Medieval Philosophy

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"Medieval philosophy" began with the African Christian Augustine of Hippo (354430), whose life and writings reflected the unsettled state of the declining Roman Empire long before the commencement of the Middle Ages proper. His rich and many-sided works display the Platonic otherworldliness of his theories of knowledge and world history. According to Augustine's vision, the true cosmic plan unfolds in the history of the City of God, and the local accidents of the Earthly City are of little account in comparison. Correspondingly, true wisdom and virtue are obtainable only in the light of the Christian faith and by the prevenience of divine grace; human nature, grossly corrupted since the Fall, is in need of a correspondingly complete divine remaking. Whereas for Plato and Aristotle the fulfillment of human capacities required the possession of a high degree of sophisticated intelligence, for Augustine such fulfillment depended on rightness of the will and the affections. These two features, a radical view of the transforming power of grace and a voluntaristic accent, may be regarded as the kernel of Augustinianism, at least insofar as it affected subsequent thought. The tremendous influence of Augustine on medieval thought is matched by that of Ancius Manlius Severinus Boethius, whose grandiose plan was to transmit to the Latin West the works of Plato and Aristotlea plan rudely cut short by his execution in 524. However, he accomplished the translation of Aristotle's logical works into Latin; his commentaries on some of them, and on the Neoplatonist Porphyry's introduction (Isagoge ) to the Categories of Aristotle, were immensely influential in shaping the technical Latin vocabulary and turns of expression that prevailed in the Middle Ages, so much so that any appreciation of medieval thought must inevitably be inadequate without a thorough acquaintance with Boethius's logical output.

The intervention of the Dark Ages presented Western scholars with a gigantic task of rethinking and reconstruction. During these centuries of insecurity and uprootedness there was little intellectual endeavor, apart from the exceptional work of the Neoplatonist John Scotus Erigena in the ninth century. The logical, theological, and classical inheritance slumbered insecurely within the libraries of threatened Western monasteries. When Anselm of Canterbury (10331109) began to exploit Boethian logic in order to render his Christian faith intelligible, he had no immediate predecessor who in any way approached his stature as a thinker. Author of the Ontological Argument and fully alive to the power of linguistic analysis as a tool for clarifying conceptual problems, Anselm was the father of Scholasticism. Working within an Augustinian framework, Anselm and other logical theologians of the eleventh and twelfth centuries attempted to bring into order and coherence the body of doctrine to which they were committed by Holy Writ, dogmatic pronouncements, and the works of earlier authoritative church writers. The formidable dimensions of the enterprise were well known to them, as is shown in the lists of clashing antitheses made explicit in the Sic et Non (For and Against) of the ill-fated logician Peter Abelard (10791142). A systematic collection of authoritative opinions, the Sentences, upon which all subsequent medieval thinkers exercised their logical and philosophical ingenuity in the form of commentary, was compiled by Peter Lombard (c. 10951160).

While the Latin West, employing a predominantly logical Aristotelianism, was engaged in the tasks described above, as well as in controversy on the topic of universals, the more advanced Islamic civilization spreading from the Middle East possessed the whole body of Aristotle's works. These received development, commentary, and a Neoplatonic flavor at the hands of a series of subtle thinkers, among whom were al-Fārābī (c. 873950), Avicenna (9801037), and Averroes (c. 1126c. 1198). From about the middle of the twelfth century on, Latin translations of their works became available; and through these, as well as through translation directly from the Greek, Western thinkers eventually knew all of Aristotle's writings.

The Jewish philosophers Solomon ben Judah ibn Gabirol (c. 10211058 or 1070) and Moses Maimonides (11351204) also contributed to the intellectual ferment of the thirteenth century, which was accompanied by the establishment of universities within which members of the recently founded orders of Dominican and Franciscan friars were soon competing with secular masters for professorships. Generally speaking, the Dominicans, following the lead of Thomas Aquinas (c. 12241274), attempted to assimilate Aristotle by adopting a framework within which divine grace was seen as completing and fulfilling human nature, rather than dramatically abrogating it in the Augustinian manner. Consequently, the Thomistic tradition represented a separation, at least in principle, of philosophy from theology and a more optimistic view of human nature, society, and the civil state, coupled with opposition to those Latin Averroists who were prepared to compartmentalize their thought to the extent of claiming that on certain points philosophy (Aristotle, as interpreted by Averroes) demonstrated conclusions incompatible with their personal Christianity. Those who preferred to remain within the Augustinian stream, especially St. Bonaventure (c. 12171274), John Duns Scotus (c. 12661308), and William of Ockham (c. 12851349), nevertheless increasingly absorbed elements of the new Aristotelianism. Concerned as they were with the sense in which theology could be a science (a form of knowing), Duns Scotus and William of Ockham evinced a tendency to bring epistemological considerations more to the forefront of their work.

Nature of Scholasticism

aristotelian empiricism: matter, form, and substance

Medieval philosophy and logic are aspects of an effort to resolve conceptual puzzles (often, but not always, theologically inspired) and to underpin such resolutions with a satisfactory theory of how things are and why they are as they are. The dominant theory, although subjected to multiple variations and modifications during the medieval period, was basically Aristotelian and therefore involved an ultraempiricist effort (not always successful) to resist the abrogation of the pretheoretical commonsense aspect of the world by the theoretical. Before the consideration of any theory, whether scientific or metaphysical, human beings are inevitably confronted with a world populated by a multiplicity of diverse kinds and sorts of beings that are subject to generation, change, and death. These diverse beings are understood to the extent that "why?" questions about them or their kinds can be answered; they are the objects of evaluation insofar as they or their qualities, quantities, states, or relations are characterized as good, bad, and so on.

In accordance with the nonabrogatory policy, a technical vocabulary is required such that the pretheoretical picture does not forfeit its basic sense by relativization to a more fundamental theory that demands radical revision of that picture. For example, an ultraempiricist account of how things are must always leave place for the attribution of a literal (and not merely metaphorical) sense to questions regarding the "makings" of sense objects, states of affairs, or processes. The term matter represents an attempt to guarantee such a literal senseit is the general reply to the always sensible question (in the context mentioned) "What is it made out of?" The detailed replies to such questions"wood," "stone," "bones and flesh," "clay," "cloth," and so forthall mention makings or materials out of which something is made, physical antecedents that are among the necessary conditions of a thing's being.

In the same context, however, explanations of why things are as they are can be given by reference to the kinds or sorts to which those things belong; for example, "Horses are self-moving because they are animals, and all animals are self-moving." Here a feature of a particular sort of being (horse) is explained by reference to its general kind (animal), and it is the notion of "form" (with its alternative medieval vocabulary, "nature," "essence," "quiddity") that represents a reminder of the fact that things fall into distinguishable sorts (species) that can in turn be subsumed under broader kinds (genera). Since truistic explanations can be given in terms of sorts and kinds, the form or essence is said to be the principle of the intelligibility, or explanation-worthiness, of things; and such general definitions as "Man is rational animal" are said to hold true in regard to the formal aspect of things. Whether or not the definitions are true of things in a scientific sense is of little import to the philosophical notion of form: Its point is to ensure the nonabrogation, by a general theory of how things are, of the pretheoretical picture of the diversity of things; realization of this point may lie behind Aquinas's agnosticism concerning the scientific value of such formal definitions.

It is plain that the replies to questions about the makings (matter) of things still involve a formal aspect, since not only are explanations in terms of the definitions of wood, stone, and the other sorts of material mentioned still possible, but it is also possible sensibly to ask what the wood or stone is made out of, or what "stuff" endures when wine becomes vinegar. In order to do justice to such possibilitiesand to the pretheoretical conviction that in processes of change the successive sorts that occur are not totally new creations but rather a sequence of diverse activizations of a common substratumthe notion of "prime" matter is employed; this is matter as mere substratum, totally devoid of any formal aspect. Prime matter was viewed schematically, by a kind of extrapolation, as pure susceptibility upon which the various formal actualities supervene, and was said to be by some medievals the principle of individuation, whereby form, the principle of intelligibility and generality, is concretized to the particularity of the various individual "this-es" that belong to a given sort. Thus, one might say that a horse is an equinizing of prime matter, a stone is a petrifying of prime matter, and so on; this use of verblike nouns helps to bring out the fact that form is act, or actuality, as opposed to the mere susceptibility of prime matter. These verblike nouns are constant, since it never makes sense to say of a horse, for example, that is it more horse or less horse (using "more" and "less" in a nonquantitative sense). Some actualizations, however, are variable, such as whiteness; one can say of a white object that it is (or becomes) more white or less white.

The real correlates of certain of the constant actualizations are called substances, objects that are pretheoretically recognized as being constantly what they are over the whole span of their existence. A horse does not become a horse, and on ceasing to be a horse, it simply ceases to be, whereas a white object can be something that becomes white in varying degrees and may cease to be white, but it is not on that account said to cease to exist. When adjectival terms such as white are used to denote subjects in sentences, such as "A white thing is coming down the road," it always makes sense (although in many instances it may be superfluous) to ask a question like "What is the thing that is white and is coming down the road?" This is true because such terms leave open the possibility of asking a question regarding the nature of the "something else" (aliquid aliud, as Aquinas has it) that is qualified (in this instance by the whiteness). When the "something else" is a substance, such as "horse," the possibility of a further question having a similar sense, but with the substance name in place of the adjective, vanishes. For example, one would not ask, "What is the thing that is a horse and is coming down the road?" Thus, this notion of substance is unlike that with which John Locke was concerned; for him it did make sense, even when a substantial sentence subject had been used, to carry on with requests for information about what he called a "something besides."

technical language, meaning, and universals

Much of medieval philosophical and logical discourse involved the endowment of old words with new senses, as part of the artificialization of natural language that is characteristic of the Schoolmen, who, according to Locke, "covered their ignorance with a curious and inexplicable web of perplexed words." The Scholastics were in fact to some extent aware of the exigencies of discourse of this sort, which constitutes a kind of halfway house between the sort of philosophy that is careful to use only a completely jargon-free natural language, and the sort that is prepared to use the resources of some totally artificial language (such as those of modern symbolic logic) as a set of coordinates whereby sense and senselessness may be distinguished. When discussing the technical sense of "in" in sentences such as "Qualities inhere in substances," Boethius had distinguished no fewer than nine ways in which the word in could be used. It was clear to him that the man of the technical sentence "Man is a species" does not play the same role as does the name man in "Socrates is a man"; if it did, then one should be able to use these two sentences as premises whence "Socrates is a species" (which is false or nonsensical) could be inferred.

How, then, are such terms as man, animal, genus, and species, as they occur in sentences like "Man is a species" and "Animal is a genus," to be understood? These are sentences of a sort that must occur in the discussion of the principles of those definitions described as efforts to do justice to the formal aspect of things. Interpretation of such sentences as consisting of two names joined by is naturally leads to the question, transmitted by Boethius when commenting on Porphyry, of what the things are that these names name. Are the things named by such specific or generic names extramental entities additional to individual human beings and animals? An affirmative answer represents one medieval form of the option for a "realist" position in the problem of universals, and throughout the period thinkers were divided on this topic. Certain early medieval antirealists, such as Roscelin and Garland the Computist, developed a solution that had been suggested by Boethius: Words such as species and genus, said Boethius, may be interpreted as "names of names" (nominum nomina ), so that "Man is a species" should be analyzed as "'Man' is a species," with species naming the word man and indicating that it is predicable specifically of many individuals. Herein lies one of the roots of the logical doctrine developed during the thirteenth and fourteenth centuries, the doctrine of suppositio.

Roscelin and Garland went further than Boethius and regarded man in "Man is a species" not as a mentioned name (a mentioned significant utterance) but as a mere utterance (vox ) undergoing mention; thus St. Anselm accused Roscelin of having reduced universals to the "breath of an utterance" (flatus vocis ). Other antirealists, observing that this extreme nominalism (as it is usually called) failed to account for the success of language as a representation of the formal aspect of things, adopted an intermediate position, according to which the universal is a natural (as opposed to a merely conventional) mental sign, or concept; such a position was designed to secure the objective reference of the universal while avoiding commitment to the plethora of extra entities demanded by realism. Abelard, Aquinas, and Ockham may be credited with having held, each in his own way, a doctrine of this type.

extent of the artificialization of language

There are several facets of the general medieval concern with the study of meaning. In the writings of Anselm of Canterbury, for example, there is an immensely powerful and pervasive realization that the overt, apparent, or grammatical form of an utterance need not show its implicit, true, or logical forma realization whose revival has been most prominently reinitiated in our own age by Bertrand Russell. Again and again Anselm's writings contain the contrast between forms of speech that are allowed by the loose texture of ordinary language (usus loquendi ) and the forms to which a strict attention to the exact sense (significatio per se ) commits one; the loose texture is methodically explored, and the results of this exploration are applied to the elucidation of difficulties raised by forms of speech found in Holy Writ and ordinary language. In their technical explanations Anselm and his successors felt compelled to make innovations that violated the grammar of the natural language (Latin) in which they wrote; for instance, in expressing the objective counterparts of assertions concerning the meaning of adjectival (as opposed to substantival) words, Anselm used the novel formula "Literate is literacy," which in its Latin version (Grammaticus est grammatica ) is about as full of scandals, from the point of view of ordinary Latin grammar, as any three-word sentence could be.

Naturally the classicists of the time, like their counterparts of the sixteenth century, took alarm at these monstrous impurities of language; a classicist rearguard action is shown in the Metalogicon of John of Salisbury (c. 11151180), who at one point explicitly argues against mixtures of abstract and concrete of the kind put forth by Anselm. A better-known example of this technical development, resulting in nonsense in respect to ordinary language, is found in Aquinas's assertion that a man is neither his humanity nor his existence, whereas God is both his essence (divinity) and his existence; these claims involve a like mixture of concrete and abstract nouns that in nontechnical speech just cannot be connected by the same "is" (or "is not").

breakdown of communication

The semiartificial language of the Scholastics was excessively clumsy, and, in the absence of the precise definitional control that goes with a totally artificial language, required for its tolerably safe employment an intuitive power extending beyond the ordinary; even when this has been achieved, the history of the period demonstrates that there is no guarantee that communication will be maintained. For example, skill in the use of such language probably reached its peak in the writings of Duns Scotus, the Subtle Doctor. He rejected the theory that matter is the principle of individuation on the grounds that this attribution leaves the individual lacking in total intelligibility and even makes problematic the possibility of an omniscient being's (God's) radical understanding of the individual object. He therefore posited that individuation is performed not by a material, but by a formal, principle; for example, by "Socrateity" in respect of the individual Socrates, and in general by the "thisness" (haecceitas ) appropriate to each individual "this." We have already observed the connection between form and intelligibility presupposed in this operation, an operation that raises a further phase of the universals controversy and at the same time exemplifies the breakdown in communication.

Ockham criticized the Scotist thing-centered formal distinction (distinctio formalis a parte rei ) alleged to hold between the universal nature in question (humanity in the case of a human being) and the individuating formal principle (Socrateity) that makes the individual into this individual. Ockham was at a loss to see how this distinction could be thing-centered (a parte rei ) and yet not commit its proponent to the admission of extra entities (humanity, Socrateity) over and above, and distinct from, individuals, in spite of the fact that the existence of universals as extra entities of this sort was denied by Scotus.

It has already been suggested that form may be best expressed by means of verblike nouns (equinizing, petrifying ); hence, the abstract nouns often used to express formal principles could be viewed as being more verblike than namelikea position taken by Aquinas from Boethius and apparently recognized by other Scholastics. If this view is accepted, then the statement that the Socrateity of Socrates is distinct from his humanity may be interpreted, using appropriate verblike forms, as asserting that Socratizing is not identical with humanizing, an analysis that yields a true thing-centered distinction and yet does not send one on a vain search for extra named entities over and above the man Socrates; this offers at least one way in which the Scotist contention may be consistently understood.

But Ockham assumed, in effect, that any distinction that holds in respect of things (a "real" distinction) can only be like that which holds between, for example, Socrates and Plato and that is expressed by a sentence such as "Socrates is not Plato," wherein "Socrates" and "Plato" are names (as opposed to the verblike Socratizing and humanizing ). When, therefore, Ockham encountered the further Scotist tenet that although a thing-centered formal distinction holds between Socrateity and humanity (for example), it is nevertheless not the case that a real distinction holds between the two, he assumed that "Socrateity" and "humanity" could be treated in the same way as such names as Socrates, Plato, Cicero, and Tully, and that even as the negation of a real distinction between Tully and Cicero amounts to a statement of their real identity as the same individual object, so also the denial of a real distinction between Socrateity and humanity amounts to a statement of real identity of this sort. In point of fact, however, once the verblike nature of the form-expressing words Socrateity and humanity has been grasped, it becomes clear that a denial of a real distinction between Socrateity and humanity should be understood as the rejection of any attempt to treat those form expressions as though they were pure names. The whole weight of Ockham's subsequent attack, aimed as it was at the consequence that the Scotists were in such contexts stating the denial of a real identity (one framed in terms of names, as opposed to verbs) is therefore totally misplaced.

The same blindness, combined with the theological premise that God is omnipotent, and hence can effect anything that does not involve a contradiction, also played havoc with other distinctions patiently established by earlier thinkers. For example, the distinction between essence and existence, some of whose associated theses were described above as embodying novel uses of words, was attacked on the grounds that the essence of a thing (a man's humanity) and its existence are (if a real distinction holds between them) two things distinct in the way that Socrates and Plato are two distinct things. In consequence, the Ockhamists considered themselves licensed to assert that the admission of a real distinction between essence and existence has as a consequence the possibility of God's omnipotence producing something's essence without at the same time producing its existence, or vice versa, however, this is patently absurd, and therefore (they concluded) there is no real distinction between essence and existence.

In the presence of such misplaced criticism it is obvious that scholastic thought could have been better expressed in a fully artificial language, armed with precise definitions and a greater capacity for generating and identifying new parts of speech than that of the semiartificial language that was used.

reaction against technical artificialization

Although the artificialization of natural language for the expression of technical truths beyond the capacity of natural language proceeded apace from the time of Anselm, the final major philosophical reaction, brought about by communication difficulties, was in the opposite direction. Ockham's attitude to the contrast between ordinary and technical discourse was the polar opposite of Anselm's attitude at the opening of the period. For Anselm, accounts of meaning could and did call for the use of, or have as consequences, technical assertions that were either nonsense from the point of view of ordinary usage, or at least involved radical departures therefromand his successors were similarly venturesome.

Ockham, although likewise constantly conscious of the contrast between ordinary speech and the technical forms of speech used by his predecessors, nevertheless placed propriety of expression on the side of ordinary speech, and not on the technical side, except in those instances where the novel locutions of his forerunners could be explained away or disarmed as mere stylistic ornament. His lists of sentences that are false if taken literally (de virtute sermonis ) because words are not therein used properly (secundum proprietatem sermonis ) are catalogs of the sort of technical assertions that for Anselm and following thinkers had been a necessary consequence of the special requirements of logical and philosophical discourse, and that for them enshrined propriety to a degree to which the looseness of ordinary speech could not aspire. This reversal of attitude, symptomatic of the breakdown of communication in terms of semiartificial language, did not, of course, immediately prevail, it was combated at great length, for instance, by John Wyclyf (c. 13201384). Nevertheless, Ockham's attitude, reinforced by Renaissance philology, ultimately triumphed and was represented in the strictures of Locke on "the frivolous use of uncouth, affected, and unintelligible terms" that made philosophy "unfit or uncapable to be brought into well-bred company and polite conversation."

ethics and politics

Augustine's severe view of the effects of the Fall of man resulted in a largely negative view of the civil state. He held that save in the ideal case of a Christian commonwealth, earthly states are merely coercive institutions that would not exist had man not fallen, and serve simply to issue punishments and remedies for the corruption of human nature. Correspondingly, divine grace is seen by Augustine as playing a dramatically elevating part in the reformation and reordination of the will. However, the thirteenth-century revival of full Aristotelianism, coupled with the Thomist view of grace as a completion rather than an abrogation of nature, allowed that civil subordination was natural to man, would exist even if the Fall had not taken place, and hence could not be written off as an extraneous penal imposition; the state possesses a positive value in its own right.

Aquinas's enormously detailed philosophical anthropology constituted the foundation of his version of Aristotelian humanist ethics and politics, to which he attempted to give a Christian completion; it cited the perfection and fulfillment of human nature in the intellect rather than in the will: Accordingly, he viewed law as essentially a rule of right reason, rather than as a species of will-based command. This doctrine was in conflict with the teachings of the Augustinian voluntarists such as Ockham, whose view has endured through Thomas Hobbes and John Austin down to modern times. Aquinas's system of rationally based natural law as a measure of the value of human actions in general, and of human law in particular, was in opposition to the absolutist tendencies evident in the coalescence of revived Roman law with Augustinianism, which were to come to final fruition in the sovereign nation-state of our own era. The distinction between the righteous prince (who remains within the bounds of the law) and the tyrant (who puts himself above the law) had been trenchantly enunciated by John of Salisbury, was supported by the non-Roman medieval legal tradition, and clearly presupposes limits to the powers of the chief legal authority.

It is clear that Aquinas's natural-law theory supports this limiting attitude and justifies resistance to tyranny; he was therefore faced with the task of coming to terms with those features of Roman law (to be emphasized in the Renaissance) according to which the prince is above the laws. This he did by distinguishing between the coercive power (vis coactiva ) and the directive, or rationally qualifying, power (vis directiva ) of law: In respect of the first the prince is above the law, but in respect of the second he is voluntarily subject to it. In his theory of law Aquinas directly influenced Richard Hooker, to whom Locke admitted his indebtedness.

It is in connection with Aquinas's defense of the right of resistance, as well as in his prima facie puzzling assertions on the relation of the papacy to civil power, that we may best see how he attempted to resolve the perennial problem of the relation between political principle and political fact through the use of exceptive (nisi forte ) clauses. Instead of rigidly carrying through principle to the bitter end and at all costs, without any regard for concrete or historical facts (in the manner, one might say, of Plato in the Republic ), Aquinas suggested that the most rational course would be to make appropriate accommodations with local conditions, if necessary by recourse to empirically based anticipation of the results of political action. For example, it follows from natural law that tyranny may rightly be resisted by force; this justification of rebellion may be acted upon, said Aquinas, except perhaps (nisi forte ) when the facts of the case make it plain that the revolution will generate worse evils than the tyranny that it is designed to displace. Again, in religious matters he declared that the ecclesiastical power is to be obeyed rather than the civil, and in civil matters the lay power is to be obeyed rather than the ecclesiastical, except perhaps (nisi forte ) in the special case of the two powers' being amalgamated in one person, such as the Roman pontiff.

Commentators discussing this last example, and not armed with a realization of the significance of its exceptive (nisi forte ) structure, have inferred from it that Aquinas here committed himself to an extreme papalist position that would endow the pope with the fullness of spiritual and temporal power. However, once the significance of that structure has been gathered from the many other available textual examples, the conclusion may be drawn that Aquinas taught the separation of these powers as a matter of principle, yet he also observed the local fact that insofar as the pope is a temporal ruler of papal territory, he, exceptionally, holds both spiritual and temporal power. A like adaptability may be seen in Aquinas's concession that the secondary precepts of natural law are mutable in accordance with changing historical conditions and in his recommendation that laws should be tailored to fit the type of population for which they are intended; to attempt to legislate a people into full virtue is futile.

Augustinianism in general, and the Augustinian theory of law as essentially will-based command, received impetus and encouragement from the archbishop of Paris's condemnation in 1277 of certain Aristotelian theses of Arabic philosophical complexion, a condemnation that also bore upon some Thomist positions. The tendency of Averroism had been toward a pantheism that diminished the freedom of God in the act of creation. Aquinas's claim that moral evaluation consists of rational assessments based upon the intrinsic nature of the cases in question was also susceptible of being interpreted as constituting a restriction on divine omnipotence. Accordingly, Duns Scotus and Ockham, in varying degrees, claimed that the rules governing the attribution of Tightness or wrongness to human actions were contingent in relation to the absolute power of God; the consequent contingency of connection between deed and merit has caused some historians to assume that in Augustinian thought one may find the basis of Martin Luther's doctrine of justification by faith alone, as well as a source for the legal aspects of the Hobbesian theory of sovereignty.

science and philosophy

Although the nonabrogatory policy of medieval philosophy outlined above served well enough to ensure that philosophers took seriously the fully human realm of reasons, purposes, hopes, and so forth, thus avoiding the split between the thinker as a human being and the thinker as a philosopher, the extrapolation of that policy's attendant ultraempiricism to sciences such as physics and cosmology tended to a greater or lesser extent to inhibit their development as practical tools. A prime and early example of such ultraempiricist inhibition is to be found in the refusal of the second-century astronomer Ptolemy to consider a sun-centered planetary system because it so obviously is at variance with things as we find them to be, a refusal that was espoused by most but not all medieval philosophers. On this point Ptolemy was in agreement with the physics-based cosmology of Aristotle, but in general he represented a rival tradition, that of the mathematicians, who were usually regarded by the medievals as devisers of ingenious fictions that served merely to "save the observed appearances." Mathematical theories were accordingly believed to lack the necessity attributable to the vast and coherent background of Aristotelian physics and metaphysics, and this attitude prevailed until the time of Galileo Galilei.

However, there was some support for the development of mathematical physics, insofar as it relies on thought experiments as opposed to exact experiment, in the very competent medieval enlargements on a point whose root lay ultimately in Aristotle's Categories ; there, when attempting to differentiate between substances (such as man, tree, stone) and qualities (such as whiteness, roundness, hardness), Aristotle pointed out that the latter are susceptible of degree, while the former are not. To this remote starting point much of modern mechanics owes its origin, for through speculation on the various kinds, rates, and degrees of "intension" and "remission" of qualities, the ideas of constant motion and acceleration and deceleration (uniform or nonuniform), and their relations to time and distance were thoroughly explored by fourteenth-century philosophers, such as those of Merton College, Oxford. Nicholas Oresme (c. 13251382) related these aspects of motion to their graphical expressions and anticipated infinitesimal calculus and coordinate geometry. Herein lies the starting point of certain segments of Galileo's mechanics.

See also Abelard, Peter; al-Fārābī; Anselm, St.; Aristotelianism; Aristotle; Artificial and Natural Languages; Augustine, St.; Augustinianism; Austin, John; Averroes; Averroism; Avicenna; Boethius, Anicius Manlius Severinus; Bonaventure, St.; Duns Scotus, John; Erigena, John Scotus; Galileo Galilei; Hobbes, Thomas; Ibn Gabirol, Solomon ben Judah; Islamic Philosophy; Jewish Philosophy; John of Salisbury; Logic, History of; Luther, Martin; Maimonides; Mathematics, Foundations of; Neoplatonism; Ontological Argument for the Existence of God; Oresme, Nicholas; Pantheism; Peter Lombard; Plato; Porphyry; Realism; Roscelin; Russell, Bertrand Arthur William; Scotism; Socrates; Sovereignty; Thomas Aquinas, St.; Thomism; Universals, A Historical Survey; William of Ockham; Wyclyf, John.


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