Albert of Saxony (ca. 1320–1390), Master of Arts at Paris, thenRector of the University of Vienna, and finally Bishop of Halberstadt(Germany). As a logician, he was at the forefront of the movement thatexpanded the analysis of language based on the properties of terms,especially their reference (in Latin:suppositio), but alsoin the exploration of new fields of logic, especially the theory ofconsequences. As a natural philosopher, he worked, along with Oresmeand Buridan, in the context of the new Parisian physics, contributingto its spread throughout Italy and central Europe.
In the later Middle Ages Albert of Saxony (Albertus deSaxonia) was sometimes calledAlbertucius (LittleAlbert), to distinguish him from the thirteenth-century theologianAlbert the Great. He is however a master of great importance in hisown right. He was born at Rickensdorf, in the region of Helmstedt(Lower Saxony) in present-day Germany, in the beginning of the 1320s.After initial schooling in his native area, and possibly a sojourn atErfurt, he made his way to Prague and then on to Paris. He was memberof the English-German Nation and became a master of arts in 1351. Hewas Rector of the University of Paris in 1353. He remained in Parisuntil 1362, during which time he taught arts and studied theology atthe Sorbonne, apparently without obtaining a degree in the latterdiscipline. His logical and philosophical works were composed duringthis period. After two years of carrying out diplomatic missionsbetween the Pope and the Duke of Austria, he was charged with foundingthe University of Vienna, of which he became the first Rector in 1365.Appointed canon of Hildesheim in 1366, he was also named Bishop ofHalberstadt the same year, serving in that office until his death onJuly 8, 1390.
Not having left any theological writings or a commentary onAristotle’sMetaphysics (at least none that we knowof), Albert is primarily known for his works on logic and naturalphilosophy. Albert’s masterwork in logic is theLogica(later designed asPerutilis logica, Very Useful Logic).Albert also composed a voluminous collection ofSophismata,which examines numerous sentences that raise difficulties ofinterpretation due to the presence of syncategorematic words —i.e., terms such as quantifiers and certain prepositions, which,according to medieval logicians, do not have a proper and determinatesignification but rather modify the signification of the other termsin the propositions in which they occur. He also wrote severalquestion commentaries:Quaestiones on theArs Vetusor Old Logic (i.e., theIsagoge of Porphyry andAristotle’sCategories andDeInterpretatione),Quaestiones on thePosteriorAnalytics, and a series of 25Quaestiones logicales(Logical Questions), addressed to semantic problems and the status oflogic. Albert of Saxony also commented the main texts of theAristotelian natural philosophy (Physica, De caelo, De generationeet corruptione, De sensu et sensato, Meteorologica) together withtheDe sphaera of John of Sacrobosco. By contrast, theQuaestiones de anima that were attributed to him are ofdubious authenticity. He also wrote commentaries onEthicsandEconomics, and texts of mathematics: a treatiseDeproportionibus, aQuaestio de quadratura circuli, aTractatus de maximo et minimo.
The most renowned philosopher when Albert studied and taught in theFaculty of Arts at Paris was John Buridan. Albert was one of severalmasters contemporary with or immediately following Buridan whose worktransformed logic and natural philosophy in the later Middle Ages. Fora long time he was thought to have been a pupil or follower ofBuridan, but this idea is now widely questioned. Some of his works onlogic and physics were composed before Buridan had lectured on thesesubjects for the last time, and Buridan clearly takes notice of them,whether for criticizing or for adopting Albert’s views. Inlogic, he seems to have been influenced by certain ideas and methodsimported from England. His logic depends very much on Ockham’s,but the influence of William Heytesbury is also evident in hisSophismata. Walter Burley was another important influence onAlbert, though this is somewhat puzzling in view of the fact that theyhad opposing views on the nature of universals. In any case, Burleyseems to have been on Albert’s mind when he wrote his commentaryon theNicomachean Ethics as well as when he was developinghis theory of consequences.
These different influences have sometimes made Albert seem no morethan an eclectic compiler of the views of others. But, in addition toproviding the context for some of his own contributions,Albert’s fluency with the views of his contemporaries gives hima unique place in the development of logic and philosophy at theUniversity of Paris in the fourteenth century.
On most topics theLogica (a text based on lectures firstgiven before 1356 and finally revised for publication before 1360) isinfluenced by Ockham’sSumma logicae, though it offersan independent approach in the treatises on obligations, insolubles,and consequences, which had assumed greater importance during thisperiod. As has been known for some time, this work is a remarkablehandbook organized into six treatises: the first defines the elementsof propositions; the second treats of the properties of terms; thethird of the truth conditions of different types of proposition; thefourth of consequences (including syllogisms, and in fact adding to itthe theory of topics); the fifth of fallacies; and the sixth ofinsolubles and obligations.
In the first part of theLogica, which sets out theterminology of the entire text, Albert returns to the Ockhamistconception of the sign and in so doing distances himself from theposition defended by Buridan. After clearly including the term (anelement of the proposition) in the genus of signs — by which heprovides, in the tradition of Ockham, a semiotic approach tologico-linguistic analysis — he establishes significationthrough a referential relation to a singular thing, defining therelation of spoken to conceptual signs as a relation of subordination.He is also an Ockhamist in his conception of universals, which heregards as spoken or conceptual signs, and in his theory ofsupposition, which essentially restates the Ockhamist divisions ofsupposition, despite of some refinements asdescensuscopulatim, perhaps influenced by Heytesbury. In particular, herestores the notion of simple supposition — i.e., the referenceof a term to the concept to which it is subordinated, when itsignifies an extra-mental thing — which is criticized andrejected by Buridan. Finally, Albert is close to theVenerabilisInceptor in his theory of the categories, where he refuses toconsider quantity as something absolutely real, reducing it instead toa disposition of substance and quality. Albert in fact contributed asmuch as Ockham to the spread of this conception of the relationbetween substance and quantity in natural philosophy in Paris andItaly.
Albert’s treatment of relations is, on the other hand, highlyoriginal. Although (like Ockham) he refuses to make relations intothings distinct from absolute entities, he clearly ascribes them to anact of the soul by which absolute entities are compared and placed inrelation to each other, an “act of the referring soul [actusanimae referentis]”. This leads him to reject completelycertain propositions Ockham had admitted as reasonable, even if he didnot construe them in quite the same way, e.g., ‘Socrates is arelation’. Both Ockham and Buridan had allowed that the term‘relation’ could refer to the things signified or connotedby concrete relative terms (whether collectively or not).
So Albert was not content with merely repeating Ockhamist arguments.More often than not, he developed and deepened them, e.g., inconnection with the notion of the appellation of form. This propertyof predicates, which had previously been used by theVenerabilisInceptor, was employed by Albert in an original manner when headopted it instead of Buridan’s appellation of reason(appellatio rationis) to analyze verbs expressingpropositional attitudes. Every proposition following a verb such as‘believe’ or ‘know’ appellates its form. Inother words, it must be possible to designate the object of the beliefvia the expression understood as identical to itself in its materialsignification and without reformulation. Another area in which Albertdeviates from Ockham is his rejection of the idea that any distinctionwith multiple senses must have an equivocal proposition as its object.According to Albert, equivocal propositions can only be conceded,rejected, or left in doubt.
He adopts the same position as Burley about the issue of the complexsubject-term (including an oblique case) in a categorical proposition,as in ‘Any man’s donkey is running [Cuiuslibet hominisasinus currit]’. He supports a logico-semantical model inwhich ‘man [homo]’ is the logical subject while‘a man’s donkey [hominis asinus]’ is thegrammatical one. This theory is criticized by Buridan, for whom thelogical subject is always the grammatical subject.
Albert’s semantics becomes innovative when he admits thatpropositions have their own proper significate, which is not identicalto that of their terms (see especially hisQuestions on thePosterior Analytics I, qq. 2, 7, 33). Like syncategorematic terms(see hisQuestions on the Categories, qu. 1 ‘OnNames’), propositions signify the “mode of a thing[modus rei]”. This position is not repeated in theLogical Questions. In any case, Albert avoids hypostatizingthese modes by explaining them as relations between the things towhich the terms refer. It cannot be said here that Albert is movingtowards the “complexly signifiable [complexesignificabile]” of Gregory of Rimini, although his remarksare reminiscent of the latter theory. Still, he uses the idea of thesignification of a proposition to define truth and to explain‘insolubles’, i.e., propositions expressing paradoxes ofself-reference. On Albert’s view, every proposition signifiesthat it is true by virtue of its form. Thus, an insoluble propositionis always false because it signifies at the same time that it is trueand that it is false.
TheQuestiones circa logicam (Questions on Logic)were written at roughly the same time as theLogica and theQuestiones circa artem veterem, that is to say about 1356.They explore in a series of disputed questions the status of logic andsemantics on topics such as the relation of words to concepts, thedifference between natural and conventional signification, etc., aswell as the theory of reference and truth. Albert definessignification byrepresentation. He distinguishes two ways ofunderstandingsuppositio, the first as the act of the minditself; the second as an operation constituting one of the propertiesof terms.
In hisSophismata, Albert usually follows Heytesbury. Thedistinction between compounded and divided senses, which is presentedin a highly systematic way in Heytesbury’sTractatus desensu composito et diviso, is the primary instrument (besides theappellation of form) for resolving difficulties connected withepistemic verbs and with propositional attitudes more generally. Thisis abundantly clear in his discussion of infinity. Rather thanappealing to the increasingly common distinction between thecategorematic and syncategorematic uses of the term‘infinite’ and then indicating the different senses it canhave depending on where it occurs in a proposition, he treats theinfinite itself as a term. Albert’s approach involves analyzingthe logical and linguistic conditions of every proposition involvingthe term ‘infinite’ that is significant and capable ofbeing true. This leads him to sketch a certain number of possibledefinitions (where he appears to take into account the teachings ofGregory of Rimini), as well as to raise other questions, e.g., on therelation between finite and infinite beings (in propositions such as‘Infinite things are finite [infinita suntfinita]’), on the divisibility of the continuum, and onqualitative infinity. There are echoes in Albert not only of theapproach Buridan had systematically implemented in hisPhysics, but also of the analyses of English authors —again, especially Heytesbury. As is often the case, the treatmentproposed by Albert in theSophismata provides good evidenceof the extent to which philosophers were gripped by questions aboutinfinity at that time.
Finally, one of the fields in which Albert is considered a majorcontributor is the theory of consequences. In the treatise of thePerutilis Logica devoted to consequences, Albert often seemsto follow Buridan. But whereas Buridan maintained the central role ofAristotelian syllogistic, Albert, like Burley, integrated syllogisticand the study of conversions into the theory of consequences.Consequence is defined as the impossibility of the antecedent’sbeing true without the consequent’s also being true —truth itself being such that howsoever the proposition signifiesthings to be, so they are. The primary division is between formal andmaterial consequences, the latter being subdivided into consequencessimpliciter andut nunc. A syllogistic consequenceis a formal consequence whose antecedent is a conjunction of twoquantified propositions and whose consequent is a third quantifiedproposition. Albert is thus led to present a highly systematic theoryof the forms of inference, which represents a major step forward inthe medieval theory of logical deduction.
It is this analysis of language together with a particularist ontologythat places Albert in the tradition of nominalism. This is combinedwith an epistemological realism that emerges, e.g., in his analysis ofthe vacuum. In certain respects, Albert’s work is an extensionof physical analysis to imaginary cases. Distinguishing, as Buridandid, between what is absolutely impossible or contradictory and whatis impossible “in the common course of nature”(Questions on De Caelo I, qu. 15), he considers hypothesesunder circumstances that are not naturally possible but imaginablegiven God’s absolute power (e.g., the existence of a vacuum andthe plurality of worlds). However, even if we can imagine a vacuumexisting by divine omnipotence, no vacuum can occur naturally(Questions on the Physics IV, qu. 8). Albert refuses toextend the reference of physical terms to supernatural, purelyimaginary possibilities. In the same way, one can certainly use theconcept of a point, although this would only be an abbreviation of aconnotative and negative expression. There is no simple concept of apoint, a vacuum, or the infinite, and although imaginary hypothesesprovide an interesting detour, physics must in the end provide anaccount of the natural order of things.
Historically, Albert’s reputation in natural philosophy is atleast as high as the one he had in logic. His commentaries on thePhysics, onDe caelo or onDe generatione etcorruptione are close to Oresme’s andBuridan’s. He appeals to the authority of his “reveredmasters from the Faculty of Arts at Paris” at the beginning ofhis questions onDe caelo. Even so, it should be noted thathisPhysics was composed soon after 1351, before the finalversion of Buridan’sQuestions on the Physics (between1355 and 1358). On some points we know that Buridan modifies hispositions between the third and the final versions of his commentary,and we can presume that this is in response sometimes to Oresme’sideas, but sometimes also to Albert’s.
On some other issues, the oppositions remain strong between the twomasters. We have already seen that on the question of the status ofthe category of quantity, then at the border of logic and physics,Albert followed Ockham and distanced himself from Buridan by reducingquantity to a disposition of substance or quality. This move becomesevident in certain physical questions, e.g., in the study ofcondensation and rarefaction, where Albert openly disagrees withBuridan by arguing that condensation and rarefaction are possible onlythrough the local motion of the parts of a body, and without needingto assume some quantity that would have a distinct reality on its own.Nevertheless, he defines the concept of a “lump of matter[materie massa]” without giving it any autonomousreality, although it does help fill out the idea of a ‘quantityof matter’, which Giles of Rome had already distinguished fromsimple extension.
Similarly, Albert is sometimes seen as standing alongside Ockham onthe nature of motion, rejecting the idea of motion as a flux(fluxus), which is the position Buridan had adopted. Incontrast to Buridan, Albert treats locomotion in the same way asalteration (movement according to quality): in neither case is itnecessary to imagine local motion as ares successivadistinct from permanent things, at least if the common course ofnature holds and one does not take into account the possibility ofdivine intervention.
Concerning the motion of projectiles, gravitational acceleration, andthe motion of celestial bodies, Albert’s position is similar toBuridan’s major innovation, i.e., the theory ofimpetus, a quality acquired by a moving body (seeBuridan’sQuestions on the Physics VIII, qu. 13, onprojectile motion). Like Buridan, he extends this approach tocelestial bodies in his commentary onDe caelo, clearlyfollowing its consequences in rejecting intelligences as agents ofmotion and in treating celestial and terrestrial bodies using the sameprinciples. Nevertheless, he formulates the idea ofimpetusin more classical terms as avirtus impressa (impressedforce) andvirtus motiva (motive force). Albert makes nopronouncements about the nature of this force, claiming that this is aquestion for the metaphysician. His work also mentions the mean speedtheorem, a method of finding the total velocity of a uniformlyaccelerated (or decelerated) body, which had been stated (thoughwithout being demonstrated) in Heytesbury’sTractatus demotu, and also adopted by Nicole Oresme. Albert was part of ageneral scientific trend which sought the first formulations of theprinciples of dynamics.
He shares with Buridan the theory according to which, to explain thefact that a part of the earth is above the water, we have todistinguish, for the earth, a centre of magnitude and a centre ofgravity, because of the evaporation of water, but also because of therarefaction of a part of the earth under the influence of the solarheath (Quaestiones in De caelo, II, q. 25 and 28). Heexplained also a number of curious natural phenomena, takingparticular interest in earthquakes, tidal phenomena, and geology.
Albert wrote a treatise on proportions dedicated to the analysis ofmotion, highly influenced by the treatiseDe proportionibusvelocitatum in motibus of Thomas Bradwardine. He explains in asynthetic way the elements of the theory of proportions, applying thistheory to different motions (local motion, alteration, augmentation,and diminution). Motion is to be studied “from the point of viewof the cause” and “from the point of view of theeffect”. Like Oresme, Albert adopts the idea that motion variesaccording to a geometrical progression when the relation of motiveforce to resistance varies arithmetically. His treatise is lessinnovative than Oresme’s, but it is a clear exposition that wasvery widely read.
Albert was interested in certain mathematical problems. In addition toauthoritative arguments and purely empirical justifications, hisquestion on the squaring of the circle uses properly mathematicalarguments appealing to both Euclid (in the version of Campanus ofNovarra) and Archimedes (translated by Gerard of Cremona). His mostoriginal contribution is a proposal to dispense with Euclid’sproposition X.1, replacing it with a postulate stating that if A isless than B, then there exists a quantity C such that A<C<B.
Finally, a treatiseDe maximo et minimo, considering thelimits of active and passive potencies, written in the tradition ofthe Oxford Calculators, at the frontiers of logic and naturalphilosophy.
Albert of Saxony is not a compiler. Even if he shares many ideas withthe contemporary masters of arts, he is often original. His teachingson logic and metaphysics were extremely influential. Although Buridanremained the predominant figure in logic, Albert’sLogica was destined to serve as a popular text because of itssystematic nature and also because it takes up and develops essentialaspects of the Ockhamist position. But it was his commentary onAristotle’sPhysics that was especially widely read.Many manuscripts of it can be found in France and Italy, but also inErfurt, Vienna and Prague. Thanks to Albert of Saxony, many new ideasraised in Parisian physics and cosmology in the later Middle Agesbecame widespread in Central Europe. Albert’sPhysics,much more than Oresme’s and even Buridan’s, basicallyguaranteed the transmission of the Parisian tradition also in Italy,where it was authoritative along with the works of Heytesbury and JohnDumbleton. His commentary on Aristotle’sDe caelo wasalso influential, eclipsing Buridan’s commentary on this text.Blasius of Parma read it in Bologna between 1379 and 1382. A littlelater, it enjoyed a wide audience at Vienna. HisTreatise onProportions was often quoted in Italy where, in addition to thetexts of Bradwardine and Oresme, it influenced the application of thetheory of proportions to motion.
Albert played an essential role in the diffusion throughout Italy andcentral Europe of new ideas discussed in the Mid-Fourteenth century byParisian masters, but which were also clearly shaped by Albert’sown grasp of English innovations. He manifests an undeniableoriginality on many topics in logic and physics.
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Bradwardine, Thomas |Buridan, John [Jean] |Burley [Burleigh], Walter |Heytesbury, William |Ockham [Occam], William
The author gratefully acknowledges Jack Zupko for translating thisentry into English.
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