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On Denoting

On Denoting is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand On Denoting rather than just read about it. In short: "On Denoting" is an essay by Bertrand Russell. It was published in the philosophy journal Mind in October 1905.

Key takeaways

  • On Denoting belongs to science; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect On Denoting to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of On Denoting from memory before moving on to harder problems.

Reference excerpt

"On Denoting" is an essay by Bertrand Russell. It was published in the philosophy journal Mind in October 1905. In it, Russell introduces and advocates his theory of denoting phrases, according to which definite descriptions and other "denoting phrases ... never have any meaning in themselves, but every proposition in whose verbal expression they occur has a meaning." This theory later became the basis for Russell's descriptivism with regard to proper names, and his view that proper names are "disguised" or "abbreviated" definite descriptions. In the 1920s, Frank P. Ramsey referred to the essay as "that paradigm of philosophy". In the Stanford Encyclopedia of Philosophy entry Descriptions, Peter Ludlow singled the essay out as "the paradigm of philosophy", and called it a work of "tremendous insight"; provoking discussion and debate among philosophers of language and linguists for over a century.

The "denoting phrase"

Russell's concept of a denoting phrase For Russell, a denoting phrase is a semantically complex expression that can serve as the grammatical subject of a sentence. Paradigmatic examples include both definite descriptions ("the shortest spy") and indefinite descriptions ("some sophomore"). A phrase does not need to have a denotation to be a denoting phrase: "the greatest prime number" is a denoting phrase in Russell's sense even though there is no such thing as the greatest prime number. According to Russell's theory, denoting phrases do not contribute objects as the constituents of the singular propositions in which they occur. Denotation, in other words, is a semantically inert property, in this view. Whereas Frege held that there were two distinct parts (or aspects) of the meaning of every term, phrase, or sentence (its sense and reference: Sinn and Bedeutung), Russell explicitly rejects the notion of sense (Sinn), and gives several arguments against it.

Reference to something that does not exist However, at the very beginning of the article, Russell distinguishes between cases where "a phrase may be denoting and yet not denote anything (e.g. 'the present King of France')" (there was no king of France in Russell's lifetime), cases where they may denote "one definite object (such as 'the present King of England')" (Edward VII was the king of England at the time of Russell's article), and cases where they may "denote ambiguously (such as 'a man')". The cases of denoting without anything to denote and ambiguous denotation are formally denoting phrases and purport to denote a singular entity, yet fail to do so. Therefore, only the second case can be the subject of true sentences.

Epistemology In any case, after clarifying the sense of the term "denoting phrase" and providing several examples to illustrate the idea, Russell explains the epistemological motivations for his theory. Russell believes at this point that there are essentially two modes of knowing: knowledge by description and knowledge by (direct) acquaintance. Knowledge by acquaintance is limited to the sense data of the phenomenal world and to one's own private inner experiences, while knowledge of everything else (other minds, physical objects, and so on) can be known only by way of general descriptions.

The theory of descriptions

Mathematical description Russell starts out by defining the "fundamental" notion of a propositional function. This is basically a modified version of Frege's idea of unsaturated concepts. Hence, "C(x) stands for a proposition in which C is a constituent and where x, the variable, is essentially and wholly undetermined." Then everything, nothing and something ("the most primitive of denoting phrases") are to be interpreted as follows:

C ( E ) ↔ ∀ x C ( x ) {\displaystyle C(E)\leftrightarrow \forall xC(x)}

C ( N ) ↔ ∀ x ¬ C ( x ) {\displaystyle C(N)\leftrightarrow \forall x\lnot C(x)}

C ( S ) ↔ ¬ ∀ x ¬ C ( x ) {\displaystyle C(S)\leftrightarrow \lnot \forall x\lnot C(x)}

where E stands for everything, N stands for nothing and S stands for something. All is taken as primitive and indefinable and the others are defined in terms of it. Russell emphasises that denoting phrases can have no meaning apart from that which is assigned to them within the propositions in which they occur, all of which are meaningful. This is the foundation of Russell's theory of descriptions as he proceeds to illustrate.

Illustration The phrase "the father of Charles II (F) was executed (E)" is interpreted as the following quantificational assertion:

∃ x ( ( F ( x ) ∧ ∀ y ( F ( y ) → x = y ) ) ∧ E ( x ) ) {\displaystyle \exists x\left(\left(F\left(x\right)\land \forall y\left(F\left(y\right)\rightarrow x=y\right)\right)\land E\left(x\right)\right)}

In other words, there is one and only one thing x such that x is the father of Charles II and x was executed. So, if C represents any statement at all about the father of Charles II, the statement 'C (the father of Charles II)' always implies:

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with On Denoting

Start with the simplest possible case. Write down what On Denoting claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to On Denoting before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about On Denoting ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of On Denoting

In research
On Denoting appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses On Denoting in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
On Denoting is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1905 essays, Essays by Bertrand Russell, Linguistic turn, so understanding it makes those chapters shorter.
In everyday life
Look for On Denoting outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study On Denoting in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what On Denoting means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain On Denoting out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is On Denoting in simple terms?

"On Denoting" is an essay by Bertrand Russell. It was published in the philosophy journal Mind in October 1905.

Why does On Denoting matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study On Denoting?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on On Denoting.

Tags

  • 1905 essays
  • Essays by Bertrand Russell
  • Linguistic turn
  • Philosophy of language literature
  • Philosophy papers
  • Works originally published in Mind (journal)

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