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medieval_overview

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Medieval Philosophy

Augustine of Hippo:

Biographical Information:

There are 3 Augustines, first the young rhetorician then the young christian and the mature catholic bishop

First autobiography of a philosopher in the west
(397-480)

During his life Augustine went to

Manicheism to Neo-Platonism to Christianity

*Before his conversion St. Augustine was a follower of the New Academy and its skepticism.

*He did not produce a solid body of doctrine, but rather many different and sometimes contradictory positions. (John Marenbon)

Philosophical Background:

“St. Augustine does not deny that man in the state of choice (liberum arbitrium), but he insists that in this state man does not enjoy liberty (libertas) because he cannot use his freedom as he should: he does not will the good, or, if he does, he cannot do the good that he wills.” (Pauline position) (Marenbon)

Augustine argued that: no predication about God can be accidental. God is not good or great because he participates in goodness and greatnes, rather he is the goodnes and greatness. (De Trinidate)

“O God, who art ever the same, let me know myself and thee.” To know himself: is that not the know his soul? (Armand Mauer)

In the city of God Augustine breaks with ancient political thinking, he rejects the idea that any city in the world can approach the ideal community ruled by justice. Augustine divides humanity into two groups–
City of God, Which is characterised by amour dei
City of Men, Which is characterised by amour sui (Marinbon)
Furthermore Augustine argues that only a community arranged to pursue the true common good can be considered a genuine commonwealth (respublika). And only Christians can identify this common good.(Marenbon)

Augustine’s gradualist ontology (NeoPlatonic but with a significant difference)

God
Angels
Human Beings
Animals
Plants
Inanimate Things

The significant difference is, that in neoplatonism the one is beyond being but in Augustine, God is the supreme being.. (Claudia Appoloni)

Texts:

  1. Augustine on evil passions and free will
  2. Augustine on insight and illumination

1.1: What is the efficient cause of evil?
Augustine’s answer: Evil has no efficient cause, evil has no reality itself rather it is a diminished being. (This is how Augustine solves the Manichean problem.)

Ontological Evil does not exist because God forsees sin and makes good use of wicked will and God composes a beautiful poem of antithesis.

The material good is not evil in itself– Evil is the desiring of the will towards it

The supreme good cannot be evil but some good can…

On Passions: Passions are not good or bad in themselves (this differs from the stoic ideal of imperturbability). Christian is a passionate human being– The good of passions depends on the objects toward which they are directed.

In mature Augustine we find the thought the fallen human beings cannot but sin (falling grace)

2.1 Augustine on Insight and Illumination

Knowledge has 2 conditions

  1. What you know is true
  2. You know that what u know is true

Words are a little in use for gaining knowledge. We can only learn sudden insight (illumination). Christ is our inner teacher. The only thing that the human teacher can do is prompt us to consult the inner light within (this is the same in Plato’s meno)

All knowledge comes from sense perception or intellectual understanding

The purpose of words is to direct our attention toı remind us to look at a thing

2.2 On Signs

“A sign is a thing that of itself causes something else to enter into thought beyond the appearance it presents to the senses.”

Signs are divided into

  • Natural signs
  • Intentional signs(given with an intention)

Intentional signs are divided into signs which are naturally given and conventional signs.

There is no direct correspondence between signs and things.

Signifying is a threepart relationship, the first part is the sign (external sign), the second part is signifying (by a mind) and the third part is the significate (thing signified in the world.

Boethius

Biographical Information:

Boethius had through education in neoplatonic philosophy. He is important to medieval philosophy in many ways. Firstly, he was the main transmitter of ancient logic, Secondly, he wrote short theological words that were innovative and influential in their method. Thirdly he wrote one of the widely read philosophical works of the latin middle ages on the consolation of philosophy.

Boethius setout to translate into latin, the complete philosophical literature of the Greeks, however he only translated the logical works of Porphry and Aristotle’s works on logic.

Philosophical Context:

Boethius gave the name Quadrivium to the other four liberal arts:
Arithmetic
Geometry
Astronomy
Music

Boethius adopts the post Aristotelian division of practical philosophy into three parts
Ethics
Politics
Economics

Position of logic is ambiguous in Boethius–
We may say logic is like a hand which is both a part of the human organism and an instrument.

On God:
God is the being who is supremely good and the source of all good things. Man can only be happy by participating in god. Furthermore, Boethius tells us, Nature is whole and perfect in the beginning and later falls away to inferior productions.

God is pure form without matter, he lacks all composition hence is absolutely one

Soul and Knowledge:
Boethius accepts Plato’s doctrine of preexistence of souls, furthermore he believes in platos doctrine on reminiscence –
He who pursues the truth must search within himself. Ideas are not abstractions of the sense world. We are born with them as memories of previous existence.

Reason as the highest power of human beings.

Text:

Boethius on Divine Foreknowledge and Future Contingent Events

Problem which Boethius seeks to solve is the problem of divine presence–
If God knows all things he also knows future contingent events, consequently these events cannot turnout other than God forknows it, however if this is the case, then there is no free will.

Boethius tries to resolve this clash by introducing three elements

  1. Modes of Cognition Principle:

“Everthing which is known is grasped not according to its own power but rather according to capability of those who know it” (256a)

  1. Eternity

“Eternity, then, is the whole simultaneous and perfect possession of boundless life.”
For Boethius God is Eternal– His relation to time is unlike ours. (Marenbon)

  1. Simple vs Conditional Necesity

“For there are really 2 necessities, the one symbol as that it is all man are mortal; the pother conditional as for example, if you know that someone is walking, it is necessary that he is walking… this conditional necessity by no means carries with it that other simplekind.

Boethius solves the problem by saying that God foreknows future contingent events through conditional necessity. Because he is eternal He sees them as though their happening in present. Due to the modes of cognition principle God has this knowledge due to his capability of being eternal, A capability which is not accessible to humans. Because conditional necessity does not imply simple necessity, human beings still retain their free will.

Peter Abelard

Biographical Information:

The turning point in his life was his forceful castration after it, he became a monk.
He attended Anselm’s classes at loan. But he was quickly forced to leave. In 1141 he was condemned and his condemnation ratified by the pope. Following it he sought refuge at Cluny. He died 1144.

Philosophical Context:

He held a nominalistic approach to logic. He was a rationalist but he did not put reason above faith or separated two.

He said: “I do not want to be a philosopher if it is necessary to deny Pope. I do not want to be Aristotle if it is necessary to be separated from Christ.”
(Acts 4.12)

For Abelard there are two types of images constructed by mind.

First type are general and confused images representing no single individual in a class distinctly but all generaly.

The Second type is particular and detailed, representing one individual alone.

Confused images evoked in the mind by common names like “man” particular images by proper names like “Socrates”. Universal concepts are nothing else than confused mental images.(Maurer)

Text

Peter Abelard, Ethics of Intention

Abelards nominalism has important repercussions on his ethical theory. His main concern is with the individual. In this case, the individual moral agent and his personal guilt&responsibility

Central notion in Abelards Ethics is intention, Abelard himself writes “An action is good not because it contains with in it some good but because it issues from a good intention”

Similarly an action is bad because it issues from a bad intention

Abelard explains for an intention to be good it is not enough to be seen good, it must be really good by corresponding Gods intention.

However, If a person is ignorant of Gods will and acts contrary to it in Good faith he does not sin. This is true of the persecutors of Christ– because they did not know what they are doing they did not sin. Furthermore It is not a sin lust after someone elses wife, the sin is rather to consent to this lust.(I 49)

In summary, Abelards ethics iss one of radical subjectivism. Human acts have no intrinstinc moral nature– the only criterion that which we can judge is the conformity of our action to divine intervention.

Just as willing is not the same as accomplishing the will so sinning isn’t same as carrying out the sin. The former is to be taken as the mind’s consent which we sin and the latter as the result of the doing. (I.67)

Sin comes about in three ways; by suggestion, by pleasure and by consent. This is exemplified in Eve’s tasting from the forbidden three.

Abelard also introduces a distinction between court trials and morality, he argues that it is justified that sometimes a penalty is greater than the sin for which somebody is penalised for. This is done to set an example for others. “For human beings don’t judge about what is hidden but about what is plain.” (I.82)

Only God can judge our intentions.

Important concepts

Morals: The minds vices or virtues thatcmakes us disposed the bad or good deeds.(I.1)

Actions under Duress: Whenever one wills something under the rest this willing should not be condemned as bad. (I.11-15)

Farabi

Biographical Information

Al Farabi was a determined follower of the Aristotelian tradition. He traced his own intellectual genealogy, teacher by teacher back to Aristotle himself. He was also the central figure of the school of Baghdad Perepatetics, who concentrated mostly on discussing Aristotle. (Marenbon, Very Short)

He was strongly influenced by Plato’s political theories.

Farabi also reasserted the ancient position that it is through the study of philosophy as practiced by Plato and Aristotle that humans can attain happiness (Marenbon, long)

Text

Al Farabi, On the Perfect State

Every human being needs many things which he cannot provide for himself– he is in need of other people.

“Everybody finds himself in the same relation to everybody in this respect. This is why humans organised themselves in societes.” (15.1)

There are 3 kinds or perfect society:
A great society– the union of all societies in the habitable world

The medium society– the union of the one nation

The small society– the union of a city

“In perfect societies are those which only exist for the sake of perfect societies such as villages, quarters and so on.” (15.2)

The most excellent good is firstly attained in a city, not in any less complete society. Felicity is only attainable in excellent cities which co-operate to produce the felicity of an excellent nation which co-operates to produce the felicity of the universal state.
The excellent city is like a healthy body– I possess a natural hierarchy that everybody does their own part. (15.3-15.4)

In this hierarchy the relation of the ruler to other parts is like the relation of the first cause to other existence.(15.6)
Rulership requires 2 conditions

  1. A predisposition in his inborn nature
  2. The acquisition of the attitude and the habit of will for rulership

(15.7)

The ruler is a person “who has reached his perfection and has become actually intellect and actually being thought.” He also apprehends also inteligables.
(15.8)

“He is the man who knows every action by which felicity can be reached”
(15.11)

“This state can only be reached by someone who possess 12 natural qualities”

  1. Strong limbs and organs
  2. Good at understanding and perceiving everything
  3. Forget almost nothing
  4. Intelligence and brightness
  5. Fine diction
  6. Found of learning
  7. Found of truth
  8. No drawings for food, drink, sexual intercourse and gambling
  9. Proud of spirit and found of honour
  10. Worldly pursuits should be a little worth to him
  11. Found of justice
  12. Strength of will

(15.12)

Because such men are rare, it is enough for somebody to fulfil only 6 conditions or 5 conditions + the gift of prophecy .

People who have all 12 qualities will be distinguished after reaching maturity by 6 additional qualities

  1. Being a Philosopher
  2. Knowing the laws and customs of the first rulers
  3. Excelling in deducing laws by analogy
  4. Excellent deliberation of new situations
  5. Good at guiding the people at his speech
  6. Mastering military art and being in tough physique

(15.13)
If a single man fulfills all the conditions he will be the king, if there are more men who together to fulfil these conditions, they will rule the city. If there are no philosophers in government, the city will perish in somepoint. (15.14)

There are 5 types of cities

  1. The Excellent City
  2. The Ignorant City (A city whose inhabitants do not know true felicity)
  3. The Wicked City ( A city who has the same views as the excellent city but the same action as the people of ignorant city.)
  4. The City which deliberately changed its character (A city whose views and actions were previously same with the excellent city)
  5. The City which missed the right path through faulty judgement (A City which aims at felicity but whose first ruler falsely pretended to receive revelation.)

The Ignorant City Divided into 6 parts

  1. City of Necessity (Whose people has their necessities fulfilled)
  2. City of Meannes (It’s people aim to acquire wealth and riches)
  3. City of the Depravity and Baseness (The aim of its people are sensual enjoyment
  4. City of Honour (Attaining honour and fame)
  5. City of Power
  6. Democratic City (Aim of its people is to be free)

(15.15-20)

The souls of people of one class are like one souls, whether that class is ruling or subordinate class. (16.1)

The people of the excellent city should know 8 things

  1. First cause and all of its qualities
  2. The immaterial existence and its specific qualities (and ranks of each of them)
  3. The celestial substances and the qualities of each of them
  4. Natural bodies which are beneath them
  5. The generation of men and how the faculties of soul come to be
  6. The first ruler and how revelation is brought about
  7. The rulers who have to take his place when he is not available
  8. That people of the excellent city attain felicity and people of other cities attain wretchedness

It is possible to have excellent nations, excellent cities whose religions differ

(17.1-2)

The cities of Ignorants and error arise when their religion is the right from a pernicious view of the ancients (18.1)

Christine de Pizan - A Medieval Feminist

Text

The main question which de Pizan asks is ‘why is it that so many men have always been so ready to say and write abominable and hateful things about women and their nature?’

The problematic of the question is that these men are reputable philosophers and writers.

In answering this question de Pizan is approached by three metaphorical figures: reason, rectitude, and justice, who help her in constructing The City of Ladies.

The first step in building this city is dispelling the hateful things said about women. The question asked is the following: do men do this because of their nature, or because of their hatred?

The answer given by reason is that this is not due to nature. Rather, the reasons are diverse:

  1. Criticizing from good intentions: attacking all women due to a small part of them which men should avoid
  2. Criticizing out of depravity: men who were frivolous in their youth attack women once they become impotent old men.
  3. Criticizing out of envy.

Further in the text, reason explains how men who have criticized women did not understand their blessings. F.e. there is a Latin proverb, which attacks women by saying that god made them to weep, talk, and weave.

However, men who use this to slander women do not understand the positive sides of these actions, as was the case, f.e., with the mother of St. Augustine, who made him join Christianity by her tears.

The text ends by giving advice to women on how they should conduct their lives: they should be humble, patient, and defend themselves against those who threaten their honor and chastity.

This advice is given to all women, whether they are aristocrat, bourgeois, or lower class, which de Pizan explicitly states.

Pizan also argues that woman cannot be a vile creature, as she was also created by God in his own image.

Thomas Aquinas

Biographical Data

He was the student of Albert the Great (Albert Magnus).

Member of the Dominican Order and the Regent Master of the University of Paris. In 1277 he was condemned, in 1323 he was canonized as a saint.

Philosophical Context

The five ways of proving the existence of God found in the Summa Theologia provide a good example of St. Thomas’ use of philosophy in his theology. These proofs are not original; each can be traced back to philosophers of antiquity or the middle ages, but in his hands are transformed not into the god of Aristotle, or the Arabic philosophers, but the god of Christianity.

(Prime Mover) The first and the most evident way of proving god’s existence is from motion: it is clear that some things are in motion; now, whatever is moved must be moved by something else. Being in motion is in potency with respect towards which it moves. Whereas a being moves insofar as it is in act. For motion is nothing but the reduction of something from potentiality to actuality.

A being cannot be brought from potentiality to actuality except by a being in act, f.e. wood that is potentially hot can be made actually hot only by something actually hot (such as fire). At first sight, the self-movement of living beings seems to be an exception to this rule. But on closer examination, we see that they have parts one of which moves the other. If the cause of motion is itself moved, it must be moved by some other mover, which in turn is moved by another, and so on…
But there cannot be an infinite regress, an infinite series of movers, because then there would be no first mover, and consequently no other movers. → God
(Maurer)

Text

Goodness precedes being only in the way the final cause precedes the efficient cause.
Every being is good insofar as it is a being. But something can be said to be evil insofar as ‘it lacks some existence,’ i.e. by the privation of good (eye can be blind through privation of sight, and thus be ‘bad’, as it would never be bad for a leg to be blind, since sight is not privated of it).

God is pure actuality.

(Compare with Saint Bonaventure’s thought, which stems from the standard Aristotelian interpretation of the time, later denied by Duns Scotus: Saint Bonaventure, for example, had argued that even angels could not be altogether immaterial; they must be compounds of form and “spiritual matter.” For matter is potentiality and form is actuality, so if the angels were altogether immaterial, they would be pure actuality without any admixture of potentiality. But only God is pure actuality (…) Scotus simply denies the unqualified equation of matter with potentiality and form with actuality. )

Olivi

Biographical Information

He was a Fransicsan monk who studies philosophy in Paris. He was against pagan philosophy and believed that its authors were deeply mislead about the nature of the world. (Marenbon Long)

He enjoyed little prestige and was forbidden to teach for period of time.
He anticipated many ideas which were later developed by Scotus. (Marenbon Short)

Philosophical Context

Olivi’s thinking about the will anticipates one of the dominant strands of 14th century thought. He believes thath almost all aspect which distinguished humans from animals depends on us having free will. (Marenbon Long)

Olivi was among the first to reject Aristotelian categories as ontological distinct. He believed that we cannot infer the ontological structure of the world from our conceptual divisions. Olivi argues that “the diversity of modes of predication does not necessarily entail a diversity of modes of being, because the mode of predication follows the mode of understanding rather than the mode of being […]”

He held a largely nominalistic position with some realist intuitions. He introduced the concept “rationes reales” whose core idea is the human mind can consider reality from different perspectives without ontological committing to any of them, for example, we can talk about Socrates in terms of his height and weight without ontological committing to the existence of quantity as a distinct thing. Even though that this quantity may not be ontological distinct it is still not mind dependent, but a property of reality. In contrast to rationes reales, Olivi also introduced rationes secundum dici which are completely mind dependent.

Olivi believed in universal hylomorphism, that is the view that every substance except God is composed of form and matter. However, following the bono venture he divided matter into radically different kinds, corporal matter and spiritual matter.

He argued against concurrentism which was a belief that God takes part in every causal process. He refused to accept this because he believed by accepting it he would also accept that God is responsible for our sins. (Stanford)

Olivi believed that our mental words are always followed by enact of thought and formed by that thought . Furthermore he believed that through these mental words we can better understand the external world.

Text

Peter John Olivi, Language and Social Object

The main question of Olivi’s text is the following:
“Does the right of royal power or authority over a kingdom and over subjects, or the right of property of one’s home, really add anything beyond the things and the persons which they are said?”

Olivi’s answer to this question is:
-No, it does not add anything.

Marsilius of Padua

Biographical Information

Marsilius of Padua was a 14th century philosopher and a Paris Arts Master. His main work “The defender of peace” was the devoted to attacking papal claims to secular power.

The historical background of his work began with Pope Gregory the 2nd reforms in the 11th century which created a rising tension between the pope and the secular rulers. This is why the work was dedicated to Ludwig of Bavaria who fought against the papal state. In some respects the work may even be seen as Ludwig’s manifesto. After the publication Marsilius had to flee Paris, he sought refuge at the court of Ludwig of Bavaria which also housed William of Ockham, Francis or Marcia and John of Jandun.

Text-Marsilius of Padua on Civil Society

The main goal of Marsilius’ text is attacking the papalist position, slash papal plenitude ie. that the pope has total jurisdiction over the secular ruler and every other human being.Marsilius opens the text by arguing for peace and against the discord. His reasoning is that a discord is the disease disposition of the civil regime. A city or a state cannot attain their prime goal unless there is peace.

One of Marsilius’ essential beliefs is that man naturally organised in communities, in order to bringforth common utilities for all. He quotes Tully’s sentence “and so, as the stoics were want to say, the things that grow in to world are all created for the use of man but man are born for the sake of man.”

Marsilius defines 4 different meanings of the term state

  1. A number of cities/provinces under one regime
  2. A certain species of a regime (temperate monarchy)
  3. A combination of 1 and 2
  4. Something common to every temperate monarchy

Furthermore, he defines tranquility as the good diposition as of the city/state whereby each of its parts is able perfectly to perform operation belongs to it accordance with reason and its establishment.

He compares the relation of the city or state and its part to tranquility with the relation of the animal and its parts to help.

In chapter 3 he outlines the origin of the civil community. His main thesis following Aristotle is that communities develop from less perfect to more perfect.

Marsilius accepts Aristotle’s definition of a city which is “ The perfect community having the full limit of self sufficiency which came into existence for the sake of living but exists for the sake of living well. Marsilius proceeds by explaining the difference between living and living well. Both of them exist in two kinds, the first being heavenly and eternal, the second being earthly. Marsilius claims that philosophers up until now have only comprehended the second through careful demonstration, but have not touched upon the first. The attainment of earthly living and living well, according to their demonstration, is possible only within a civil community. Men organized in communities in order to attain sufficiency, but were in necessity for moral teachers to resolve disputes and quarrels.

Furthermore, in order to attain all the different needs of sufficiency which stem from the differences among human beings, the city is organized into different offices. There are sixed kinds of offices, divided into the honorable class, which includes the priestly, the warrior and the judicial, and the vulgar class, which consists of the agricultural, the artisanal and the financial.

Marislius explains the reasoning behind the existence for each of the classes,

The necessity of the judical class is mending the excesses of certain acts in such a way that they accord with the correct proportion. The necessity of the warrior class is the protect the city from falling into slavery, because living well cannot be attained by citizens cast into slavery. The necessity of the financial class is treasure keeping of those resources which are in some years plentiful while in other years scarce. The necessity of priestşy class is keeping the city in order by instilling fear in wrongdoing. Priests should be righteous and respected men which is why neither farmers nor artisans should be priests. The final causes of the city as a whole and of its parts are different.

Besides final causes every part has also material, formal and efficient causes. The material causes are man habituated by diverse arts and disciplines. The efficient causes are the minds and the wills of men through thoughts and desires individually or collectively. The formal causes are the commands (which is the efficient cause impressed upon the man who exercises the terminate function in the city.)

  1. Kingly Monarchy: One ruler who rules for the common benefit i accordance with the consent of the subjects

  2. Thranny: Opposite of Kingly Monarchy, single ruler which wh rules for his private benefit apart from the will of his subjects

  3. Aristocracy: An Honorable class rules in accordance with will/consent of the subjects with common benefit

  4. Oligarchy: Group of people rules for their own benefit, apart from the wills of their subjects

  5. Polity: Any citizen participates in some way in the government according to his rank, ability/condition for the common benefit and with the will/consent of the citizens

  6. Democracy: Opposite of polity, a government in which the vulgar, establish the rule alone apart from the will/concent of the other citizens and not entirely for the common benefit

    There are 5 methods of establishing a kingly monarchy:

  7. The monarch is appointed for 1 determined function with respect to the ruling of the community. (e.g Agamennon being made the leader of the achean league)

  8. Receiving authority according to hereditary succession

  9. Electing the king

  10. The first ruler is elected with subsequent hereditary selection

  11. The ruler rules over everything in the community

Every government can govern over voluntary or involuntary subjects. The first is the genus of the well tampered governments, the second of diseased governments…
This is why the king should be chosen by election, and he should be the best men in polity. As Marsilius says “… the method of election which can never fail so long as the generation of men does not fail. Furthermore, a well tempered government requires good laws. In order to achieve this laws should also be made by the very people they applied to (ie to the whole body citizens or the waiter part they off)

Marsilius defines the best law as that which is made for the common benefit of all citizens (ARİSTOTLE POLITICS)

Citizens are part of a city which is a community of freeman, as the man are free they should not be made to respect the laws. However Marsilius’ argument is not only theoretical but also practical– Even though the law might be less useful it will be respected by more people, because people themselves have made it.

“Since all the citizens must be measured by the law according to due proportion, and no one knowingly harms or wishes injustice to himself, it follows all or most wish a law conducing to the common benefit of the citizens.”

As a counter argument to those who say that the majority of men are unlearned or stupid, Marsilius answers, That even though most people do not have the necessary skills to make laws they do have the knowledge to recognise bad laws. This is proven by induction, as many men can judge rightly, a quality of a picture, a house, a ship and so on even without being abşe to produce them.

“Scotus calls the extra-mental universal the “common nature” (natura communis) and the principle of individuation the “haecceity” (haecceitas). The common nature is common in that it is “indifferent” to existing in any number of individuals. But it has extra-mental existence only in the particular things in which it exists, and in them it is always “contracted” by the haecceity. So the common nature humanity exists in both Socrates and Plato, although in Socrates it is made individual by Socrates’s haecceitas and in Plato by Plato’s haecceitas.” - SEP

John Duns Scotus

Biographical Information:

One of the most influential philosophers in the high middle ages, his complex thought earned him the nickname, “the subtle doctor”. (Marenbon Short) He is seen as second in importance only to Aquianus. He was a Franciscan monk.(Marenbon Long)

Philosophical Context

Accidental change– a change in which the objective preserves its numerical identity. (e.g going from being pale to being tan). Contrast this with substantial change in which substance does not persist for the change.

Scotus denied universal hylomorphism and argued that some substances have more than one substantial form. (SEP)

Text

Scotus was a realist about universals. The central problem which Scotus addresses in the text is one of İbn-i Sina– How can a horseness be neither numerically one or diverse in number. Ibn-i Sina solves it in the following way, a horseness cannot be numerically one because in that case one thing would be present in many things, nor can it be diverse in number because in that case it would not explain how two different horses both participate in horseness.

Scotus on the other hand, solves the question by proposing the notion of a “less-than-numerical-unity”, Scotus proposes 7 arguments in favor of less-than-numerical-unity.

One of them for instance is that if every real unity or a numerical unity then every real diversity would be a numerical diversity which is obviously false. Numerical diversity would entail all things are equally distinct, if this were the case then the intellect could not abstract something common from Socrates and Plato anymore than it could from Socrates and a line. Another argument is that if we were to consider the opposite of a black thing it would be a white thing, and It must be a real thing too, since everything real is one, it must be one. But it is not numerically one, since any white thing is the opposite of a black thing.

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