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Objects are, in the first instance, just what are ordinarily called “objects”—tables, chairs, rocks, planets, stars, and human and animal bodies, among innumerable other things. Physicists sometimes talk further about “unobservable” objects, such as molecules, atoms, and subatomic particles; and psychologists have posited unobservable objects such as drives, instincts, memory traces, egos, and superegos. All of these are objects in the philosophical sense. Particularly problematic examples, to be discussed below, are “apparent” objects such as pains, tickles, and mental images. Abstract and concrete

Most objects one thinks of are located somewhere in space and time. Philosophers call anything that is potentially located in space and time “concrete.” Some apparent objects, however, seem to be neither in space nor in time. There exists, after all, a positive square root of nine, namely, the number three; by contrast, the positive square root of -1 does not exist. But the square root of nine is not located in any particular part of space. It seems to exist outside of time entirely, neither coming into existence nor passing out of it. Objects of this sort are called “abstract.”

Some mental phenomena are straightforwardly abstract—for example, the thoughts and beliefs that are shared between the present-day citizens of Beijing and the citizens of ancient Athens. But other mental phenomena are especially puzzling in this regard. For example, Brutus might have had regretful thoughts after stabbing Julius Caesar, and these thoughts might have caused him to blush. But precisely where did these regretful thoughts occur so that they could have had this effect? Does it even make sense to say they occurred at a point one millimeter away from Brutus’s hypothalamus? Sensations are even more peculiar, since they often seem to be located in very specific places, as when one feels a pain in one’s left forearm. But, as occurs in the case of phantom limb syndrome, one could have such a pain without actually having a forearm. And mental images seem downright paradoxicaclass="underline" people with vivid visual imaginations may report having images of a cow jumping over the Moon, for example, but no one supposes that there is an actual image of this sort in anyone’s brain. Properties and relations

Objects seem to have properties: a tennis ball is spherical and fuzzy; a billiard ball is spherical and smooth. To a first approximation, a property can be thought of as the thing named by that part of a simple sentence that is left over when the subject of the sentence is omitted; thus, the property expressed by is spherical (or the property of sphericality, or being spherical) is obtained by omitting a tennis ball from A tennis ball is spherical. As these examples show, a property such as sphericality can be shared by many different objects (for this reason, properties have traditionally been called universals). Mental properties, such as being conscious and being in pain, can obviously be shared by many people and animals—and, much more controversially, perhaps also by machines.

Relations are what is expressed by what is left when not only the subject but also the direct and indirect object (or objects) of a sentence are omitted. Thus, the relation of kissing is obtained by omitting both Mary and John from Mary kissed John; and the relation of giving is obtained by omitting Eve, Adam, and an apple from Eve gave Adam an apple. Likewise, the relation of understanding is obtained by omitting both Mary and that John is depressed from Mary understands that John is depressed. In this case the object that Mary understands is often called a thought (see below Thoughts and propositions).

Properties and relations are often spoken of as being “instantiated” by the things that have them: a ball instantiates sphericality; the trio of Eve, Adam, and the apple instantiates the relation of giving. A difficult question over which philosophers disagree is whether properties and relations can exist even if they are completely uninstantiated. Is there a property of being a unicorn, a property of being a round square, or a relation of “being the reincarnation of”? This question will be left open here, since there is widespread disagreement about it. In general, however, one should not simply assume without argument that an uninstantiated property or relation exists. States and events

States consist simply of objects having properties or standing in relations to other objects. For example, Caesar’s mental state of being conscious presumably ended with the event of his death. An event consists of objects’ losing or acquiring various properties and relations; thus, Caesar’s death was an event that consisted of his losing the property of being alive, and John’s seeing Mary is an event that consists of John’s and Mary’s coming to stand in the relation of seeing. Thoughts and attitudes Thoughts and propositions

It was noted above that understanding is a relation that someone can bear to a thought. But what sort of thing is a thought? This is a topic of enormous controversy, but one can begin to get a grasp of it by noticing that thoughts are typically referred to, or expressed by, sentential complements, or clauses beginning with that. Thus, one may have the thought that Venus is uninhabitable or the thought that 26 + 26 = 52. (There are, of course, other ways of expressing thoughts—a mere gesture can suffice—but it will be useful to take “that” clauses to be standard.) That a thought is different from the sentence that expresses it is entailed by the fact that different sentences can express the same thought: the thought expressed by Snow is white is also expressed in German by Der Schnee ist weiss and in French by La neige est blanche. Indeed, thoughts are often taken to be the meanings of sentences, in which case they are called “propositions.” (Meaning is an enormously controversial topic in its own right; see semantics and philosophy of language.) Types and tokens

Thoughts regarded as propositions are clearly shareable. Two people can have the same thought—e.g., that snow is white. But thoughts in this sense must be distinguished from the individual thoughts that people have at particular times, which are not shareable, even if they may be expressed by the same sentences. In this sense, different people may have their own particular thoughts that snow is white.

This ambiguity also arises in the case of language. One can, for example, write “the same word” twice, once on a blackboard and once on a piece of paper. When philosophers want to talk about words (or sentences or books) that are located in specific places for specific periods of time, they use the term tokens of the word (or sentence or book); when they want to talk about words (or sentences or books) that can appear in different places and times, they use the term types of word (or sentence or book). In the terminology introduced above, one can say that word tokens are concrete and word types are abstract—indeed, word types can be regarded as simply the set of all word tokens that are spelled the same. (Notice that word tokens need not be written down; many of them might merely be pronounced, and others might be encoded on magnetic discs, for example.) In an analogous fashion, philosophers often also distinguish between tokens and types of thoughts: two people may have different tokens of the same type of thought, that snow is white. Concepts

To a first approximation, concepts are constituents of thoughts or propositions in much the same way that words are constituents of the sentential complements by which thoughts or propositions are expressed. Thus, someone who thinks that Venus is uninhabitable has the concept of Venus and the concept of being uninhabitable. Concepts are obviously subject to the type-token distinction, which enables one to understand otherwise peculiar sentences such as John’s concept of God is different from Mary’s. It could be that John and Mary are both having thoughts involving the type-concept God but that John’s token-concept involves connections to beliefs that are different from the beliefs to which Mary’s token-concept is connected (e.g., John might think that God loves all human beings, and Mary might think that he is more selective).