The Medieval Problem of Universals: Boethius and Ockham

First off a big Happy New Year to you all and I hope 2014 brings you a proprous year ahead 🙂

To kick off 2014 here is some medieval philosophy, a look at the problem of universals has debated between William of Ockham and Boethius. It was this argument that helped push metaphysics forward from the classical teachings of Aristotle and Plato into its next age where it would soon make way for Renaissance thinkers to revive philosophy in a glourious burst of light surging forward Western Civilisation:

In his categories Aristotle says that things can be named in three ways: equivocally, univocally and derivatively. By equivocally he means two things that have a shared name but their definition is different like a bear and a cuddly bear, they are both animals but plainly are not the same thing. Univocally is when two things share a name and a definition like cat and dog, they are both animals and share that name and definition. Finally things that are named as derivatives are objects that get their name from an unrelated subject like a musician, a musician is still an animal and a human etc. they just happen to play a musical instrument but they do not fit into the category of music (Categories 1). There are also two types of speech, simple and composite, this is pretty straight forward, simple is individual words like ‘cat’, ‘dog’, ‘eats’, and ‘sleeps’, and composite is when they are combined to form sentences like ‘the cat sleeps’ and ‘the dog eats’. The other semantic confusion that is cleared up is that when he writes ‘present’  he means a thing being incapable of existing without it’s subject, like colour (Categories 2).

            Aristotle then goes on to discuss the four fold division (Studtmann 2007). Firstly when something is predicable of a subject, but never present within it e.g.  ‘cat’ is predicable of an individual cat and is never present in the subject. Others are present in a subject and never predicable of a subject like the tabby pattern of a cats coat, it is present in a tabby cats coat but without the cat there would be no tabby pattern. The third possibility is being present in an subject and predicable of a subject, Aristotle’s example here is very good, he says that knowledge is present in the human mind and at the same time is predicable in grammar. Lastly there are things that are neither present in the subject or predicable of a subject like an individual cat. (Categories 2)

             Section 3 of the categories discusses how predicates work and how they relate to genus and species. “When one thing is predicated of another, all that which is predicable of the predicate will be predicable also of the subject” (Categories 3). So a cat is predicated of an individual cat, and at the same time ‘animal’ is predicated of ‘cat’ and therefore it’s predicable of the individual cat as well, this is because a ‘cat’ is both ‘cat’ and ‘animal’.

            If we look at the genus ‘animal’ and ‘knowledge’ as examples to help the explanation. ‘four footed’, ‘has a tail’ ‘aquatic’ are all differentiae of the genus ‘animal’, and whilst ‘knowledge’ is not defined by the same differentiae does not stop it from having both ‘knowledge’ and ‘with tail’. This shows that genera are different and co-ordinated, and their differentiae can be different in kind. Genuses are subordinate to each other in a certain respect, they can also share differentiae because “the greater class is predicated of the lesser class” (Categories 3). For instance ‘cat’ will be part of the genus ‘animal’, ‘with instinct’, and ‘living’ but we know that ‘living’ will contain the genius ‘animal’ which in turn will contain the genus ‘instinct’. This means that all differentiae  of predicables will also be differentiaes of subjects. (Categories 3)

            Aristotle’s  fourth chapter in the categories does warrant a mention, more to list his categories and clear up a few semantics than to clear up his argument on universals. His ten categories are substance, quantity, quality, relation, place, time, position, state, action and affection.  Statements that only contain one of these does not involve an affirmation of that statement, a combination of the categories must be present to be able to get a positive or negative statement. Every assertion has to be true or false meaning that composite statements cannot be true or false because they have no quality to judge them on as they are not quantified in any way.   

            Boethius was an Italian philosopher writing around 480-524/5. He translated  Aristotles logical works from the Greek to Latin to give more people access to them. Among these he translated Aristotle’s categories and Porphyry’s third century Isagoge (meaning ‘introduction’) to Aristotle’s categories, this is where the problem of Universals is first bought up, Porphyry says “I shall decline for the present to say (a) whether, if they subsist or are posited in bare understandings only, (b) whether, if they subsist, they are corporeal or incorporeal, and (c) whether they are separated from sensibles or posited in sensibles and agree with them.” (Spade 1994 pg20). Porphyry says that there are five main categories or predicates; genus, species, difference, property and accident and also their possible combinations. These come from  Porphyry who states that there are three levels of Aristotelian predication, the first is the genus and their differences, the second species and how the differences from the first level influence this, and the third is the subject or substance of which they are predicated (Categories 1b15-24). These possess the properties of accidents and essentials. Species and genus are secondary substances, that can be predicated of the subject or substance proper (Categories 2a13-18). Each increase in generality must have a corresponding decrease of substantiality, within the category of substance, because it is in the primary substance that these individual substances are predicates.

            In his secondary commentary Boethius first argues that the likenesses of members of a species is what the mind tells us constitutes said species, secondly that a genus is made of similarities that are perceived in our mind between member species, and, thirdly that both genera and species exist only in our minds but they must be thought of as real or else they would be empty and inconsequential.

            In section 10 Boethius said that “Genera and species either exist and subsist or are formed by the understanding and by thought alone” (Spade pg 21). This outlines the problem that Boethius faces. He then puts forward his arguments against universals, he says that their existence is not possible because things that are common to a number of objects at the same time cannot possibly be one. Boethius then argues that if there are more than one genera which gets round the separability problem there will still be no genera that everything belongs to. This would result in each individual thing having it’s own genera as must each similarity, by this Boethius means that if an object is both red and round e.g. a ball and there is a balloon that is both red and round then there needs to be a genera for red and for round as well as one for ball and one for balloon etc. this process unfortunately continues ad infinitum and is the main problem with this theory.

            Boethius follows this with the case for universals,if genera and species are grasped by understanding alone, and that these understandings come from subjects, then they are not in understanding alone but actually exist in reality. He quickly counters this with the claim that if this understanding comes from the object itself, but not as it is in itself, then the understanding itself is false and that as genus and species don’t exist, then debating the existence of the five predicables must be discarded. He claims that it is “not inquiring about a thing that exists, or about a thing about which something true can be understood or stated” (Spade pg 23).

            Boethius’ solution agrees with Alexander (of Aphrodisias), false reasoning does not necessarily occur when we misinterpret a subject, but occurs when composition is mistaken, when we compose something in our brain that is not possible in nature e.g. horse and horn results in unicorn, we know this is a false impression. But if division and abstraction is where this understanding arises from, then the object is not understood in the way that it is in itself,  but the understanding is still not false. This is because there are several things which exist only as part of something, if they are separated from that object they can no longer exist but our minds can see them separately even though they cannot be e.g. the marking on a tabby cats coat, it cannot exist apart from the cat. The sense faculty gives us all the incorporeal things which subsist within such objects, the mind then sees the incorporeal qualities along with the corporeal ones and can separate them or join them as it decides. This is because the incorporeal qualities are separate from the corporeal ones even if they cannot be separated and both still exist in physical reality.

            Boethius says that because of that, genera and species can be found in both corporeal and incorporeal things. When found in incorporeal things then an incorporeal understanding of the genus is gained. However if the genus and species of corporeal things are observed then the mind separates them and sees them as pure form. Everything we learn from incorporeal qualities is not false and falsity should not be assumed, in fact it is through the minds division and abstraction that we can discover what is actually true. Therefore things like this are understood separately from sensibles but they do exist in corporals and sensibles, this means that they can be observed and their individualities understood. Because of this when we think of genera and species the information we consider is always sourced from the individual objects they exist in. “For example, from single men, dissimilar among themselves, the likeness of humanity is gathered.” (Spade pg 24). This similarity is the species and this likeness which cannot exist except in the species or it’s individuals is what makes up the genus.

            Consequently these things exist in singulars and are thought of as universals, so species is simply the likeness of if individuals that are unlike in number whilst genus is what the mind gathers as the likeness between species. “This likeness becomes sensible when it exists in singulars, and becomes intelligible when it is in universals” (Spade pg 25)

            Boethius gives succinct answers to the three questions that Porphyry decided to omit from his Isagoge. The answer to (a) is that both genera and species are understood one way and subsist in another. For (b) he says that they are incorporeal but are a part of sensibles and therefore joined to them but they are understood as individuals that are separate from the individual objects. Finally for (c) Boethius outlines Plato’s theory that these exist as universals but contra to what both Boethius and Aristotle say, Plato thinks that they also exist as physical entities separate from their original objects, where Aristotle thinks that they are understood as incorporeal and universal whilst subsisting in sensibles as parts or qualities of objects, not apart from them.

            William of Ockham begins by setting up the case for realism, before arguing against it until he is in a position to advance his nominalist account. Ockham is the author of ‘Ockham’s Razor’ which is a simple rule where we must not multiply entities beyond necessity; this rule allows Ockham to build on the Aristotelian criticisms of Platonic Ideas within the third man argument.

            To do this he uses three main arguments. The first argument concerns single substances in regard to universals. A universal cannot be a single substance else every single substance would require a universal. This cannot be the case else universals would be meaningless. Also there is no reason for some single substances to have universals and not others. This leads to his second argument. If single substances are not universals then universals must contain multiple single substances of the same type, but this would be a collection of particulars rather than a universal so this does not work either. The other way to understand this would be as multiple universal things. However as has been shown with Platonic forms this leads to infinite regress and as a result is still not a satisfying answer. This again leads us to the final argument, if universals are neither single nor multiple substances, it appears to lead to a dead end. Ockham suggest a novel way of resolving what universals could be. He poses the idea that universals can be a single substance within multiple single things. If we take the universal cat and apply this idea , two objections arise, the first is that the universal will pre-exist each instantiation of itself, so the cat would exist before the cat exists. This clearly is not an option. The objection is that when a cat dies part of the universal will be destroyed with it. Again this doesn’t work.

            So Ockham comes to the conclusion that universals do not have substance, they are incorporeal to tie it in with Boethius’ terms. Ockham argues that the universal is not a product of the mind but is really in the things that share it as it is one and the same in each, and is really distinct from each of them. A second argument of his follows the same point but rejects it is one and the same but multiplied an argument similar to Boethius’.

            Later on Ockham changes his argument again so that all that remains from the original position is the only difference between universals and particulars is the difference in our reason not in reality.

            After this Ockham starts to advance his own theory on metaphysics by claiming that universals are inside the mind and they are only universal in the sense of being predicated of many. A claim which reflects Aristotle’s nominalist position,

            Ockham’s next stage is to pose the question ‘Is a universal really outside the soul, distinct from the individual, although not really distinct?’, this question is an attack against Scotus who argued that universals are the subjects existing outside the soul where are different from the individual but only because each is made of a different type of material.

            Ockham answers his question by saying that anything which is individual by nature cannot be universal, which contradicts Scotus’ argument. Ockham then goes on to demonstrate how a substance can either be or not be a universal but never both as it breaks the law of non-contradiction, if (on the off-chance) that it is possible for universals and particulars to be one and the same then one will be left incomplete due to the nature of the other, thus we end up with something that is less that what we grasp of it.

            Ockham provides four ways that the universal nature causes contradiction either: it is a particular, or it is a numerical unity, if not then it is a universal, and finally if none of the first three then it must be a less than numerical unity. By rejecting the notion that it is a singular Scotus argues that the nature of the substance is prior to the contradiction so that its nature and contraction form two separate things. Hence the nature is not a numerical unity, yet is numerically one breaking the law of non-contradiction. Therefore it must be a universal in which case the nature of the universal is less than universal (according to Scotus). Hence the nature of a universal cannot be singular, numerical or universal leaving only the possibility that it is less than numerical but still many things.

            One of the prevalent theories of Ockhams time was that of Walter Burley who was like Scotus a moderate realist. He appeared to try and soften both Ockham and Scotus. Burley agrees with the first half of Scotus’ argument but not the later here he reverts to Aristotle by saying that the “Indiscernibility of Identicles is our chief criterion of distinction among real things.” (Kretzmann 1982 pg423).

            Burleys next step is to state that universals exist or partake in many particulars and are defined, but that particulars do not and are not defined either. This means that for Burley universals and particulars are distinct from each other. He still holds that different categories are distinct from one another and like Scotus thinks that these differences and indeed similarities must also have something in common but that this thing is again distinct.

            Added to this Burley states that it is universals and individuating principles that make up particulars, but that they do not separate the particular, instead “The whole universal (secundum se totum) exists in each of it’s particulars and is not numerically multiplied  by its existence in numerically distinct particulars” (Kretzmann 1982 pg423).

            Ockham has two main criticisms of this theory, firstly that arguing that universals and particulars are distinct and that “both the nature and the contracting differences exist in reality as constituents of a particular and they can exist in reality only as such” (Kretzmann 1982 pg414) would mean that universals can exist without particulars and vice versa. Now the one side of this is perfectly acceptable, for example courage can exist without an individual particular exemplifying it at a particular moment. The second statement taken from this by Ockham that he rejects is that the individual adds to the nature of a thing and that added with the universal which then makes the ‘one’ this leads to the statement that given that there is no universal nature there is no reason why God should not preserve what is added. Whilst these criticisms are interesting and do apply, they do not dismiss Burleys position completely, they more cause him an inconvenience

            For Ockham, the only universal entities it makes sense to talk about are universal concepts, and derivative on them, universal terms in spoken and written language. Metaphysically, these universal concepts are singular entities like all others; they are universal only in the sense of being predicable of many. So to conclude it is stated that there are particulars and universals, however universals exist only within the mind and particulars within nature, therefore Ockham is a nominalist and agrees with Boethius.


  • M. M. Adams, ‘Ockham’s Nominalism and Unreal Entities’, Philosophical Review 86 (1977), 144-76
  • P. Boehner, Ockham: Philosophical Writings (Edinburgh: Nelson, 1957; repr. Hackett, 1990)
  • A. Hyman & J. J. Walsh, Philosophy in the Middle Ages (Indianapolis: Hackett, 1973)
  • A. Kenny, Medieval Philosophy, A New History of Western Philosophy II (Oxford: Clarendon Press, 2005),
  • N. Kretzmann, A. Kenny, J. Pinborg, eds, The Cambridge History of Later Medieval Philosophy (Cambridge: Cambridge University Press, 1982)
  • J. Marenbon, Medieval Philosophy (London: Routledge, 2007),
  • J. Marenbon, ed., The Cambridge Companion to Boethius (Cambridge: Cambridge University Press, 2009)
  • M. J. Loux, Ockham’s Theory of Terms: Part I of the Summa Logicae (South Bend: St Augustine’s Pres, 1998)
  • P. V. Spade, Five Texts on the Mediaeval Problem of Universals (Indianapolis:

Hackett, 1994)

  • P. V. Spade, ed., The Cambridge Companion to Ockham (Cambridge: Cambridge

University Press, 1999)



Posted on January 1, 2014, in metaphysical, philosophical and tagged , , , , , , , , , , , . Bookmark the permalink. Leave a comment.

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