore, a type of “fore-knowing” is involved that can be discussed in a treatise on foreknowledge.
the existence of a property: Lat. An de passione praecognoscendum sit quia est. The quia est here is the equivalent of an sit or quod est, the first of the scientific questions (F3.1.9 n. 30). By its very nature a property is a type of accidental being and as such its mode of existence is that of existing in another as in a subject. This mode of existence poses special problems for its foreknowledge that do not arise, for example, when discussing the foreknowledge of subjects, most of which are substances that exist by themselves and so do not depend on others for their existence.
the apodictic reason why it is present: Lat. propter quid insit, the fourth of the scientific questions, F3. I.9 n. 30.
of a proper attribute: Lat. de propria passione, as in n. 1 above.
demonstration of the fact: Lat. demonstratio quia, as noted in F3.5 n. 2; for a full treatment of the kinds of demonstration, see the last disputation in the treatise on demonstration, D3; also Secs. 4.4a and 4.9a of Galileo’s Logic of Discovery and Proof. Vallius-Carbone note that the threefold distinction given here is attributable to Averroes.
demonstration of the reasoned fact: Lat. demonstratio propter quid.
most powerful demonstration: Lat. demonstratio potissima.
convertible with its subject: Lat. reciprocam cum suo subiecto, usually understood to be a property in the strict sense, found solely in the subject and in every instance, as the croak of a frog, the bark of a dog.
not convertible: Lat. non convertibilem, as round said of the earth.
nominal definition: Lat. quid nominis, F2.2 n. 1.
essence: Lat. essentia. The essence of a property would be its quid rei or real definition, and a real definition could not be shown of something whose existence was in doubt.
the property: Lat. passio; in their corresponding conclusion Vallius-Carbone give passio convertibilis cum subiecto. That the intended reference here is to a convertible property is clarified by Galileo in paragraph [8].
not convertible...convertible: Lat. non reciproca...reciproca, as in n. 9 above.
absolutely and simply speaking: Lat. absolute et simpliciter. The sense is that it is possible for a property such as roundness to be known from experience with nature, say, in an orange, before one comes to know that it is also a property of the earth.
never...not: the double negative obscures the sense. What Galileo means is that in a demonstration of the reasoned fact, as opposed to a most powerful demonstration, the property’s existence must always be foreknown, since the point of the demonstration is to manifest why that property is found in the particular subject.
Aristotle makes no mention: that is, in text 2, as explained in F3.6 n. 1.
two general kinds of foreknowledge: see the comment at F.3.6.4 n. 12.
“acting” knowledge... “directing” knowledge: see F2.2.5 n. 8.
real definition: Lat. quid rei. Galileo uses this query to add a corollary about foreknowledge of the real definition of the property, as opposed to its nominal definition, to which a special question was devoted by some commentators. See Lat. Ed. 165.
at the same time: Lat. simul tempore, simultaneously.
with the same priority: Lat. [simul] natura, an additional qualification, since another sense of priority is discernible in events that take place at the same time, as explained in the first notation of paragraph [1]; for example, even though the hand and the pen move simultaneously, the motion of the hand precedes that of the pen, since it is the hand that moves the pen and not vice versa.
major and minor premises: in a demonstrative syllogism, usually written M is P; S is M; therefore S is P, where S and P are the subject and predicate of the conclusion and M is the middle term. The first premise, M is P, is called the major premise because it contains P, a term of broader extension: the second premise, S is M, on the other hand, is called the minor premise because it contains S, a term of narrower extension.
as cause to effect: that is, the way in which the motion of the hand precedes that of the pen, as in the example given in F4.2 n. 2, even though both are temporally simultaneous.
{the path}: Lat. via, written incorrectly by Galileo as quia and here emended, following the reading in Vallius-Carbone.
as things are related...in being...so...in knowing: Lat. sicut se habet ad esse, ita ad cognosci, a principle invoked repeatedly by Galileo; see F3.1.4, D1.1.11, D2.2.7, D2.2.9, D2.5.12, and D3.1.11.
by the same act: The basis for this teaching, as noted by Vallius-Carbone, may be found in Aristotle, but it was extensively developed by St. Thomas and his school, notably Capreolus, Ferrariensis, and Cajetan; see Lat. Ed. 168–169.
I say, third...: This conclusion is essentially the same as the third in Vallius-Carbone, except that they state it as probable rather than certain.
{assent}: Lat. assensum, emending Galileo’s sensum, which is unintelligible in this context and probably an error in copying.
its premises {affirmative} and the conclusion {negative}: correcting Galileo’s text, which reads “its premises negative and its conclusion affirmative,” clearly a copying error, since the phrase does not cohere with the rest of the sentence. Again, one can have a valid syllogism with a negative conclusion and an affirmative premise, but not one with a negative premise and a positive conclusion, for this would violate the rules of the syllogism.
{then}: Lat. tunc, emending Galileo’s tum, obviously a writing error.
{at the same time}: Lat. simul, emending Galileo’s simus, another slip of the pen.
every cause that is sufficient to produce its effect...: a statement that is important for understanding Galileo’s conception of causality, as explained in Sec. 4.5 of Galileo’s Logic of Discovery and Proof. A similar principle is employed in D2.6.6; see also D2.6.6 n. 17.
[not]: supplying the negation, missing from Galileo’s text, but required for sense.
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Galilei, G. (1992). Treatise on Foreknowledges and Foreknowns. In: Galileo’s Logical Treatises. Boston Studies in the Philosophy of Science, vol 138. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8036-6_2
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