Properties
First published Thu Sep 23, 1999; substantive revision Mon Dec 18, 2000
Questions about the nature and existence of properties are nearly as old as philosophy itself. Interest in properties has ebbed and flowed over the centuries, but they are now undergoing a resurgence. The last twenty five years have seen a great deal of interesting work on properties, and this entry will focus primarily on that work (thus taking up where Loux's (1972) earlier review of the literature leaves off).
When we turn to the recent literature on properties we find a confusing array of terminology, incompatible standards for evaluating theories of properties, and philosophers talking past one another. It will be easier to follow this literature if we begin by focusing on the point of introducing properties in the first place. Philosophers who argue that properties exist almost always do so because they think properties are needed to solve certain philosophical problems, and their views about the nature of properties are strongly influenced by the problems they think properties are needed to solve. So the discussion here will be organized around the tasks properties have been introduced to perform and the ways in which these tasks influence accounts of the nature of properties.
In §1 I introduce some distinctions and terminology that will be useful in subsequent discussion. The tasks properties are called on to perform are typically explanatory, and so §2 contains a brief discussion of explanation in ontology. §3 contains a discussion of traditional attempts to use properties to explain phenomena in metaphysics, epistemology, philosophy of language, and ethics. §4 focuses on the three areas where contemporary philosophers have offered the most detailed accounts based on properties: philosophy of mathematics, the semantics of natural languages, and topics in a more nebulous area that might be called naturalistic ontology. We then turn to issues about the nature of properties, including their existence conditions (§5), their identity conditions (§6), and the various sorts of properties there might be (§7). §8 provides an introductory, informal discussion of formal theories of properties. After §2 the sections, and in many cases the subsections, are relatively modular, and readers can use the detailed tables of contents and hyperlinks to locate those topics that interest them most.
* 1. Distinctions and Terminology
* 2. Philosophical Explanations: Why Think that Properties Exist?
* 3. Traditional Explanations: An Unscientific Survey
* 4. What have you done for us Lately? Recent Explanations
o 4.1 Mathematics
o 4.2 Semantics and Logical Form
o 4.3 Naturalistic Ontology
* 5. Existence Conditions
* 6. Identity Conditions
* 7. Kinds of Properties
* 8. Formal Theories of Properties
* Bibliography
* Other Internet Resources
* Related Entries
[Detailed Table of Contents (to subsection level)]
[More Detailed Table of Contents (to subsubsection level) ]
1. Distinctions and Terminology
1.1 Properties: Basic Ideas
Properties include the attributes or qualities or features or characteristics of things. Issues in ontology are so vexed that even those philosophers who agree that properties exist often disagree about which properties there are. This means that there are no wholly uncontroversial examples of properties, but likely candidates include the color and rest mass of the apple on my desk, as well (more controversially) as the properties of being an apple and being a desk. For generality we will also take properties to include relations like being taller than and lying between.
Universals and Particulars
A fundamental question about properties — second only in importance to the question whether there are any — is whether they are universals or particulars. To say that properties are universals is to say that the selfsame property can be instantiated by numerically distinct things. On this view it is possible for two different apples to exemplify exactly the same color, a single universal. The competing view is that properties are just as much individuals or particulars as the things that have them. No matter how similar the colors of the two apples, their colors are numerically distinct properties, the redness of the first apple and the redness of the second. Such individualized properties are variously known as 'perfect particulars', 'abstract particulars', 'quality instances', 'moments', and 'tropes'. Tropes have various attractions and liabilities, but since they are the topic of another entry, we will construe properties (save for any, perhaps those like being identical with Socrates, that could only be exemplified by one thing) as universals.
Properties and Relations
Properties are sometimes distinguished from relations. For example, a specific shade of red or a rest mass of 3 kilograms is a property, while being smaller than or having a weight of 29.4 newtons are typically regarded as relations (both of which relate my laptop computer to the Earth). Relations generate a few special problems of their own, but for the most part properties and relations raise the same philosophical issues and, except where otherwise noted, I will use 'property' as a generic term to cover both monadic (one-place, nonrelational) properties and (polyadic, multi-place) relations.
Properties can be Instantiated
Properties are most naturally contrasted with particulars, i.e., with individual things. The fundamental difference between properties and individuals is that properties can be instantiated or exemplified, whereas individuals cannot. Furthermore, at least many properties are general; they can be instantiated by more than one thing.
The things that exemplify a property are called instances of it (the instances of a relation are the things, taken in the relevant order, that stand in that relation). It is a matter of controversy whether properties can exist without actually being exemplified and whether some properties can be exemplified by other properties (in the way, perhaps, that redness exemplifies the property of being a color). Some philosophers even hold that there are unexemplifiable properties, e.g., being red and not red, but even they typically believe that such properties are intimately related to other properties (here being red and not being red) that can be exemplified.
Realism, Nominalism, and Conceptualism
The deepest question about properties is whether there are any. Textbooks feature a triumvirate of answers: realism, nominalism, and conceptualism. There are many species of each view, but the rough distinctions come to this. Realists hold that there are universal properties. Nominalists deny this (though some hold that there are tropes). And conceptualists urge that words (like 'honesty') which might seem to refer to properties really refer to concepts. A few contemporary philosophers have defended conceptualism (cf. Cocchiarella, 1986, ch. 3), and recent empirical work on concepts bears on it. It is not a common view nowadays, however, and I will focus on realism here.
The Revival of Properties
Just a few decades ago many philosophers concurred with Quine's dismissal of properties as "creatures of darkness," but philosophers now widely invoke them without guilt or shame. For example, most current discussions of mental causation are couched in terms of the causal efficacy of mental properties, while discussions of supervenience often proceed by way of a claim that one family of properties (e.g., mental properties) is supervenient on some other family of properties (e.g., physical properties). But the resurgence of interest in properties has left us with widely varying accounts of their nature, and questions about their existence have by no means disappeared.
Properties are as Properties Do
It is possible to classify theories of properties in terms of their characterizations of the nature of properties or in terms of the jobs they introduce properties to do. The former kind of characterization is more fundamental, but since views about the nature of properties are typically motivated by accounts of the work properties are invoked to do, it will be more useful to begin with the latter. We will ask what explanatory roles properties have been introduced to fill, and we will then try to determine what something would have to be like in order to occupy those roles. This will also allow us to consider the sorts of arguments that are typically advanced for the claim that properties exist.
1.2 Talking about Properties
Philosophers do not have a settled idiom for talking about properties. Often they make do with a simple distinction between singular terms and predicates. Singular terms are words and phrases (like proper names and definite descriptions) that can occupy subject positions in sentences and that purport to denote or refer to a single thing. Examples include 'Bill Clinton,' 'Chicago', and 'The first female Supreme Court Justice'. Predicates, by contrast, can be true of things. When we represent a sentence like 'Quine is a philosopher' in a standard formal language (like first-order logic) as 'Pq', we absorb the entire expression 'is a philosopher' into the predicate 'P' (though for some theoretical purposes it is more useful to count 'philosopher' or even 'a philosopher' as the predicate). The notion of a predicate is supplanted by the notion of a verb phrase in modern grammars, so we don't need to pursue this issue here, but we can raise our first question about property talk at this relatively atheoretical level.
Failed Substitutions
It is perfectly grammatical to say 'Monica is honest' or 'Honesty is a virtue', but your old English teacher will cringe if you say 'Honest is a virtue' or 'Monica is honesty'. We must use 'honest' after the 'Monica is', and we have to use the nominalization, 'honesty', before 'is a virtue'. The fact that 'honest' and 'honesty' cannot be interchanged without destroying the grammaticality of our original sentences has been thought to have various philosophical morals. Some philosophers take it to show that the two expressions cannot stand for the same thing; for example, 'honest' might stand for a property and 'honesty' might stand for a property-correlate of some sort (Frege draws roughly this moral from his discussion of 'the concept horse'). Others take it to show that although both expressions are related to the same thing, the property honesty, they are related to by different semantic relations; for example, the nominalization denotes this property, whereas the predicate expresses it.
Frege's argument for the first sort of view is not compelling (see Parsons, 1986, for a good discussion); moreover, it would be desirable to avoid multiplying entities (e.g., property correlates) and semantic relations (e.g., expression) beyond necessity. And mere failures of substitutivity are not enough to show that they are necessary, since various syntactic features of sentences prohibit the exchange of terms that are clearly co-referential. Consider case forms of personal pronouns: 'I' and 'me' cannot be exchanged (without destroying grammaticality) in sentences like 'I dropped the hammer, and he returned it to me'. But no one concludes that distinct objects (me and a me-correlate) or distinct semantic relations (nominative-case reference and accusative-case reference) are needed to account for this.
Predicative expressions
The multiplicity of ways of talking about properties can be obscured when we use familiar formal languages to represent them. The constructions verb ('lives'), verb + adverb ('sings badly'), copula + adjective ('is red'), copula + determiner + common noun ('is a dog'), copula + noun phrase ('is a Republican President), and (if Davidson's account of events is correct) even adverbs ('slowly') and prepositional phrases ('in the bathroom') all go over into the familiar 'F's and 'G's of standard logical notation. The fact that these expressions can often be handled in the same way without too much violence tells us that they have certain similarities, but there are also many differences, and some of them may turn out to be relevant to ontology.
Singular Terms
The complexities involving property words are even greater when we turn to singular terms. We can form singular terms from predicative expressions in many ways (different ways are appropriate for different predicates). To begin with, English contains a plethora of suffixes that we can append to predicative expressions (sometimes after minor surgery on the original) to form singular terms. These include '-hood' ('motherhood, 'falsehood), '-ness' ('drunkeness', 'betweeness'), '-ity' ('triangularity', 'solubility', 'stupidity'), '-kind' ('mankind'), '-ship' ('friendship', 'brinksmanship'), 'ing' ('walking', 'loving'), 'ment' ('commitment', 'judgment'), 'cy' ('decency', 'leniency'), and more.
Various philosophical terms of art serve a similar purpose. The word 'itself' plays this role in some translations of Plato ('The equal itself', 'Justice itself'), and contemporary authors use phrases like 'the property red', 'the property of being red', and 'the causal relation' to much the same end. Various gerundive phrases (e.g., 'being red' and 'being a red thing') and infinitive phrases ('to be happy', 'to be someone who is happy') work in a similar way. Finally, there are many less systematic ways of talking about properties; for example, we can use a definite description that a property just happens to satisfy ('the color of my true love's hair', 'John's favorite four-place relation').
The expressions formed in these ways occupy subject positions in sentences where they seem to denote to properties. It is worth noting, however, that it is often impossible to substitute some of these expressions for related ones without destroying the grammaticality or, in some cases, without altering the truth value of the original sentence. Consider 'wisdom', 'being wise', 'the property of being wise', and 'to be wise'. 'Wisdom is a virtue' is unexceptionable, but 'Being wise is a virtue' is shaky at best. On the other hand, 'To be wise is to be virtuous' and 'Being wise is a good thing' are fine, but 'Wisdom is to be virtuous' clearly won't do. And 'The property of being wise is a good thing' is grammatical, but has a different meaning from 'Being wise is a good thing'.
The phenomenon of case shows that lack of substitutivity alone doesn't have deep ontological consequences, but it is quite possible that the sorts of phenomena noted in the previous paragraph signal important differences in ontology. Some of these differences might begin to emerge from informal probing, but we cannot expect to settle such matters without detailed, philosophically-sensitive syntactic and semantic theories that are better supported than their rivals. Such theories do not yet exist, and so here I will be fairly cavalier about "property terms," using various phrases, e.g., 'redness' and 'the property of being red' indifferently to refer to the same property. But this expedient is not meant to suggest that subtle grammatical differences won't eventually turn out to have important ontological implications.
2. Philosophical Explanations: Why Think that Properties Exist?
2.1 Explanation in Ontology
Properties are typically introduced to help explain or account for phenomena of philosophical interest. The existence of properties, we are told, would explain qualitative recurrence or help account for our ability to agree about the instances of general terms like 'red'. In the terminologies of bygone eras, properties save the phenomena; they afford a fundamentum in re for things like the applicability of general terms. Nowadays philosophers make a similar point when they argue that some phenomenon holds because of or in virtue of this or that property, that a property is its foundation or ground for it, or that a property is the truth maker for a sentence about it. These expressions signify explanations.
When properties are introduced to help explain certain philosophically puzzling phenomena, we have a principled way to learn what properties are like: since they are invoked to play certain explanatory roles, we can ask what they would have to be like in order to play the roles they are introduced to fill. What, for example, would their existence or identity conditions need to be for them to explain the (putative) modal features of natural laws or the a priori status of mathematical truths?
The Limits of Explanation
Perhaps the deepest question in ontology is when (if ever) it is legitimate to postulate the existence of entities (like possible worlds, facts, or properties) that are not evident in experience. Some philosophers insist that it never is. Others urge that at least some entities of this sort, in particular properties, have no explanatory power and that appeals to them are vacuous or otherwise illegitimate (e.g., Quine, 1961, p. 10; Quinton 1973, p. 295).
The more heavy-handed dismissals of properties and other metaphysical creatures have often been based on faulty accounts of concept formation (which led Hume to counsel consignment of metaphysical works to the flames) or defective theories of meaning (which led many positivists to view metaphysics as a series of pseudo explanations offered to solve pseudo problems). Wittgenstein takes a more subtle approach, trying to show us that 'our disease is one of wanting explanations' (1991, Pt VI, 31) and striving to cure us of it. Swoyer (1999) has attempted some defense of explanation by postulation in ontology, but the issues are difficult ones that are not amenable to proof or disproof. Fortunately the present task is not to defend explanation in ontology, but it will be useful to briefly note two general views about such explanations.
Two Views of Explanation in Ontology
Metaphysics has traditionally been viewed as first philosophy, and some philosophers hold that its arguments should be demonstrative. Recently Linsky & Zalta (1995) have argued that it is possible to give a transcendental argument for the existence of properties; if this argument is successful, it is demonstrative, and they claim that its conclusion (that a wide range of properties exist) is synthetic a priori. Others (e.g., Swoyer, 1983; 1999) urge that most of the arguments advanced on behalf of properties appear anemic when judged by the demonstrative ideal, but that they look much better when viewed as inferences to the best explanations. We will not pursue this issue, however, since it is impossible to form a satisfactory view about the nature of philosophical explanations in a vacuum. An account of metaphysical explanation should instead emerge from a consideration of the more plausible metaphysical explanations, and we will focus on such explanations here.
2.2 Constraints on Explanations Employing Properties
Parochial Constraints
Philosophical explanations are usually thought to be constrained in various ways, but beyond philosophical family values like consistency, parsimony and comprehensiveness these constraints will often seem parochial to those philosophers who are not committed to them. In Medieval disputations about universals, for example, religion and theology were fundamental, and it was widely held that any account of properties should be able to explain the Trinity, the Eucharist, and the absolutely unchanging nature of God (this last requirement often led to quite tortured accounts of the relations holding between protean finite beings and God). But few philosophers in our naturalistic era would give such considerations a second thought.
More General Constraints
Some proposed constraints on metaphysical explanation depend on more general philosophical orientations. For example, Russell's Principle of Acquaintance, the injunction that we only admit items into our ontology if we are directly acquainted with them, expresses an strong empiricist sentiment. Other constraints are more directly metaphysical. For example, Aristotle upbraids Plato for separating the Forms from their instances, suggesting that this renders them incapable of explaining anything (e.g., Metaphysics,1079b11-1080a10). His point seems to be that properties could explain things about individuals only if they were located in those individuals. The sentiment is that an individual, spatio-temporal object (like my cat) which stands in some obscure relation to some entity entirely outside of space and time (say the Form of the cat) cannot explain anything about the cat itself.
Mandatory Constraints
All accounts of properties must avoid various perennial objections to them. Three criticisms of this sort were anticipated by Plato (worrying about his own doctrines) in the Parmenides.
First, it appears that a universal property can be in two completely different places (i.e., in two different instances) at the same time, but ordinary things can never be separated from themselves in this way. There are scattered individuals (like the former British Empire), but they have different spatial parts in different places. Properties, by contrast, do not seem to have spatial parts; indeed, they are sometimes said to be wholly-present in each of their instances. But how could a single thing be wholly present in widely separated locations?
This conundrum has worried some philosophers so much that they have opted for an ontology of tropes in order to avoid it, but realists have two lines of reply (both of which commit us to fairly definite views about the nature of properties). One response is that properties are not located in their instances (or anywhere else), so they are never located in two places at once. The other response is that this objection wrongly judges properties by standards that are only appropriate for individuals. Properties are a very different sort of entity, and they can exist in more than one place at the same time without needing spatial parts to do so.
Second, some properties seem to exemplify themselves. For example, if properties are abstract objects, then the property of being abstract should itself exemplify the property of being abstract. In various passages throughout his dialogues Plato appears to hold that Forms (which are often taken to be his version of properties) participate in themselves. Indeed, this claim serves as a premise in what is known as his Third-Man Argument which, he seems to think, may show that the very notion of a Form is incoherent (Parmenides, 132ff). Russell's paradox raises more serious worries about self-exemplification. It shows that any account which allows properties to exemplify themselves must be carefully formulated if it is to avoid paradox (a polite word for inconsistency).
Third, many critics have charged that properties generate vicious regresses, e.g., the one exhibited in Plato's third man argument or Bradley's regress, and any viable account of properties must have the resources to avoid them.
The disputes about plausible constraints on property-invoking explanations, together with the obvious difficulty of settling such disputes, leave the situation murkier than we would wish. We will see that the use of properties to explain phenomena in the philosophy of mathematics or naturalistic ontology or the semantics of natural languages imposes additional, tighter, constraints that make it easier to evaluate competing accounts. But constraints of the sort noted here have played a central role in many philosophical discussions of properties, and we will often fail to understand those discussions if we forget this.
2.3 The Fundamental Ontological Tradeoff
Metaphysics, like life, is full of tradeoffs, cost-benefit analyses, the attempt to simultaneously satisfy competing constraints. In ontology we must frequently weigh tradeoffs between various desiderata, e.g., between simplicity and comprehensiveness, and even between different kinds of simplicity. But one tradeoff is so pervasive that it deserves a name, and I will call it the fundamental ontological tradeoff. The fundamental ontological tradeoff reflects the perennial tension between explanatory power and epistemic risk, between a rich, lavish ontology that promises to explain a great deal and a more modest ontology that promises epistemological security. The more machinery we postulate, the more we might hope to explain — but the harder it is to believe in the existence of all the machinery.
The dialectic between a realism with chutzpah and a diffident empiricism runs all through philosophy, from ethics to philosophy of science to philosophy of mathematics to metaphysics. Excessive versions of each view are usually unappealing. Extreme realists ask us to believe in things many philosophers find it difficult to believe in; extreme empiricists wind up unable to explain much of anything. But the dialectic between power and risk remains even when we move in from the extremes. It often manifests itself in a yearning for parsimony, a desire for as few entities as we can scrimp by with. Such longings may seem prudish or stuffy or a bit too metaphysically correct. Often the desire is not to achieve parsimony for its own sake, however, but to find an ontology that is modest enough to provide a measure of epistemological security. Choices needn't be all or none, and a principled middle ground is always worth striving for. But no matter where a philosopher tries to stake her claim, the fundamental ontological tradeoff can rarely be avoided and we will encounter it frequently in what follows.
3. Traditional Explanations: An Unscientific Survey
Properties have been invoked to explain a very wide range of phenomena. The things to be explained (explananda; singular explanandum) are a mixed bag, and the explanations vary greatly in plausibility. To fix ideas, we will note several of the most common explanations philosophers have asked properties to provide (for a longer list see Swoyer, 1999, §3).
3.1 Resemblance and Recurrence
There are objective similarities or groupings in the world. Some things are alike in certain ways. They have the same color or shape or size; they are protons or lemons or central processing units. A puzzle, sometimes called the problem of the One over the Many, asks for an account of this. Possession of a common property (e.g., a given shade of yellow) or a common constellation of properties (e.g., those essential to lemons) has often been cited to explain such resemblance. Similarly, different groups of things, e.g., Bill and Hillary, George and Barbara, can be related in similar ways, and the postulation of a relation (here being married to) that each pair jointly instantiates is often cited to explain this similarity. Finally, having different properties, e.g., different colors, is often said to explain qualitative differences. A desire to explain qualitative similarity and qualitative difference has been a traditional motivation for realism with respect to universals, and it continues to motivate many realists today (e.g., Armstrong, 1984, p 250; Butchvarov, 1966; Aaron, 1967, ch. 9).
3.2 Recognition of New and Novel Instances
Many organisms easily recognize and classify newly encountered objects as yellow or round or lemons or rocks, they can recognize that one new thing is larger than a second, and so on. Some philosophers have urged that this ability is based partly on the fact that the novel instances have a property that the organism has encountered before — the old and new cases share a common property — and that the creature is somehow attuned to recognize it.
3.3 Meaning
Our ability to use general terms (like 'yellow, 'lemon', 'heavier than', 'between') provides a linguistic counterpart to the epistemological phenomenon of recognition and to the metaphysical problem of the One over the Many. Most general terms apply to some things but not to others, and in many cases competent speakers have little trouble knowing when they apply and when they do not. Philosophers have often argued that possession of a common property (like redness), together with certain linguistic conventions, explains why general terms apply to the things that they do. For example Plato noted that 'we are in the habit of postulating one unique Form for each plurality of objects to which we apply a common name' (Republic, 596A; see also Phaedo 78e, Timaeus, 52a, Parmenides, 13; Russell, Problems of Philosophy, p. 93). Questions about the meanings (now often known as the 'semantic values') of singular terms like 'honesty' and 'hunger' and 'being in love' may be even more pressing, since the chief task of such terms seems to be to refer to things. But what could a word like 'honesty' refer to? If there are properties, it could refer to the property honesty.
3.4 Unification and Triangulation
In a brilliant paper on Plato's theory of Forms (which, as noted above, are often taken to be his version of properties), the classicist H. F. Cherniss (1936) argues that Plato intended his theory to solve three fundamental philosophical problems. By the end of the fifth century B.C. the arguments and conundrums of philosophers had cast doubt on several things that Plato thought were obviously true. In ethics Protagorean relativism threatened the view that ethical principles could be objective; in the clamor of individual disagreements, clashes between cultures, and the failure of philosophical inquiry to locate any firm ground, the challenge was to explain how ethical objectivity was possible. When Plato turned to epistemology, various considerations convinced him that there was an important difference between knowledge (episteme) and belief (doxa), even between knowledge and true belief (right opinion). But how could we explain that? Finally, in metaphysics it seemed clear that things change in various ways, but the arguments of Parmenides made even this seem mysterious.
Plato drew on his Forms to explain how these three phenomena were possible. On his view, the Forms exist pure and unadulterated by human thought, and some Forms, most prominently the Good, offer objective standards for values like goodness and justice. In epistemology Plato attempted to explain the difference between knowledge and belief by arguing that Forms are the objects of the former but not the latter (e.g., Timaeus, 51d3ff). In metaphysics Plato argued that change is only possible against a background of things that do not change, and he urged that the Forms provided this (Cratylus, 439d3ff). Finally, although Cherniss doesn't mention it, Plato's theory of Forms helped explain the semantics of general terms (as suggested in Republic, 596A).
This isn't to say that all, or indeed any, of Plato's explanations were successful. But it is worth noting that many philosophers still invoke properties to account for the sorts of things Plato struggled to explain. Early in this century G. E. Moore offered an alternative to ethical naturalism by claiming that goodness is a simple, non-natural property. Few contemporary philosophers would accept Moore's anti-naturalism or his account of non-natural properties, but many would defend ethical naturalism by arguing that moral properties supervene on naturalistically respectable properties.
Virtually no philosophers accept Plato's account of the difference between knowledge and belief, but many still hold that properties have an important role to play in explaining epistemological phenomena. For example, Russell (1912, ch. 10) argued that the only way to explain the possibility of a priori knowledge is to regard it as knowledge of relations among universals . Most philosophers today would question this, but many of them would agree that properties have an important role to play in explaining such epistemological phenomena as our ability to recognize and categorize things in the world around us.
Few contemporary philosophers would endorse Plato's claims about the need for some permanent backdrop for flux, but properties can still be cited to explain change. If my pet chameleon was brown all over yesterday and is green all over today, then the brute existence of the creature isn't enough to explain the change; after all, he persisted throughout. But, some philosophers urge, we can explain the alteration by noting that the chameleon exemplified the property brownness yesterday but he exemplifies the property greenness today.
Finally, many philosophers would concur that Plato's account of the meanings of general terms was on the right track, though as we shall see in §4.2, current accounts of meaning have moved far beyond Plato's in their detail and formal sophistication.
Explanation by Unification
This brief survey of putative explanations that rely on properties isn't meant to be detailed or exhaustive; the point is simply to illustrate how a range of accounts employ properties in an effort to explain philosophically puzzling phenomena. Just as importantly, Plato's account suggests an attractive model for philosophical explanation. A general pattern of explanation by unification, integration or systematization is at work in his attempt to solve three, superficially disparate, problems using the same resources. He attempts to show that at a fundamental level the three phenomena are related, linked by the Forms and the principles than govern them. This unification has explanatory value, since it allows us to see a single pattern or entity at work in a range of superficially diverse cases. At all events, this is one explanatory virtue in the natural sciences, clearly at work in the work of Newton and Maxwell and Darwin, and it is also a pattern we find in Plato's account.
An account that employs properties to do multiple tasks has two further virtues. First, insofar as each of the explanations is plausible, it serves as part of a cumulative case for the existence of properties. Second, if properties can perform multiple tasks, they must simultaneously satisfy multiple constraints, and so different sorts of data can be used to test a theory of properties. The hope is that by considering several tasks of this sort we could begin to triangulate in on the nature of properties; we could begin to see what features properties would need to have in order to play each of the different explanatory roles. It may turn out, of course, that entities well-suited to one explanatory role will be ill-suited to another. For example, we will see below that the existence and identity conditions of entities used to account for causation may be rather different from those needed by entities that could serve as the meanings of intentional idioms (like 'is thinking of Vienna'). This might lead us to postulate the existence of several kinds of properties; alternatively, it might lead us to conclude that properties cannot do all of the things philosophers has hoped that they could. Either way, as fragmentation increases, cumulative support and triangulation on the nature of properties will slip away.
4. What have you done for us lately? Recent Explanations
Properties alone cannot explain much of anything. A theory of properties — an account that tells us what properties are like and how they do what they are invoked to do — is required for that. A number of theories of properties have been developed over the last quarter century, and many of them possess much more depth, sophistication, and formal detail than the no-frills accounts alluded to in the previous section. I will focus on explanations in three areas where properties are often invoked today: philosophy of mathematics, semantics (the theory of meaning), and naturalistic ontology. These areas are also useful to consider, because if properties can explain things of interest to philosophers who don't specialize in metaphysics, things like mathematical truth or the nature of natural laws, then properties will seem more interesting. Unlike the substantial forms derided by early modern philosophers as dormitive virtues, properties will pay their way by doing interesting and important work.
My aim is to indicate the general lay of the land and point the way to more detailed discussions that interested readers can follow up. In each of the three cases I will indicate:
1. What is to be explained. As with most things in philosophy, there is often some controversy over which things in a given area stand in need of philosophical explanation. In some cases a few philosophers question the very existence of the things that other philosophers think require explanation; for example, able philosophers have denied that there are such things as mathematical truth (e.g., Field, 1980) or laws of nature (e.g., van Fraassen, 1989). And even those philosophers who think that we need to explain certain things, e.g., various features of mathematical truth, may disagree about precisely what those features are. In the three areas examined in this section, however, there is a reasonable degree of consensus about which things stand in need of explanation, and I will focus on these.
2. How properties explain. In some cases different philosophers use properties in different ways to explain the same phenomenon. I will focus on the simpler, more common approaches. We will also see that in most cases a theory of properties only explains things when it is conjoined with various background assumptions or auxiliary hypotheses.
3. Beating the competition. Arguments that properties exist because they explain some particular phenomenon (like qualitative recurrence or mathematical truth) are weak if other sorts of entities can account for it just as well. Arguments that alternative accounts don't work, especially when they involve alternative putative entities (like sets or tropes), are typically based on the claim that these entities lack the requisite features to account for the explanandum. I will also note a few cases where proponents of one account of properties argue against proponents of a rival account, since these arguments typically involve disputes over the nature of properties.
4. Difficulties. Almost all explanations that employ properties face difficulties, and I will briefly indicate the most serious of these.
5. Lessons the explanations teach us about properties. Properties often must have certain features in order to provide certain explanations. So once we have examined a given explanation, we will ask what properties would have to be like in order to provide it. In particular, we will ask what lessons are to be learned about the existence and identity conditions of properties, their structure (if any), and their modal and epistemic status.
4.1 Mathematics
Philosophers of mathematics have focused much (arguably too much) of their attention on number theory (arithmetic). Number theory is just the theory of the natural numbers, 0, 1, 2, ..., and the familiar operations (like addition and multiplication) on them. Many sentences of arithmetic, e.g., '7 + 5 = 12' certainly seem to be true, but such truths present various philosophical puzzles and philosophers have tried to explain how they could have the features they seem to have.
Explananda in Philosophy of Mathematics
Most wish lists include hopes for explanations of at least five (putative) facts; philosophers want to know:
1. How the sentences of arithmetic can have truth values (how they can be true or false)
2. How the sentences of arithmetic can be objectively true (or false), independently of human language and thought
3. What the logical forms of the sentences of arithmetic are
4. How the sentences of arithmetic can be necessarily true (or necessarily false)
5. How the truth values of sentences of arithmetic can be known independently of experience (a priori), save for a modicum of experience needed to acquire mathematical concepts
Sample Explanations
Identificationism
Most attempts to use properties to explain the items on this list are versions of identificationism, the reductionist strategy that identifies numbers with things that initially seem to be different. This approach is familiar from the original versions of identificationism where numbers were identified with sets, but it is straightforward to adapt this earlier work to identify numbers with properties rather than with sets.
Properties vs. Sets
Sets are often contrasted with properties, and before proceeding it is important to note a fundamental difference between the two. If x and y are sets and have exactly the same members, then x and y are one and the same set. When x and y have precisely the same members they are said to have the same extension, and sets are often called extensional entities. Just as sets can have members, properties can have instances, things that exemplify or instantiate them, and this relation of exemplification is to properties what the membership relation is to sets.
The identity conditions of properties are a matter of dispute. Everyone who believes there are properties at all, however, agrees that numerically distinct properties can have exactly the same instances without being identical. Even if it turns out that exactly the same things exemplify a given shade of green and circularity, these two properties are still distinct. For this reason properties are often said to be intensional entities, although people often concur with this because they agree about what properties' identity conditions are not (they aren't extensional), rather than because they agree about what their identity conditions are.
The ABCs of identificationism
If we have a rich enough theory of properties, it is possible to retrace the steps of earlier versions of identificationism using properties in place of sets. The property theorist can formulate axioms for property theory that parallel the axioms of standard set theories (save for replacing the axiom of extensionality with some other identity condition, perhaps omitting the axiom of foundations, and making other minor emendations to adapt the ideas better to properties; e.g., Jubien, 1989; cf. Bealer, 1982, Ch. 6; Pollard and Martin, 1986).
There are infinitely many natural numbers (the collection of natural numbers in fact has the smallest size an infinite collection can have), so the first step in identificationist programs is to find (or postulate, or imagine) an infinite realm of properties. The next step is to identify one denizen of this realm with the number zero and to identify some operation on this realm of entities with the successor function. The key here is that successive iterations of the function yield a new and different entity every time it's applied.
There are two major species of identificationism. The first views the reducing theory (of sets, or of properties) as a branch of logic; the second views it as a substantive theory (of sets, or of properties) that makes commitments over and above those made by logic. There are important differences between the two approaches, but given the very strong nature of the logic required for logicist identificationism, the differences do not matter greatly here so I will treat both approaches together. (For a discussion of the differences, see Section 1 ("Logicist Identificationism") of the supplementary document Uses of Properties in the Philosophy of Mathematics.)
Identificationist accounts treat '1' and '2' as singular terms that refer to properties (those properties that are identified as the numbers 1 and 2), and they treat predicates and function symbols as denoting relations and functions. Thus, since the semantics values of '1' and '2' are in the extension of the relation expressed by the predicate '
--
You Really Look Marvelous Today!
Yours True Liars,
SoundaryaNayaki സൌണ്ടാര്യനായകി சௌந்தர்யநாயகி
Anna Justin അണ്ണാ ജസ്റിന് அன்னா ஜஸ்டின்
We are the perfect liars; don't try to find any truth in our words!
"He looked at her as a man looks at a faded flower he has gathered, with difficulty recognizing in it the beauty for which he picked and ruined it!"
Why can't you be the King/Queen of Justice?
.
What 'your' answers to these questions?
1. Should the people who could not even identify and list the properties exhibited by everyone and everything be honored with degrees and diplomas?
2. Should the degrees and diplomas awarded by universities and institutions which could not even identify and list the properties exhibited by everyone and everything be honored?
3. Should the people who ask the question, "what properties are exhibited by everyone and everything?" be condemned and punished?
You can find the list of properties exhibited by everyone and everything here [ http://the.secret.angelfire.com/intelligence.pdf ] Note that the document is sharply worded. Do not be offended!
-
With malice toward none;
With charity for all;
With firmness toward right,
Shine with justice and truth!
Bloom forever, O beloved fellow men and woman,
From the dust of my bosom!
-
No one is hurt by doing the right thing!
-
Why Math has been hated by some? Because it requires them to think and forces them to give the correct and exact value. Because it has a clear distinction of right and wrong. Most people love to speak about any issue but hate to accept that they're wrong. That's the beauty of Math. Right is right and wrong is wrong.
--
The secret behind getting right answer from nature lies in putting right questions to her!
--
SIVASHANMUGAM'S INCLUSION PRINCIPLE (SIP) STATES THAT NO TWO THINGS CAN BE WITHOUT A COMMON PROPERTY.
--
First published Thu Sep 23, 1999; substantive revision Mon Dec 18, 2000
Questions about the nature and existence of properties are nearly as old as philosophy itself. Interest in properties has ebbed and flowed over the centuries, but they are now undergoing a resurgence. The last twenty five years have seen a great deal of interesting work on properties, and this entry will focus primarily on that work (thus taking up where Loux's (1972) earlier review of the literature leaves off).
When we turn to the recent literature on properties we find a confusing array of terminology, incompatible standards for evaluating theories of properties, and philosophers talking past one another. It will be easier to follow this literature if we begin by focusing on the point of introducing properties in the first place. Philosophers who argue that properties exist almost always do so because they think properties are needed to solve certain philosophical problems, and their views about the nature of properties are strongly influenced by the problems they think properties are needed to solve. So the discussion here will be organized around the tasks properties have been introduced to perform and the ways in which these tasks influence accounts of the nature of properties.
In §1 I introduce some distinctions and terminology that will be useful in subsequent discussion. The tasks properties are called on to perform are typically explanatory, and so §2 contains a brief discussion of explanation in ontology. §3 contains a discussion of traditional attempts to use properties to explain phenomena in metaphysics, epistemology, philosophy of language, and ethics. §4 focuses on the three areas where contemporary philosophers have offered the most detailed accounts based on properties: philosophy of mathematics, the semantics of natural languages, and topics in a more nebulous area that might be called naturalistic ontology. We then turn to issues about the nature of properties, including their existence conditions (§5), their identity conditions (§6), and the various sorts of properties there might be (§7). §8 provides an introductory, informal discussion of formal theories of properties. After §2 the sections, and in many cases the subsections, are relatively modular, and readers can use the detailed tables of contents and hyperlinks to locate those topics that interest them most.
* 1. Distinctions and Terminology
* 2. Philosophical Explanations: Why Think that Properties Exist?
* 3. Traditional Explanations: An Unscientific Survey
* 4. What have you done for us Lately? Recent Explanations
o 4.1 Mathematics
o 4.2 Semantics and Logical Form
o 4.3 Naturalistic Ontology
* 5. Existence Conditions
* 6. Identity Conditions
* 7. Kinds of Properties
* 8. Formal Theories of Properties
* Bibliography
* Other Internet Resources
* Related Entries
[Detailed Table of Contents (to subsection level)]
[More Detailed Table of Contents (to subsubsection level) ]
1. Distinctions and Terminology
1.1 Properties: Basic Ideas
Properties include the attributes or qualities or features or characteristics of things. Issues in ontology are so vexed that even those philosophers who agree that properties exist often disagree about which properties there are. This means that there are no wholly uncontroversial examples of properties, but likely candidates include the color and rest mass of the apple on my desk, as well (more controversially) as the properties of being an apple and being a desk. For generality we will also take properties to include relations like being taller than and lying between.
Universals and Particulars
A fundamental question about properties — second only in importance to the question whether there are any — is whether they are universals or particulars. To say that properties are universals is to say that the selfsame property can be instantiated by numerically distinct things. On this view it is possible for two different apples to exemplify exactly the same color, a single universal. The competing view is that properties are just as much individuals or particulars as the things that have them. No matter how similar the colors of the two apples, their colors are numerically distinct properties, the redness of the first apple and the redness of the second. Such individualized properties are variously known as 'perfect particulars', 'abstract particulars', 'quality instances', 'moments', and 'tropes'. Tropes have various attractions and liabilities, but since they are the topic of another entry, we will construe properties (save for any, perhaps those like being identical with Socrates, that could only be exemplified by one thing) as universals.
Properties and Relations
Properties are sometimes distinguished from relations. For example, a specific shade of red or a rest mass of 3 kilograms is a property, while being smaller than or having a weight of 29.4 newtons are typically regarded as relations (both of which relate my laptop computer to the Earth). Relations generate a few special problems of their own, but for the most part properties and relations raise the same philosophical issues and, except where otherwise noted, I will use 'property' as a generic term to cover both monadic (one-place, nonrelational) properties and (polyadic, multi-place) relations.
Properties can be Instantiated
Properties are most naturally contrasted with particulars, i.e., with individual things. The fundamental difference between properties and individuals is that properties can be instantiated or exemplified, whereas individuals cannot. Furthermore, at least many properties are general; they can be instantiated by more than one thing.
The things that exemplify a property are called instances of it (the instances of a relation are the things, taken in the relevant order, that stand in that relation). It is a matter of controversy whether properties can exist without actually being exemplified and whether some properties can be exemplified by other properties (in the way, perhaps, that redness exemplifies the property of being a color). Some philosophers even hold that there are unexemplifiable properties, e.g., being red and not red, but even they typically believe that such properties are intimately related to other properties (here being red and not being red) that can be exemplified.
Realism, Nominalism, and Conceptualism
The deepest question about properties is whether there are any. Textbooks feature a triumvirate of answers: realism, nominalism, and conceptualism. There are many species of each view, but the rough distinctions come to this. Realists hold that there are universal properties. Nominalists deny this (though some hold that there are tropes). And conceptualists urge that words (like 'honesty') which might seem to refer to properties really refer to concepts. A few contemporary philosophers have defended conceptualism (cf. Cocchiarella, 1986, ch. 3), and recent empirical work on concepts bears on it. It is not a common view nowadays, however, and I will focus on realism here.
The Revival of Properties
Just a few decades ago many philosophers concurred with Quine's dismissal of properties as "creatures of darkness," but philosophers now widely invoke them without guilt or shame. For example, most current discussions of mental causation are couched in terms of the causal efficacy of mental properties, while discussions of supervenience often proceed by way of a claim that one family of properties (e.g., mental properties) is supervenient on some other family of properties (e.g., physical properties). But the resurgence of interest in properties has left us with widely varying accounts of their nature, and questions about their existence have by no means disappeared.
Properties are as Properties Do
It is possible to classify theories of properties in terms of their characterizations of the nature of properties or in terms of the jobs they introduce properties to do. The former kind of characterization is more fundamental, but since views about the nature of properties are typically motivated by accounts of the work properties are invoked to do, it will be more useful to begin with the latter. We will ask what explanatory roles properties have been introduced to fill, and we will then try to determine what something would have to be like in order to occupy those roles. This will also allow us to consider the sorts of arguments that are typically advanced for the claim that properties exist.
1.2 Talking about Properties
Philosophers do not have a settled idiom for talking about properties. Often they make do with a simple distinction between singular terms and predicates. Singular terms are words and phrases (like proper names and definite descriptions) that can occupy subject positions in sentences and that purport to denote or refer to a single thing. Examples include 'Bill Clinton,' 'Chicago', and 'The first female Supreme Court Justice'. Predicates, by contrast, can be true of things. When we represent a sentence like 'Quine is a philosopher' in a standard formal language (like first-order logic) as 'Pq', we absorb the entire expression 'is a philosopher' into the predicate 'P' (though for some theoretical purposes it is more useful to count 'philosopher' or even 'a philosopher' as the predicate). The notion of a predicate is supplanted by the notion of a verb phrase in modern grammars, so we don't need to pursue this issue here, but we can raise our first question about property talk at this relatively atheoretical level.
Failed Substitutions
It is perfectly grammatical to say 'Monica is honest' or 'Honesty is a virtue', but your old English teacher will cringe if you say 'Honest is a virtue' or 'Monica is honesty'. We must use 'honest' after the 'Monica is', and we have to use the nominalization, 'honesty', before 'is a virtue'. The fact that 'honest' and 'honesty' cannot be interchanged without destroying the grammaticality of our original sentences has been thought to have various philosophical morals. Some philosophers take it to show that the two expressions cannot stand for the same thing; for example, 'honest' might stand for a property and 'honesty' might stand for a property-correlate of some sort (Frege draws roughly this moral from his discussion of 'the concept horse'). Others take it to show that although both expressions are related to the same thing, the property honesty, they are related to by different semantic relations; for example, the nominalization denotes this property, whereas the predicate expresses it.
Frege's argument for the first sort of view is not compelling (see Parsons, 1986, for a good discussion); moreover, it would be desirable to avoid multiplying entities (e.g., property correlates) and semantic relations (e.g., expression) beyond necessity. And mere failures of substitutivity are not enough to show that they are necessary, since various syntactic features of sentences prohibit the exchange of terms that are clearly co-referential. Consider case forms of personal pronouns: 'I' and 'me' cannot be exchanged (without destroying grammaticality) in sentences like 'I dropped the hammer, and he returned it to me'. But no one concludes that distinct objects (me and a me-correlate) or distinct semantic relations (nominative-case reference and accusative-case reference) are needed to account for this.
Predicative expressions
The multiplicity of ways of talking about properties can be obscured when we use familiar formal languages to represent them. The constructions verb ('lives'), verb + adverb ('sings badly'), copula + adjective ('is red'), copula + determiner + common noun ('is a dog'), copula + noun phrase ('is a Republican President), and (if Davidson's account of events is correct) even adverbs ('slowly') and prepositional phrases ('in the bathroom') all go over into the familiar 'F's and 'G's of standard logical notation. The fact that these expressions can often be handled in the same way without too much violence tells us that they have certain similarities, but there are also many differences, and some of them may turn out to be relevant to ontology.
Singular Terms
The complexities involving property words are even greater when we turn to singular terms. We can form singular terms from predicative expressions in many ways (different ways are appropriate for different predicates). To begin with, English contains a plethora of suffixes that we can append to predicative expressions (sometimes after minor surgery on the original) to form singular terms. These include '-hood' ('motherhood, 'falsehood), '-ness' ('drunkeness', 'betweeness'), '-ity' ('triangularity', 'solubility', 'stupidity'), '-kind' ('mankind'), '-ship' ('friendship', 'brinksmanship'), 'ing' ('walking', 'loving'), 'ment' ('commitment', 'judgment'), 'cy' ('decency', 'leniency'), and more.
Various philosophical terms of art serve a similar purpose. The word 'itself' plays this role in some translations of Plato ('The equal itself', 'Justice itself'), and contemporary authors use phrases like 'the property red', 'the property of being red', and 'the causal relation' to much the same end. Various gerundive phrases (e.g., 'being red' and 'being a red thing') and infinitive phrases ('to be happy', 'to be someone who is happy') work in a similar way. Finally, there are many less systematic ways of talking about properties; for example, we can use a definite description that a property just happens to satisfy ('the color of my true love's hair', 'John's favorite four-place relation').
The expressions formed in these ways occupy subject positions in sentences where they seem to denote to properties. It is worth noting, however, that it is often impossible to substitute some of these expressions for related ones without destroying the grammaticality or, in some cases, without altering the truth value of the original sentence. Consider 'wisdom', 'being wise', 'the property of being wise', and 'to be wise'. 'Wisdom is a virtue' is unexceptionable, but 'Being wise is a virtue' is shaky at best. On the other hand, 'To be wise is to be virtuous' and 'Being wise is a good thing' are fine, but 'Wisdom is to be virtuous' clearly won't do. And 'The property of being wise is a good thing' is grammatical, but has a different meaning from 'Being wise is a good thing'.
The phenomenon of case shows that lack of substitutivity alone doesn't have deep ontological consequences, but it is quite possible that the sorts of phenomena noted in the previous paragraph signal important differences in ontology. Some of these differences might begin to emerge from informal probing, but we cannot expect to settle such matters without detailed, philosophically-sensitive syntactic and semantic theories that are better supported than their rivals. Such theories do not yet exist, and so here I will be fairly cavalier about "property terms," using various phrases, e.g., 'redness' and 'the property of being red' indifferently to refer to the same property. But this expedient is not meant to suggest that subtle grammatical differences won't eventually turn out to have important ontological implications.
2. Philosophical Explanations: Why Think that Properties Exist?
2.1 Explanation in Ontology
Properties are typically introduced to help explain or account for phenomena of philosophical interest. The existence of properties, we are told, would explain qualitative recurrence or help account for our ability to agree about the instances of general terms like 'red'. In the terminologies of bygone eras, properties save the phenomena; they afford a fundamentum in re for things like the applicability of general terms. Nowadays philosophers make a similar point when they argue that some phenomenon holds because of or in virtue of this or that property, that a property is its foundation or ground for it, or that a property is the truth maker for a sentence about it. These expressions signify explanations.
When properties are introduced to help explain certain philosophically puzzling phenomena, we have a principled way to learn what properties are like: since they are invoked to play certain explanatory roles, we can ask what they would have to be like in order to play the roles they are introduced to fill. What, for example, would their existence or identity conditions need to be for them to explain the (putative) modal features of natural laws or the a priori status of mathematical truths?
The Limits of Explanation
Perhaps the deepest question in ontology is when (if ever) it is legitimate to postulate the existence of entities (like possible worlds, facts, or properties) that are not evident in experience. Some philosophers insist that it never is. Others urge that at least some entities of this sort, in particular properties, have no explanatory power and that appeals to them are vacuous or otherwise illegitimate (e.g., Quine, 1961, p. 10; Quinton 1973, p. 295).
The more heavy-handed dismissals of properties and other metaphysical creatures have often been based on faulty accounts of concept formation (which led Hume to counsel consignment of metaphysical works to the flames) or defective theories of meaning (which led many positivists to view metaphysics as a series of pseudo explanations offered to solve pseudo problems). Wittgenstein takes a more subtle approach, trying to show us that 'our disease is one of wanting explanations' (1991, Pt VI, 31) and striving to cure us of it. Swoyer (1999) has attempted some defense of explanation by postulation in ontology, but the issues are difficult ones that are not amenable to proof or disproof. Fortunately the present task is not to defend explanation in ontology, but it will be useful to briefly note two general views about such explanations.
Two Views of Explanation in Ontology
Metaphysics has traditionally been viewed as first philosophy, and some philosophers hold that its arguments should be demonstrative. Recently Linsky & Zalta (1995) have argued that it is possible to give a transcendental argument for the existence of properties; if this argument is successful, it is demonstrative, and they claim that its conclusion (that a wide range of properties exist) is synthetic a priori. Others (e.g., Swoyer, 1983; 1999) urge that most of the arguments advanced on behalf of properties appear anemic when judged by the demonstrative ideal, but that they look much better when viewed as inferences to the best explanations. We will not pursue this issue, however, since it is impossible to form a satisfactory view about the nature of philosophical explanations in a vacuum. An account of metaphysical explanation should instead emerge from a consideration of the more plausible metaphysical explanations, and we will focus on such explanations here.
2.2 Constraints on Explanations Employing Properties
Parochial Constraints
Philosophical explanations are usually thought to be constrained in various ways, but beyond philosophical family values like consistency, parsimony and comprehensiveness these constraints will often seem parochial to those philosophers who are not committed to them. In Medieval disputations about universals, for example, religion and theology were fundamental, and it was widely held that any account of properties should be able to explain the Trinity, the Eucharist, and the absolutely unchanging nature of God (this last requirement often led to quite tortured accounts of the relations holding between protean finite beings and God). But few philosophers in our naturalistic era would give such considerations a second thought.
More General Constraints
Some proposed constraints on metaphysical explanation depend on more general philosophical orientations. For example, Russell's Principle of Acquaintance, the injunction that we only admit items into our ontology if we are directly acquainted with them, expresses an strong empiricist sentiment. Other constraints are more directly metaphysical. For example, Aristotle upbraids Plato for separating the Forms from their instances, suggesting that this renders them incapable of explaining anything (e.g., Metaphysics,1079b11-1080a10). His point seems to be that properties could explain things about individuals only if they were located in those individuals. The sentiment is that an individual, spatio-temporal object (like my cat) which stands in some obscure relation to some entity entirely outside of space and time (say the Form of the cat) cannot explain anything about the cat itself.
Mandatory Constraints
All accounts of properties must avoid various perennial objections to them. Three criticisms of this sort were anticipated by Plato (worrying about his own doctrines) in the Parmenides.
First, it appears that a universal property can be in two completely different places (i.e., in two different instances) at the same time, but ordinary things can never be separated from themselves in this way. There are scattered individuals (like the former British Empire), but they have different spatial parts in different places. Properties, by contrast, do not seem to have spatial parts; indeed, they are sometimes said to be wholly-present in each of their instances. But how could a single thing be wholly present in widely separated locations?
This conundrum has worried some philosophers so much that they have opted for an ontology of tropes in order to avoid it, but realists have two lines of reply (both of which commit us to fairly definite views about the nature of properties). One response is that properties are not located in their instances (or anywhere else), so they are never located in two places at once. The other response is that this objection wrongly judges properties by standards that are only appropriate for individuals. Properties are a very different sort of entity, and they can exist in more than one place at the same time without needing spatial parts to do so.
Second, some properties seem to exemplify themselves. For example, if properties are abstract objects, then the property of being abstract should itself exemplify the property of being abstract. In various passages throughout his dialogues Plato appears to hold that Forms (which are often taken to be his version of properties) participate in themselves. Indeed, this claim serves as a premise in what is known as his Third-Man Argument which, he seems to think, may show that the very notion of a Form is incoherent (Parmenides, 132ff). Russell's paradox raises more serious worries about self-exemplification. It shows that any account which allows properties to exemplify themselves must be carefully formulated if it is to avoid paradox (a polite word for inconsistency).
Third, many critics have charged that properties generate vicious regresses, e.g., the one exhibited in Plato's third man argument or Bradley's regress, and any viable account of properties must have the resources to avoid them.
The disputes about plausible constraints on property-invoking explanations, together with the obvious difficulty of settling such disputes, leave the situation murkier than we would wish. We will see that the use of properties to explain phenomena in the philosophy of mathematics or naturalistic ontology or the semantics of natural languages imposes additional, tighter, constraints that make it easier to evaluate competing accounts. But constraints of the sort noted here have played a central role in many philosophical discussions of properties, and we will often fail to understand those discussions if we forget this.
2.3 The Fundamental Ontological Tradeoff
Metaphysics, like life, is full of tradeoffs, cost-benefit analyses, the attempt to simultaneously satisfy competing constraints. In ontology we must frequently weigh tradeoffs between various desiderata, e.g., between simplicity and comprehensiveness, and even between different kinds of simplicity. But one tradeoff is so pervasive that it deserves a name, and I will call it the fundamental ontological tradeoff. The fundamental ontological tradeoff reflects the perennial tension between explanatory power and epistemic risk, between a rich, lavish ontology that promises to explain a great deal and a more modest ontology that promises epistemological security. The more machinery we postulate, the more we might hope to explain — but the harder it is to believe in the existence of all the machinery.
The dialectic between a realism with chutzpah and a diffident empiricism runs all through philosophy, from ethics to philosophy of science to philosophy of mathematics to metaphysics. Excessive versions of each view are usually unappealing. Extreme realists ask us to believe in things many philosophers find it difficult to believe in; extreme empiricists wind up unable to explain much of anything. But the dialectic between power and risk remains even when we move in from the extremes. It often manifests itself in a yearning for parsimony, a desire for as few entities as we can scrimp by with. Such longings may seem prudish or stuffy or a bit too metaphysically correct. Often the desire is not to achieve parsimony for its own sake, however, but to find an ontology that is modest enough to provide a measure of epistemological security. Choices needn't be all or none, and a principled middle ground is always worth striving for. But no matter where a philosopher tries to stake her claim, the fundamental ontological tradeoff can rarely be avoided and we will encounter it frequently in what follows.
3. Traditional Explanations: An Unscientific Survey
Properties have been invoked to explain a very wide range of phenomena. The things to be explained (explananda; singular explanandum) are a mixed bag, and the explanations vary greatly in plausibility. To fix ideas, we will note several of the most common explanations philosophers have asked properties to provide (for a longer list see Swoyer, 1999, §3).
3.1 Resemblance and Recurrence
There are objective similarities or groupings in the world. Some things are alike in certain ways. They have the same color or shape or size; they are protons or lemons or central processing units. A puzzle, sometimes called the problem of the One over the Many, asks for an account of this. Possession of a common property (e.g., a given shade of yellow) or a common constellation of properties (e.g., those essential to lemons) has often been cited to explain such resemblance. Similarly, different groups of things, e.g., Bill and Hillary, George and Barbara, can be related in similar ways, and the postulation of a relation (here being married to) that each pair jointly instantiates is often cited to explain this similarity. Finally, having different properties, e.g., different colors, is often said to explain qualitative differences. A desire to explain qualitative similarity and qualitative difference has been a traditional motivation for realism with respect to universals, and it continues to motivate many realists today (e.g., Armstrong, 1984, p 250; Butchvarov, 1966; Aaron, 1967, ch. 9).
3.2 Recognition of New and Novel Instances
Many organisms easily recognize and classify newly encountered objects as yellow or round or lemons or rocks, they can recognize that one new thing is larger than a second, and so on. Some philosophers have urged that this ability is based partly on the fact that the novel instances have a property that the organism has encountered before — the old and new cases share a common property — and that the creature is somehow attuned to recognize it.
3.3 Meaning
Our ability to use general terms (like 'yellow, 'lemon', 'heavier than', 'between') provides a linguistic counterpart to the epistemological phenomenon of recognition and to the metaphysical problem of the One over the Many. Most general terms apply to some things but not to others, and in many cases competent speakers have little trouble knowing when they apply and when they do not. Philosophers have often argued that possession of a common property (like redness), together with certain linguistic conventions, explains why general terms apply to the things that they do. For example Plato noted that 'we are in the habit of postulating one unique Form for each plurality of objects to which we apply a common name' (Republic, 596A; see also Phaedo 78e, Timaeus, 52a, Parmenides, 13; Russell, Problems of Philosophy, p. 93). Questions about the meanings (now often known as the 'semantic values') of singular terms like 'honesty' and 'hunger' and 'being in love' may be even more pressing, since the chief task of such terms seems to be to refer to things. But what could a word like 'honesty' refer to? If there are properties, it could refer to the property honesty.
3.4 Unification and Triangulation
In a brilliant paper on Plato's theory of Forms (which, as noted above, are often taken to be his version of properties), the classicist H. F. Cherniss (1936) argues that Plato intended his theory to solve three fundamental philosophical problems. By the end of the fifth century B.C. the arguments and conundrums of philosophers had cast doubt on several things that Plato thought were obviously true. In ethics Protagorean relativism threatened the view that ethical principles could be objective; in the clamor of individual disagreements, clashes between cultures, and the failure of philosophical inquiry to locate any firm ground, the challenge was to explain how ethical objectivity was possible. When Plato turned to epistemology, various considerations convinced him that there was an important difference between knowledge (episteme) and belief (doxa), even between knowledge and true belief (right opinion). But how could we explain that? Finally, in metaphysics it seemed clear that things change in various ways, but the arguments of Parmenides made even this seem mysterious.
Plato drew on his Forms to explain how these three phenomena were possible. On his view, the Forms exist pure and unadulterated by human thought, and some Forms, most prominently the Good, offer objective standards for values like goodness and justice. In epistemology Plato attempted to explain the difference between knowledge and belief by arguing that Forms are the objects of the former but not the latter (e.g., Timaeus, 51d3ff). In metaphysics Plato argued that change is only possible against a background of things that do not change, and he urged that the Forms provided this (Cratylus, 439d3ff). Finally, although Cherniss doesn't mention it, Plato's theory of Forms helped explain the semantics of general terms (as suggested in Republic, 596A).
This isn't to say that all, or indeed any, of Plato's explanations were successful. But it is worth noting that many philosophers still invoke properties to account for the sorts of things Plato struggled to explain. Early in this century G. E. Moore offered an alternative to ethical naturalism by claiming that goodness is a simple, non-natural property. Few contemporary philosophers would accept Moore's anti-naturalism or his account of non-natural properties, but many would defend ethical naturalism by arguing that moral properties supervene on naturalistically respectable properties.
Virtually no philosophers accept Plato's account of the difference between knowledge and belief, but many still hold that properties have an important role to play in explaining epistemological phenomena. For example, Russell (1912, ch. 10) argued that the only way to explain the possibility of a priori knowledge is to regard it as knowledge of relations among universals . Most philosophers today would question this, but many of them would agree that properties have an important role to play in explaining such epistemological phenomena as our ability to recognize and categorize things in the world around us.
Few contemporary philosophers would endorse Plato's claims about the need for some permanent backdrop for flux, but properties can still be cited to explain change. If my pet chameleon was brown all over yesterday and is green all over today, then the brute existence of the creature isn't enough to explain the change; after all, he persisted throughout. But, some philosophers urge, we can explain the alteration by noting that the chameleon exemplified the property brownness yesterday but he exemplifies the property greenness today.
Finally, many philosophers would concur that Plato's account of the meanings of general terms was on the right track, though as we shall see in §4.2, current accounts of meaning have moved far beyond Plato's in their detail and formal sophistication.
Explanation by Unification
This brief survey of putative explanations that rely on properties isn't meant to be detailed or exhaustive; the point is simply to illustrate how a range of accounts employ properties in an effort to explain philosophically puzzling phenomena. Just as importantly, Plato's account suggests an attractive model for philosophical explanation. A general pattern of explanation by unification, integration or systematization is at work in his attempt to solve three, superficially disparate, problems using the same resources. He attempts to show that at a fundamental level the three phenomena are related, linked by the Forms and the principles than govern them. This unification has explanatory value, since it allows us to see a single pattern or entity at work in a range of superficially diverse cases. At all events, this is one explanatory virtue in the natural sciences, clearly at work in the work of Newton and Maxwell and Darwin, and it is also a pattern we find in Plato's account.
An account that employs properties to do multiple tasks has two further virtues. First, insofar as each of the explanations is plausible, it serves as part of a cumulative case for the existence of properties. Second, if properties can perform multiple tasks, they must simultaneously satisfy multiple constraints, and so different sorts of data can be used to test a theory of properties. The hope is that by considering several tasks of this sort we could begin to triangulate in on the nature of properties; we could begin to see what features properties would need to have in order to play each of the different explanatory roles. It may turn out, of course, that entities well-suited to one explanatory role will be ill-suited to another. For example, we will see below that the existence and identity conditions of entities used to account for causation may be rather different from those needed by entities that could serve as the meanings of intentional idioms (like 'is thinking of Vienna'). This might lead us to postulate the existence of several kinds of properties; alternatively, it might lead us to conclude that properties cannot do all of the things philosophers has hoped that they could. Either way, as fragmentation increases, cumulative support and triangulation on the nature of properties will slip away.
4. What have you done for us lately? Recent Explanations
Properties alone cannot explain much of anything. A theory of properties — an account that tells us what properties are like and how they do what they are invoked to do — is required for that. A number of theories of properties have been developed over the last quarter century, and many of them possess much more depth, sophistication, and formal detail than the no-frills accounts alluded to in the previous section. I will focus on explanations in three areas where properties are often invoked today: philosophy of mathematics, semantics (the theory of meaning), and naturalistic ontology. These areas are also useful to consider, because if properties can explain things of interest to philosophers who don't specialize in metaphysics, things like mathematical truth or the nature of natural laws, then properties will seem more interesting. Unlike the substantial forms derided by early modern philosophers as dormitive virtues, properties will pay their way by doing interesting and important work.
My aim is to indicate the general lay of the land and point the way to more detailed discussions that interested readers can follow up. In each of the three cases I will indicate:
1. What is to be explained. As with most things in philosophy, there is often some controversy over which things in a given area stand in need of philosophical explanation. In some cases a few philosophers question the very existence of the things that other philosophers think require explanation; for example, able philosophers have denied that there are such things as mathematical truth (e.g., Field, 1980) or laws of nature (e.g., van Fraassen, 1989). And even those philosophers who think that we need to explain certain things, e.g., various features of mathematical truth, may disagree about precisely what those features are. In the three areas examined in this section, however, there is a reasonable degree of consensus about which things stand in need of explanation, and I will focus on these.
2. How properties explain. In some cases different philosophers use properties in different ways to explain the same phenomenon. I will focus on the simpler, more common approaches. We will also see that in most cases a theory of properties only explains things when it is conjoined with various background assumptions or auxiliary hypotheses.
3. Beating the competition. Arguments that properties exist because they explain some particular phenomenon (like qualitative recurrence or mathematical truth) are weak if other sorts of entities can account for it just as well. Arguments that alternative accounts don't work, especially when they involve alternative putative entities (like sets or tropes), are typically based on the claim that these entities lack the requisite features to account for the explanandum. I will also note a few cases where proponents of one account of properties argue against proponents of a rival account, since these arguments typically involve disputes over the nature of properties.
4. Difficulties. Almost all explanations that employ properties face difficulties, and I will briefly indicate the most serious of these.
5. Lessons the explanations teach us about properties. Properties often must have certain features in order to provide certain explanations. So once we have examined a given explanation, we will ask what properties would have to be like in order to provide it. In particular, we will ask what lessons are to be learned about the existence and identity conditions of properties, their structure (if any), and their modal and epistemic status.
4.1 Mathematics
Philosophers of mathematics have focused much (arguably too much) of their attention on number theory (arithmetic). Number theory is just the theory of the natural numbers, 0, 1, 2, ..., and the familiar operations (like addition and multiplication) on them. Many sentences of arithmetic, e.g., '7 + 5 = 12' certainly seem to be true, but such truths present various philosophical puzzles and philosophers have tried to explain how they could have the features they seem to have.
Explananda in Philosophy of Mathematics
Most wish lists include hopes for explanations of at least five (putative) facts; philosophers want to know:
1. How the sentences of arithmetic can have truth values (how they can be true or false)
2. How the sentences of arithmetic can be objectively true (or false), independently of human language and thought
3. What the logical forms of the sentences of arithmetic are
4. How the sentences of arithmetic can be necessarily true (or necessarily false)
5. How the truth values of sentences of arithmetic can be known independently of experience (a priori), save for a modicum of experience needed to acquire mathematical concepts
Sample Explanations
Identificationism
Most attempts to use properties to explain the items on this list are versions of identificationism, the reductionist strategy that identifies numbers with things that initially seem to be different. This approach is familiar from the original versions of identificationism where numbers were identified with sets, but it is straightforward to adapt this earlier work to identify numbers with properties rather than with sets.
Properties vs. Sets
Sets are often contrasted with properties, and before proceeding it is important to note a fundamental difference between the two. If x and y are sets and have exactly the same members, then x and y are one and the same set. When x and y have precisely the same members they are said to have the same extension, and sets are often called extensional entities. Just as sets can have members, properties can have instances, things that exemplify or instantiate them, and this relation of exemplification is to properties what the membership relation is to sets.
The identity conditions of properties are a matter of dispute. Everyone who believes there are properties at all, however, agrees that numerically distinct properties can have exactly the same instances without being identical. Even if it turns out that exactly the same things exemplify a given shade of green and circularity, these two properties are still distinct. For this reason properties are often said to be intensional entities, although people often concur with this because they agree about what properties' identity conditions are not (they aren't extensional), rather than because they agree about what their identity conditions are.
The ABCs of identificationism
If we have a rich enough theory of properties, it is possible to retrace the steps of earlier versions of identificationism using properties in place of sets. The property theorist can formulate axioms for property theory that parallel the axioms of standard set theories (save for replacing the axiom of extensionality with some other identity condition, perhaps omitting the axiom of foundations, and making other minor emendations to adapt the ideas better to properties; e.g., Jubien, 1989; cf. Bealer, 1982, Ch. 6; Pollard and Martin, 1986).
There are infinitely many natural numbers (the collection of natural numbers in fact has the smallest size an infinite collection can have), so the first step in identificationist programs is to find (or postulate, or imagine) an infinite realm of properties. The next step is to identify one denizen of this realm with the number zero and to identify some operation on this realm of entities with the successor function. The key here is that successive iterations of the function yield a new and different entity every time it's applied.
There are two major species of identificationism. The first views the reducing theory (of sets, or of properties) as a branch of logic; the second views it as a substantive theory (of sets, or of properties) that makes commitments over and above those made by logic. There are important differences between the two approaches, but given the very strong nature of the logic required for logicist identificationism, the differences do not matter greatly here so I will treat both approaches together. (For a discussion of the differences, see Section 1 ("Logicist Identificationism") of the supplementary document Uses of Properties in the Philosophy of Mathematics.)
Identificationist accounts treat '1' and '2' as singular terms that refer to properties (those properties that are identified as the numbers 1 and 2), and they treat predicates and function symbols as denoting relations and functions. Thus, since the semantics values of '1' and '2' are in the extension of the relation expressed by the predicate '
--
You Really Look Marvelous Today!
Yours True Liars,
SoundaryaNayaki സൌണ്ടാര്യനായകി சௌந்தர்யநாயகி
Anna Justin അണ്ണാ ജസ്റിന് அன்னா ஜஸ்டின்
We are the perfect liars; don't try to find any truth in our words!
"He looked at her as a man looks at a faded flower he has gathered, with difficulty recognizing in it the beauty for which he picked and ruined it!"
Why can't you be the King/Queen of Justice?
.
What 'your' answers to these questions?
1. Should the people who could not even identify and list the properties exhibited by everyone and everything be honored with degrees and diplomas?
2. Should the degrees and diplomas awarded by universities and institutions which could not even identify and list the properties exhibited by everyone and everything be honored?
3. Should the people who ask the question, "what properties are exhibited by everyone and everything?" be condemned and punished?
You can find the list of properties exhibited by everyone and everything here [ http://the.secret.angelfire.com/intelligence.pdf ] Note that the document is sharply worded. Do not be offended!
-
With malice toward none;
With charity for all;
With firmness toward right,
Shine with justice and truth!
Bloom forever, O beloved fellow men and woman,
From the dust of my bosom!
-
No one is hurt by doing the right thing!
-
Why Math has been hated by some? Because it requires them to think and forces them to give the correct and exact value. Because it has a clear distinction of right and wrong. Most people love to speak about any issue but hate to accept that they're wrong. That's the beauty of Math. Right is right and wrong is wrong.
--
The secret behind getting right answer from nature lies in putting right questions to her!
--
SIVASHANMUGAM'S INCLUSION PRINCIPLE (SIP) STATES THAT NO TWO THINGS CAN BE WITHOUT A COMMON PROPERTY.
--
No comments:
Post a Comment
Set all books on fire because no knowledge in them can be repeated and no knowledge in them should be repeated. Do not listen to your teachers or pastors, or mom and dad because none of their knowledge can be repeated and none of their knowledge should be repeated. But, do not forget to buy our books because we need your money. Do not forget to send your children to our schools and colleges, because we need your money. Listen to us, because we want you and your children to be our employees, slaves.