| 21345 | Aristotle said relations are not substances, so (if they exist) they must be accidents [Aristotle, by Heil] |
| Full Idea: Aristotle categorised relations as accidents - Socrates's whiteness, the sphericity of this ball - entities dependent on substances. Relations are not substances, so they must be, if anything at all, accidents. | |
| From: report of Aristotle (Categories [c.331 BCE], §7) by John Heil - Relations 'Historical' | |
| A reaction: Heil says this thought encouraged anti-realist views of relations, which became the norm until Russell. |
| 16656 | The separation from here to there is not the same as the separation from there to here [Aristotle] |
| Full Idea: Even though two separated things have a single interval between them, still the separation from here to there is not one and the same as the separation from there to here. | |
| From: Aristotle (Physics [c.337 BCE], 202b19) | |
| A reaction: His example is the road from Athens to Thebes. Since we tend to quantify distances between places more than Aristotle did, we are less impressed by this distinction, which seems a bit subjective. Aristotle seems to be thinking of vectors. |
| 16658 | The only reality in the category of Relation is things from another category [Henry of Ghent] |
| Full Idea: There is beyond a doubt nothing real in the category of Relation, except what is a thing from another category. | |
| From: Henry of Ghent (Quodlibeta [1284], VII:1-2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 12.3 | |
| A reaction: This seems to have been the fairly orthodox scholastic view of relations. |
| 16659 | Relations do not add anything to reality, though they are real aspects of the world [Olivi] |
| Full Idea: It does not seem that a relation adds anything real to that on which it is founded, but only makes for another real aspect belonging to the same thing. It is real since an aspect exists in re, not solely in the intellect, but it is not another thing. | |
| From: Peter John Olivi (Summa quaestionum super Sententias [1290], II.54), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 12.4 |
| 18528 | The single imagined 'interval' between things only exists in the intellect [Auriol] |
| Full Idea: It appears that a single thing, which must be imagined as some sort of interval [intervallum] existing between two things, cannot exist in extramental reality, but only in the intellect. | |
| From: Peter Auriol (Sentences [1316], I fols318 v a-b), quoted by John Heil - The Universe as We Find It 7 | |
| A reaction: This is the standard medieval denial of the existence of real relations. It contrasts with post-Russell ontology, which seems to admit relations as entities. Heil and Auriol and right. |
| 18529 | Relations are expressed either as absolute facts, or by a relational concept [William of Ockham] |
| Full Idea: Socrates and Plato are similar if they are both white. Yet the mind can express this either by an 'absolute concept' (as 'Socrates is white' and 'Plato is white'), or by a 'relative concept', as 'Socrates is similar to Plato with respect to whiteness. | |
| From: William of Ockham (Seven Quodlibets [1332], VI q.25), quoted by John Heil - The Universe as We Find It 7 | |
| A reaction: Presumably he takes the facts of the matter to be the absolute concept, and the relative concept to be a contribution of the intellect. |
| 21346 | The ratio between two lines can't be a feature of one, and cannot be in both [Leibniz] |
| Full Idea: If the ratio of two lines L and M is conceived as abstracted from them both, without considering which is the subject and which the object, which will then be the subject? We cannot say both, for then we should have an accident in two subjects. | |
| From: Gottfried Leibniz (Letters to Samuel Clarke [1716], 5th Paper, §47), quoted by John Heil - Relations 'External' | |
| A reaction: [compressed] Leibniz is rejecting external relations as having any status in ontology. It looks like a mistake (originating in Aristotle) to try to shoehorn the ontology of relations into the substance-properties framework. |
| 19383 | A man's distant wife dying is a real change in him [Leibniz] |
| Full Idea: No one can become a widower in India because of the death of his wife in Europe unless a real change occurs in him. | |
| From: Gottfried Leibniz (Letters to Burcher De Volder [1706], GP ii 240), quoted by Richard T.W. Arthur - Leibniz 7 'Nominalist' | |
| A reaction: This is Leibniz heroically denying so-called 'Cambridge Change'. It is hard to see how a widower is changed if he has not yet heard the bad news. But his situation in life has changed. Compare eudaimonia, which you can lose without realising it. |
| 10419 | If relations can be reduced to, or supervene on, monadic properties of relata, they are not real [Leibniz, by Swoyer] |
| Full Idea: Leibniz argued that relations could be reduced to monadic properties and so were dispensable, and some still agree, saying relations supervene on monadic properties of the relata, and are not actually real. | |
| From: report of Gottfried Leibniz (works [1690]) by Chris Swoyer - Properties 7.4 | |
| A reaction: At the very least a background of space and/or time seem required, in addition to any properties the relata may have. y only becomes 'to the left of x' when x appears to its right, so the relation doesn't seem to be intrinsic to y. |
| 13078 | Relations aren't in any monad, so they are distributed, so they are not real [Leibniz] |
| Full Idea: The relations which connect two monads are not in either the one or the other, but equally in both at once; and therefore properly speaking, in neither. I do not think you would wish to posit an accident which would inhere simultaneously in two subjects. | |
| From: Gottfried Leibniz (works [1690], G II:517), quoted by Cover,J/O'Leary-Hawthorne,J - Substance and Individuation in Leibniz 2.4.3 | |
| A reaction: Where Russell affirms relations as universals, and scholastics make them properties of individuals, Leibniz denies their reality entirely. It seems obvious that once the objects and properties are there, the relations come for free. |
| 13498 | Peirce and others began the mapping out of relations [Peirce, by Hart,WD] |
| Full Idea: It was Peirce and Schröder in the nineteenth century who began a systematic taxonomy of relations. | |
| From: report of Charles Sanders Peirce (works [1892], 4) by William D. Hart - The Evolution of Logic 4 |
| 21576 | With asymmetrical relations (before/after) the reduction to properties is impossible [Russell] |
| Full Idea: When we come to asymmetrical relations, such as before and after, greater and less etc., the attempt to reduce them to properties becomes obviously impossible. | |
| From: Bertrand Russell (Our Knowledge of the External World [1914], 2) | |
| A reaction: The traditional Aristotelian reduction to properties is attributed by Russell to logic based on subject-predicate. As an example he cites being greater than as depending on more than the mere magnitudes of the entities. Direction of the relation. |
| 21534 | The only thing we can say about relations is that they relate [Russell] |
| Full Idea: It may be doubted whether relations can be adequately characterised by anything except the fact that they relate. | |
| From: Bertrand Russell (Meinong on Complexes and Assumptions [1904], p.27) | |
| A reaction: We can characterise a rope that ties things together. If I say 'stand to his left', do I assume the existence of one of the relata and the relation, but without the second relata? How about 'you two stand over there, with him on the left'? |
| 21540 | Relational propositions seem to be 'about' their terms, rather than about the relation [Russell] |
| Full Idea: In some sense which it would be very desirable to define, a relational proposition seems to be 'about' its terms, in a way in which it is not about the relation. | |
| From: Bertrand Russell (Meinong on Complexes and Assumptions [1904], p.53) | |
| A reaction: Identifying how best to specify what a proposition is actually 'about' is a very illuminating mode of enquiry. You can't define 'underneath' without invoking a pair of objects to illustrate it. A proposition can still focus on the relation. |
| 21341 | Philosophers of logic and maths insisted that a vocabulary of relations was essential [Russell, by Heil] |
| Full Idea: Relations were regarded with suspicion, until philosophers working in logic and mathematics advanced reasons to doubt that we could provide anything like an adequate description of the world without developing a relational vocabulary. | |
| From: report of Bertrand Russell (The Principles of Mathematics [1903], Ch.26) by John Heil - Relations | |
| A reaction: [Heil cites Russell as the only reference] A little warning light, that philosophers describing the world managed to do without real relations, and it was only for the abstraction of logic and maths that they became essential. |
| 5371 | Because we depend on correspondence, we know relations better than we know the items that relate [Russell] |
| Full Idea: We can know the properties of the relations required to preserve the correspondence between sense-data and reality, but we cannot know the nature of the terms between which the relations hold. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 3) | |
| A reaction: Thus Russell always puts great emphasis on relations in his metaphysics. I would say that he is right, and that what he calls the 'nature of the terms' are essences, and that these are knowable, by inference and explanation. |
| 5407 | That Edinburgh is north of London is a non-mental fact, so relations are independent universals [Russell] |
| Full Idea: Nothing mental is presupposed in the fact that Edinburgh is north of London, but this involves the universal 'north of', so we must admit that relations are not dependent upon thought, but belong to the independent world which thought apprehends. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 9) | |
| A reaction: We cannot deny that Edinburgh being north of London is independent of our minds, but we might deny that 'north of' is a universal. 'North' is clearly a human convention, but 'nearer a pole' isn't. Distances exist in space, rather than as relations. |
| 21562 | There is no complexity without relations, so no propositions, and no truth [Russell] |
| Full Idea: Relations in intension are of the utmost importance to philosophy and philosophical logic, since they are essential to complexity, and thence to propositions, and thence to the possibility of truth and falsehood. | |
| From: Bertrand Russell (Substitutional Classes and Relations [1906], p.174) | |
| A reaction: Should we able to specify the whole of reality, if we have available to us objects, properties and relations? There remains indeterminate 'stuff', when it does not compose objects. There are relations between pure ideas. |
| 14217 | The 'standard' view of relations is that they hold of several objects in a given order [Fine,K] |
| Full Idea: The 'standard' view of relations, held by philosophers and logicians alike, is that we may meaningfully talk of a relation holding of several objects in a given order (which works for examples like 'loves' and 'between'). | |
| From: Kit Fine (Neutral Relations [2000], Intro) | |
| A reaction: The point of Fine's paper is that there are many relations for which this model seems to fail. |
| 14216 | The 'positionalist' view of relations says the number of places is fixed, but not the order [Fine,K] |
| Full Idea: The 'positionalist' view of relations is that each relation is taken to be endowed with a given number of argument places, or positions, in no specified order. [...The argument-places are specific entities, such as 'lover' and 'beloved'] | |
| From: Kit Fine (Neutral Relations [2000], Intro) | |
| A reaction: Fine offers this as an alternative to the 'standard' view of relations, in which the order of the objects matters. He then adds, and favours, the 'anti-positionalist' view, where there are not even a fixed number of places. |
| 14218 | A block on top of another contains one relation, not both 'on top of' and 'beneath' [Fine,K] |
| Full Idea: If block a is on block b, it is hard to see how this state of affairs might consist of both 'on top of' and 'beneath'. Surely if the state is a genuine relational complex, there must be a single relation for these relata? | |
| From: Kit Fine (Neutral Relations [2000], 1) | |
| A reaction: He has already shown that if such relations imply their converses, then that gives you two separate relations. He goes on to observe that you cannot pick one of the two as correct, because of symmetry. He later offers the 'vertical placement' relation. |
| 14219 | Language imposes a direction on a road which is not really part of the road [Fine,K] |
| Full Idea: Roads in the directional sense (A-to-B or B-to-A) are merely roads in the adirectional sense up which a direction has been imposed. | |
| From: Kit Fine (Neutral Relations [2000], 1) | |
| A reaction: This is Fine's linguistic objection to the standard view of relations. It is undeniable that language imposes an order where it may not exist ('Bob and Jane play tennis'), and this fact is very significant in discussing relations. |
| 14220 | Explain biased relations as orderings of the unbiased, or the unbiased as permutation classes of the biased? [Fine,K] |
| Full Idea: A 'biased' relation can be taken to be the result of imposing ordering on the argument-places of an unbiased relation, ..or we can take an unbiased relation to be a 'permutation class' of biased relations. This is a familiar metaphysic predicament. | |
| From: Kit Fine (Neutral Relations [2000], 3) | |
| A reaction: 'Biased' relations such as 'on top of' have an ordering to their places, but 'unbiased' relations such as 'vertical placement' do not. This is a nice question in the metaphysics of grounding relations between key concepts. |
| 21339 | We want the ontology of relations, not just a formal way of specifying them [Heil] |
| Full Idea: A satisfying account of relations must be ontologically serious. This means refusing to rest content with abstract specifications of relations as sets of ordered n-tuples. | |
| From: John Heil (Relations [2009], Intro) | |
| A reaction: A set of ordered entities would give the extension of a relation, which wouldn't, among other things, explain co-extensive relations (if all the people to my left were also taller than me). Heil's is a general cry from the heart about formal philosophy. |
| 21349 | Two people are indirectly related by height; the direct relation is internal, between properties [Heil] |
| Full Idea: If Simmias is taller than Socrates, they are indirectly related; they are related via their possession of properties that are themselves directly - and internally - related. Hence relational truths are made true by non-relational features of the world. | |
| From: John Heil (Relations [2009], 'Founding') | |
| A reaction: This seems to be a strategy for reducing external relations to internal relations, which are intrinsic to objects, which thus reduces the ontology. Heil is not endorsing it, but cites Kit Fine 2000. The germ of this idea is in Plato. |
| 21340 | Maybe all the other features of the world can be reduced to relations [Heil] |
| Full Idea: A striking idea is that relations are ontologically primary: monadic, non-relational features of the world are constituted by relations. A view of this kind is defended by Peirce, and contemporary 'structural realists' like Ladyman. | |
| From: John Heil (Relations [2009], 'Relational') | |
| A reaction: I can't make sense of this proposal, which seems to offer relations with no relata. What is a relation? What is it made of? How do you individuate two instances of a relations, without reference to the relata? |
| 18508 | Most philosophers now (absurdly) believe that relations fully exist [Heil] |
| Full Idea: It is a measure of how far we have fallen that so few philosophers nowadays see any difficulty at all in the idea that relations have full ontological standing. | |
| From: John Heil (The Universe as We Find It [2012], 01.4) | |
| A reaction: We have 'fallen' because medieval metaphysicians didn't believe it. Russell seems to have started, and the tendency to derive ontology from logic has secured the belief in relations. How else can you be allowed to write aRb? I agree with Heil. |
| 13076 | Scholastics treat relations as two separate predicates of the relata [Cover/O'Leary-Hawthorne] |
| Full Idea: The scholastics treated it as a step in the right explanatory direction to analyze a relational statement of the form 'aRb' into two subject-predicate statements, attributing different relational predicates to a and to b. | |
| From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 2.2.1) | |
| A reaction: The only alternative seems to be Russell's view of relations as pure universals, having a life of their own, quite apart from their relata. Or you could take them as properties of space, time (and powers?), external to the relata? |
| 13683 | A relation is a feature of multiple objects taken together [Sider] |
| Full Idea: A relation is just a feature of multiple objects taken together. | |
| From: Theodore Sider (Logic for Philosophy [2010], 1.8) | |
| A reaction: Appealingly simple, especially for a logician, who can then just list the relevant objects as members of a set, and the job is done. But if everyone to the left of me is also taller than me, this won't quite do. |
| 21354 | It may be that internal relations like proportion exist, because we directly perceive it [MacBride] |
| Full Idea: Some philosophers maintain that we literally perceive proportions and other internal relations. These relations must exist, otherwise we couldn't perceive them. | |
| From: Fraser MacBride (Relations [2016], 3) | |
| A reaction: [He cites Mulligan 1991, and Hochberg 2013:232] This seems a rather good point. You can't perceive the differing heights of two people, yet fail to perceive that one is taller. You also perceive 'below', which is external. |
| 14009 | It is a necessary condition for the existence of relations that both of the relata exist [Bourne] |
| Full Idea: It is widely held, and I think correctly so, that a necessary condition for the existence of relations is that both of the relata exist. | |
| From: Craig Bourne (A Future for Presentism [2006], 3.III Pr4) | |
| A reaction: This is either trivial or false. Relations in the actual world self-evidently relate components of it. But I seem able to revere Sherlock Holmes, and speculate about relations between possible entities. |
| 14010 | All relations between spatio-temporal objects are either spatio-temporal, or causal [Bourne] |
| Full Idea: If there are any genuine relations at all between spatio-temporal objects, then they are all either spatio-temporal or causal. | |
| From: Craig Bourne (A Future for Presentism [2006], 3.III Pr4) | |
| A reaction: This sounds too easy, but I have wracked my brains for counterexamples and failed to find any. How about qualitative relations? |
| 14926 | Relations without relata must be treated as universals, with their own formal properties [Ladyman/Ross] |
| Full Idea: The best sense that can be made of a relation without relata is the idea of a universal. Thus the relation 'larger than' has formal properties that are independent of the contingencies of their instantiation. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.4) | |
| A reaction: Russell was keen on the idea that relations are universals, and presumably for this reason. I struggle to grasp uninstantiated but nevertheless real 'greater than' relations. They are abstractions from things, not separate universals. |
| 14929 | A belief in relations must be a belief in things that are related [Ladyman/Ross] |
| Full Idea: Many philosophers say that one cannot intelligibly subscribe to the reality of relations unless one is also committed to the fact of some things that are related. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.5) | |
| A reaction: Ladyman and Ross try to argue against this view, but the idea makes a strong impression on me. Your ontology seems to be rather strange if you have a set of structural relations that await things to slot into the structure. |
| 22606 | Neo-Humeans say there are no substantial connections between anything [Ingthorsson] |
| Full Idea: Neo-Humean metaphysics holds the view that there are no substantial connections between anything in this world. | |
| From: R.D. Ingthorsson (A Powerful Particulars View of Causation [2021], 1) | |
| A reaction: A very illuminating comment. This exactly fits Lewis's great 'mosaic' of facts. The challenge is to say what 'substantial' relations there might be, but I'm quite happy to have a go at that. |