Is the statement "a basketball is a physical object" a contradiction?

Question

All of us would presumably agree that the statement "the basketball on Fred's table is a physical object" is true, assuming that there's a basketball on Fred's table. This statement is about a specific basketball that actually exists in the physical world.

And all of us would presumably agree that the statement "a basketball is a physical object" is also true. This second statement is about a non-specific basketball that doesn't actually exist in the physical world. (If it does exist in the physical world, then where is it?)

Therefore, this second statement says that an object that doesn't exist in the physical world exists in the physical world, which is a contradiction. Where have I gone wrong?

Answer 1

A basketball is a physical object

translates into

ALL basketballs are physical objects

translates into

IF something is a basketball, THEN it is a physical object

This is equivalent to

IF something is not a physical object, THEN it is not a basketball

In other words, the initial statement is not about any particular (physical) object. The statement does not refer to any particular physical object that you would be able to name or point to (as in "That is my red basketball"). But this does not imply that therefore it refers to "a non-specific object".

You can interpret "a basketball" as indicating a "non-specific" (non-physical) abstract object, which could be, for instance, the platonic Ideal Basketball, or the concept of Basketball, or the set of all basketballs. Read in that way, the statement says

The set of all basketballs is a subset of the set of all physical objects.

So it still does not say that that set (or that platonic form, that abstract object) itself is a physical object. Linguistically the statements

That basketball is a physical object

and

A basketball is a physical object

show the same superficial schema "___ is a physical object". But the logic underneath these statements is very different. The first one uses "is a ..." to indicate set-membership (a relation between a member of a set and the set), while the second uses "is a ..." to indicate a subset-relation (a relation between two sets). Natural language is in this case not vague, but ambiguous, and this ambiguity can cause confusion.

Answer 2

Where you have gone wrong is that you have inappropriately interpreted a statement in colloquial English. When a construction of the sort 'a noun verb' is used in English, the noun is not usually taken to refer to the word itself or to an abstraction. Consider, for example:

A broken slate can be the cause of a leaking roof.

A late train can be an intolerable nuisance.

A jaguar can run faster than a hamster.

A thorn punctured my space hopper.

In the last example, a thorn referred to a specific thorn. In the other three, the noun referred to broken slates, late trains and jaguars in general. In that light your statement about a basketball makes perfect sense.

Answer 3

You ask:

Is the statement "a basketball is a physical object" a contradiction?

At first glance, yes, but we can eliminate the contradiction by pointing out a distinction that has been argued about for more the 2,500 years. By adopting language to deal with universals and particulars we can eliminate the paradox that our intuitions tell us exists. (The physical basketball is a "particular" of the idea or concept of a physical basketball, itself the "universal".) Hang on to your hat for some philosophical jargon from the philosophy of language.

Your first example is a correspondent truth. We accept that there exists a physical object, and that the language corresponds or refers to the object. In the language of Frege and his ideas of Sinn und Bedeutung, in modern philosophy of language, we would say that the token 'basketball' refers to the referent, physical basketball in the world. That is, the reference is more or less the correspondent truth that aligns language, to borrow from Wittgenstein, to the state of affairs in the world. We might refer to that basketball as an extension.

The second example is a little more complicated and controversial, but Frege used the term sense and while there is quibbling over the details in the literature, the sense might be thought of as the idea or concept of a thing, or a collection of its properties that form the intension. Rather than something physical, it refers to the properties that inhere to what we are "pointing at" with the word. It refers to an abstractum. We can think of this as Aristotelian essence if it helps, though again, things can become controversial. Is it a contradiction to refer to an idea as physical?

No, if you understand that a physical basketball (a particular) is abstracted towards a category represented by 'physical basketball', a piece of language that denotes a collection of things with the same property (a universal). Historically in philosophy, whether or not the latter thing exists is known as the problem of universals. Note that we can resolve the apparent paradox by separating our tokens by representing one token without delimiters and the other with:

A 'physical basketball' is a phrase that represents a physical basketball in the world.

This resolves the contradiction by pointing out that sometimes in language, we use language to mention things ('physical basketball'), and sometimes we are using the language (physical things), and is called use-mention distinction. This distinction also helps to resolve the traditional debate between Platonists who were realist and argued that the mention was somehow real and nominalists who argued the mention was just language, obviously in favor of the nominalists. The failure to recognize use-mention distinction can often lead to woo or hilarity as the late Dennett points out in his video on deepities (YT).

So, like many paradoxes, when we create a framework of language to address some fine distinctions, we dissolve it and are left with an important philosophical distinction. You'll come across different views regarding this issue over the history of philosophy, and many have restated the problem in different ways. Ogden and Richards in their Meaning of Meaning, for example, extend Frege's thinking using the terms 'symbol', 'reference', and 'referent'. And the infamous Quine addressed the issue and took a unique ontological stance too while introducing the terminology 'ontological commitment' which is handy in discussing these matters. For more terminology that is useful, also read WP's "De dicto and de re".

Answer 4

In Kantian terms the statement "a basketball is a physical object" is an assertion of 'mere' position: the notion is posited that the basketball (concept) has the predicate of having physical form. It is still only an idea, the essence, in this case with 'physicality' as an attribute. In Kant's terms, the copula of a judgement: a basketball is physical.

In contrast, the basketball on Fred's table as say, acknowledged by Fred, has 'absolute' position because Fred handled the so-called basketball and is now pretty sure about it so he thinks the basketball exists. The possibility combined with perception results in actuality.

In either case the basketball is no different. For Kant, existence is not a predicate of the basketball. The existence of the basketball is in Fred's mind. Same situation in Kant's famous $100 phrase:-

the actual contains nothing more than the merely possible. A hundred actual dollars do not contain the least bit more than a hundred possible ones. – Critique of Pure Reason, B627.

This remains the case in modern phenomenology although focus also moves onto the existence of Fred and his mind, which is a different order of existence hence 'the ontological difference'.

Heidegger clarifies the Kantian position in The Basic Problems of Phenomenology, page 40.

In the proposition "A exists," "A is extant," an absolute positing is involved. Being qua existence must not be confused with being in the sense of "mere position" (being something). Whereas in the Beweisgrund (p. 77) Kant characterizes existence as absolute position, he says in the Critique: "It is merely the position of a thing, or of certain determinations in themselves. In logical use it is merely the copula of a judgment."¹⁹

19. Critique of Pure Reason, B626.

The preliminary interpretation of being as "mere position" and of exis­tence as "absolute position" should be kept in mind.  . . .   the mere what of a thing, is posited in the pure representing of the thing as in a certain way in itself. But this positing is merely the positing of the possible, "mere position." In one place Kant says that "as possibility was . . . merely a position of the thing in relation to the understanding, so actuality [existence] is at the same time a combining of it [the thing] with perception."²⁰ Actuality, existence, is absolute position; possibility, in contrast, is mere position.

20. Ibid., B287 n.; see also Beweisgrund, p. 79.

Answer 5

You could look at the theory of word meaning - semantics. One way to look at it is via extensions, useful if you want to work in a formal setting, e.g. use a formal logic. Extension just means all the exemplars of a concept, in this case basketballs. Now you can, as in @Jo Wehler's answer, quantify over all the exemplars.

But many concepts are vague. E.g., there probably is a definition of 'Basketball', say from the NBA, but in practice, it still is used vaguely. Else we'd have true sentences like "before 1955,..." (suppose it was defined then) "...Basketballers mostly didn't use Basketballs". Which sounds unituitive. How about two definitions, Basketball_pre55 and Basketball_post55? But then, we may find, the definition had been accepted in Europe only in 1960, leading to more and more definitions. Strictly demarcating concepts seems, in general, too hard.

You can eschew the extension concept and adopt other, "intensional" semantic ideas, for example, that word meaning is generally learned (as in: learning to cook), thus explaining why it might be hard to concretely specify extensions. Your cooking style might slightly differ from mine. In this case, however, semantic meaning becomes something of a "base layer" of argumentation, since it's hard to dispute someone's (subjective) "feeling" of a word's meaning. In this case, one has to start with "surely, you would call something a Basketball".

Answer 6

The SEP entry that covers this topic from the quantification-theoretic perspective is the one on generic generalizations:

Generics are statements such as “tigers are striped”, “a duck lays eggs”, “the dodo is extinct”, and “ticks carry Lyme disease”. Generics express generalizations, but unlike quantified statements, generics do not carry information about how many members of the kind or category have the property. For example, if asked “how many ravens are black?” one could reply “all [or some, or most, etc.] ravens are black”, but one cannot felicitously reply with the generic “ravens are black” (Carlson 1977).

Generics have proved quite difficult to analyze semantically. For example, “dogs are mammals” seems to require for its truth that all dogs be mammals. “A tiger is striped” or “ravens are black”, however, are somewhat more forgiving, since they are compatible with the existence of a few stripeless tigers and white albino ravens. “Ducks lay eggs” and “a lion has a mane” are more forgiving still; these generics are true even though it is only the mature members of one sex that possess the relevant properties. Notice, however, that we do not accept “ducks are female”, even though every egg-laying duck is a female duck. Finally, we accept “ticks carry Lyme disease”, even though very few ticks (approximately one percent) actually have the property, while also rejecting “humans are right-handed”, when over ninety percent of humans are right-handed.

As these examples illustrate, generics are not equivalent in meaning to any of the quantifying determiners such as “all”, “some”, or “most”. They also differ in meaning from sentences containing adverbs of quantification (Lewis 1975) such as “generally”, “usually”, or “often”. For example, the generic “books are paperbacks” is false, yet the insertion of any of these adverbs of quantification would render the statement true: “books are generally/usually/often paperbacks”.

One suggestion made later in the article is introducing a special "generically" quantifier, see this section for an overview of the standard accounts.

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On another level: the concept of being physical is metaphysically ineffective. If a basketball's being a physical object generally or generically obtains, and if it does so by virtue of a property to be had by an abstract basketball, then the abstract basketball is a physical object. So either the definition of "being physical" is contradictory (since abstract objects are otherwise defined as non-physical) and hence trivial, or it is just trivial (because intrinsically vacuous, open to being stretched to accommodate any phenomena whatsoever, e.g. as with emergent-spacetime theories in physics, which are theories of physical things that contradict the declaration that abstract objects are not spatiotemporal or collapse such a declaration in such a way that "if an object is abstract, it's not physical" is negated). (Cf. the concept of a predication-theoretic trope when these are cashed out as "abstract particulars.")

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Alternatively... If, "Basketballs are physical objects," is generically true, this truth is compatible with exceptions (like, "Tigers are striped," is compatible with a few tigers that aren't striped). A basketball that's not physical is then compatible with the generic statement, though it remains to be asked whether physical objects are exemplars of an abstract property of being physical, such that their instances of the property are physical, but the property per se is non-physical. (That is, if we say, "Basketballs are physical," are we asserting a correlation between an abstract concept "being a basketball" and another abstract concept "being physical"?)

Answer 7

Your statement “a basketball is a physical object” considered as a general statement translates into

For each basketball x holds: x is a physical object.

After that translation you are in the situation of your first passage, which does not provide any ontological problem.