Other Words from ostensive ostensively adverb. Synonyms for ostensive Synonyms apparent , assumed , evident , ostensible , presumed , prima facie , putative , reputed , seeming , supposed Visit the Thesaurus for More.
Examples of ostensive in a Sentence the ostensive purpose of his visit was to discuss the terms of his will. Recent Examples on the Web Ask this question to a random group of people, the answer will most likely be ostensive. First Known Use of ostensive , in the meaning defined at sense 1. Learn More About ostensive.
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The standards by which definitions are judged are thus liable to vary from case to case. The different definitions can perhaps be subsumed under the Aristotelian formula that a definition gives the essence of a thing. In philosophy, too, several different kinds of definitions are often in play, and definitions can serve a variety of different functions e. But, in philosophy, definitions have also been called in to serve a highly distinctive role: that of solving epistemological problems.
For example, the epistemological status of mathematical truths raises a problem. Immanuel Kant thought that these truths are synthetic a priori , and to account for their status, he offered a theory of space and time—namely, of space and time as forms of, respectively, outer and inner sense.
More precisely, they attempted to construct a derivation of arithmetical principles from definitions of arithmetical concepts, using only logical laws.
For the Frege-Russell project to succeed, the definitions used must have a special character. They must be conceptual or explicative of meaning; they cannot be synthetic. It is this kind of definition that has aroused, over the past century or so, the most interest and the most controversy.
And it is this kind of definition that will be our primary concern. Let us begin by marking some preliminary but important distinctions. The chemist aims at real definition, whereas the lexicographer aims at nominal definition. Under the former conception, we are aiming at a nominal definition; under the latter, at a real definition.
Fine defends the conception that a real definition defines an object by specifying what the object is; in other words, a real definition spells out the essence of the object defined. Rosen offers an explanation of real definition in terms of grounding: the definition provides the ground of the essence of the object.
Nominal definitions—definitions that explain the meaning of a term—are not all of one kind. A dictionary explains the meaning of a term, in one sense of this phrase. Dictionaries aim to provide definitions that contain sufficient information to impart an understanding of the term. It is a fact about us language users that we somehow come to understand and use a potential infinity of sentences containing a term once we are given a certain small amount of information about the term.
Exactly how this happens is a large mystery. But it does happen, and dictionaries exploit the fact. Note that dictionary entries are not unique. Different dictionaries can give different bits of information and yet be equally effective in explaining the meanings of terms. Definitions sought by philosophers are not of the sort found in a dictionary. The philosophical quest for definition can sometimes fruitfully be characterized as a search for an explanation of meaning. A stipulative definition imparts a meaning to the defined term, and involves no commitment that the assigned meaning agrees with prior uses if any of the term.
Stipulative definitions are epistemologically special. They yield judgments with epistemological characteristics that are puzzling elsewhere. Philosophers have found it tempting to explain the puzzling cases of, e. Saul Kripke has drawn attention to a special kind of stipulative definition. We can stipulatively introduce a new name e. In such a stipulation, Kripke pointed out, the description serves only to fix the reference of the new name; the name is not synonymous with the description.
For, the judgment. Kripke used such reference-fixing stipulations to argue for the existence of contingent a priori truths— 1 being an example. Reference-fixing stipulative definitions can be given not only for names but also for terms in other categories, e. See Frege for a defense of the austere view that, in mathematics at least, only stipulative definitions should be countenanced.
Descriptive definitions, like stipulative ones, spell out meaning, but they also aim to be adequate to existing usage. When philosophers offer definitions of, e. It is useful to distinguish three grades of descriptive adequacy of a definition: extensional, intensional, and sense.
A definition is extensionally adequate iff there are no actual counterexamples to it; it is intensionally adequate iff there are no possible counterexamples to it; and it is sense adequate or analytic iff it endows the defined term with the right sense. When definitions are put to an epistemological use, intensional adequacy is generally insufficient. For such definitions cannot underwrite the rationality or the aprioricity of a problematic subject matter.
Horty offers some ways of thinking about senses of defined expressions, especially within a Fregean semantic theory. An explication aims to respect some central uses of a term but is stipulative on others. The explication may be offered as an absolute improvement of an existing, imperfect concept. The quoted phrase is due to Alan Ross Anderson; see Belnap , A simple illustration of explication is provided by the definition of ordered pair in set theory.
And it can be verified that the above definition satisfies the principle. The definition does have some consequences that do not accord with the ordinary notion. But the mismatch is not an objection to the explication. What is important for explication is not antecedent meaning but function. So long as the latter is preserved, the former can be let go.
It is this feature of explication that led W. The truth-functional conditional provides another illustration of explication. This conditional differs from the ordinary conditional in some essential respects. Nevertheless, the truth-functional conditional can be put forward as an explication of the ordinary conditional for certain purposes in certain contexts.
Whether the proposal is adequate depends crucially on the purposes and contexts in question. That the two conditionals differ in important, even essential, respects does not automatically disqualify the proposal. Ostensive definitions typically depend on context and on experience. Suppose the conversational context renders one dog salient among several that are visible. We can think of experience as presenting the subject with a restricted portion of the world. This portion can serve as a point of evaluation for the expressions in an ostensive definition.
See Gupta for an account of the contribution of experience to the meaning of an ostensively defined term. An ostensive definition can bring about an essential enrichment of a language. Unlike other familiar definitions, ostensive definitions can introduce terms that are ineliminable. So, ostensive definitions can fail to meet the Eliminability criterion explained below; they can fail to meet also the Conservativeness criterion, also explained below.
The capacity of ostensive definitions to introduce essentially new vocabulary has led some thinkers to view them as the source of all primitive concepts. Thus, Russell maintains in Human Knowledge that.
Such foundationalist pictures were decisively criticized by Ludwig Wittgenstein in his Philosophical Investigations. Ostensive definitions are important, but our understanding of them remains at a rudimentary level.
They deserve greater attention from logicians and philosophers. The kinds into which we have sorted definitions are not mutually exclusive, nor exhaustive.
A stipulative definition of a term may, as it happens, be extensionally adequate to the antecedent uses of the term. A dictionary may offer ostensive definitions of some words e. An ostensive definitions can also be explicative. Moreover, as we shall see below, there are other kinds of definition than those considered so far. Such definitions can be represented thus:.
We are setting aside ostensive definitions, which plainly require a richer representation. When the defined term is clear from the context, the representation may be simplified to. Not all definitions found in the logical and philosophical literature fit under scheme 2.
Partial definitions, for example, fall outside the scheme; another example is provided by definitions of logical constants in terms of introduction and elimination rules governing them. Nonetheless, definitions that conform to 2 are the most important, and they will be our primary concern. Let us focus on stipulative definitions and reflect on their logic. Some of the important lessons here carry over, as we shall see, to descriptive and explicative definitions. For simplicity, let us consider the case where a single definition stipulatively introduces a term.
Multiple definitions bring notational complexity but raise no new conceptual issues. What requirements must the definition fulfill? Before we address these questions, let us take note of a distinction that is not marked in logic books but which is useful in thinking about definitions. In one kind of definition—call it homogeneous definition—the defined term and the definiendum belong to the same logical category. So, a singular term is defined via a singular term; a general term via a general term; a sentence via a sentence; and so on.
Let us say that a homogenous definition is regular iff its definiendum is identical to the defined term. Here are some examples of regular homogeneous definitions:. It is sometimes said that definitions are mere recipes for abbreviations. In the second kind of definition—call it a heterogenous definition—the defined term and the definiendum belong to different logical categories.
So, for example, a general term e. For another example, a singular term e. Heterogeneous definitions are far more common than homogenous ones. In a heterogeneous definition, however, the definiens can easily be complex; for example,. If the language has a device for abstraction—e. Observe that a heterogenous definition such as 4 is not a mere abbreviation. Moreover, if such definitions were abbreviations, they would be subject to the requirement that the definiendum must be shorter than the definiens, but no such requirement exists.
On the other hand, genuine requirements on definitions would make little sense. The following stipulation is not a legitimate definition:. Some stipulative definitions are nothing but mere devices of abbreviation e. However, many stipulative definitions are not of this kind; they introduce meaningful items into our discourse.
But what is the source of the difference? Why is 4 legitimate, but not 6? More generally, when is a definition legitimate? What requirements must the definiens fulfill? And, for that matter, the definiendum? Must the definiendum be, for instance, atomic, as in 3 and 4? If not, what restrictions if any are there on the definiendum?
It is a plausible requirement on any answer to these questions that two criteria be respected. We should not be able to establish, by means of a mere stipulation, new things about, for example, the moon.
It is true that unless this criterion is made precise, it is subject to trivial counterexamples, for the introduction of a definition materially affects some facts. Nonetheless, the criterion can be made precise and defensible, and we shall soon see some ways of doing this. There are complications here, however. For example, a definition of quotient may leave some occurrences of the term undefined e.
The orthodox view is to rule such definitions as illegitimate, but the orthodoxy deserves to be challenged here. Let us leave the challenge to another occasion, however, and proceed to bypass the complications through idealization. Let us confine ourselves to ground languages that possess a clearly determined logical structure e. A variant formulation of the Use criterion is this: the definition must fix the meaning of the definiendum. Note that the two criteria govern all stipulative definitions, irrespective of whether they are single or multiple, or of whether they are of form 2 or not.
The traditional account of definitions is founded on three ideas. The first idea is that definitions are generalized identities; the second, that the sentential is primary; and the third, that of reduction.
These are, put crudely, that i any occurrence of the definiendum can be replaced by an occurrence of the definiens Generalized Definiendum Elimination ; and, conversely, ii any occurrence of the definiens can be replaced by an occurrence of the definiendum Generalized Definiendum Introduction.
The second idea—the primacy of the sentential—has its roots in the thought that the fundamental uses of a term are in assertion and argument: if we understand the use of a defined term in assertion and argument then we fully grasp the term.
The sentential is, however, primary in argument and assertion. Sentential items are here understood to include sentences and sentence-like things with free variables, e. The issues the second idea raises are, of course, large and important, but they cannot be addressed in a brief survey. Download PDF. Copy to Clipboard.
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