science

Unity of the proposition

Unity of the proposition 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 Unity of the proposition rather than just read about it. In short: In philosophy, the unity of the proposition is the problem of explaining how a sentence in the indicative mood expresses more than just what a list of proper names expresses. History The problem was discussed under this name by Bertrand Russell, but can be traced back to Plato.

Key takeaways

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

Reference excerpt

In philosophy, the unity of the proposition is the problem of explaining how a sentence in the indicative mood expresses more than just what a list of proper names expresses.

History The problem was discussed under this name by Bertrand Russell, but can be traced back to Plato. In Plato's Sophist, the simplest kind of sentence consists of just a proper name and a universal term (i.e. a predicate). The name refers to or picks out some individual object, and the predicate then says something about that individual. The difficulty is to explain how the predicate does this. If, as Plato thinks, the predicate is the name of some universal concept or form, how do we explain how the sentence comes to be true or false? If, for example, "Socrates is wise" consists of just a name for Socrates, and a name for the universal concept of Wisdom, how could the sentence be true or false? In either case, the "Socrates" signifies Socrates, and the predicate signifies Wisdom. But the sentence asserts that Socrates is wise. The assertion of wisdom must consist in the assertion of some relation between Socrates and Wisdom. What is this relation? The problem was discussed much later by Francis Bradley. If we assume that a sentence consists of two objects and a relation that connects them, and we represent this by three names, say John, loving, Mary, how do we express the fact that John loves Mary? For "John", "loving" and "Mary" would name the objects they do, even if this were not a fact. This is known as Bradley's regress.

Frege, Russell, Wittgenstein The problem became significant in the early development of set theory. Set membership is a formal representation of the relation between the two parts of the proposition, and there are certain philosophical problems connected with this, as Frege realised when he investigated the distinction between concept and object. Assume that "Shergar is a horse" analyses into what "Shergar" names (an "Object", according to Frege), and what "is a horse" names (a "Concept"). Objects are fundamentally different from concepts, otherwise we get the problem of the unity of the proposition. A predicate cannot function as the subject of a sentence. But what are we doing when we talk about the concept is a horse? Aren't we using the expression "the concept is a horse", and isn't that a subject expression, which refers (on Frege's account) to an Object? Yes, says Frege, and on that account the concept is a horse is not a concept at all. This is a dogma that even Frege's most faithful followers found difficult to swallow. The difficulty was discussed in detail in The Principles of Mathematics by Russell, who saw no resolution.

There appears to be an ultimate notion of assertion, given by the verb, which is lost as soon as we substitute a verbal noun, and is lost when the proposition in question is made the subject of some other proposition. ...Thus the contradiction which was to have been avoided, of an entity which cannot be made a logical subject, appears to have here become inevitable. This difficulty, which seems to be inherent in the very nature of truth and falsehood, is one with which I do not know how to deal with satisfactorily. ...I therefore leave this question to the logicians with the above brief indication of a difficulty. (§ 52) Consider e.g. "A differs from B". The constituents of this proposition are simply A, difference and B. The proposition relates A and B, using the words "is ... from" in "A is different from B". But if we represent this contribution by words for relations, as e.g. "A <R> difference <R> B" we are back to a list of terms, we are essentially back at Bradley's regress.

A proposition, in fact, is essentially a unity, and when analysis has destroyed the unity, no enumeration of constituents will restore the proposition. The verb, when used as a verb, embodies the unity of the proposition, and is thus distinguishable from the verb considered as a term, though I do not know how to give a clear account of the distinction. (§ 52) Ludwig Wittgenstein addresses the problem early on in the Tractatus Logico-Philosophicus. In section 2.01 he claims that "states of affairs" are combinations of objects. In section 2.03 he explains that nothing is needed to link the objects, since the objects hang together. The arrangement of words in the sentence corresponds to the arrangement or structure of objects in the state of affairs expressed by the sentence. This is the so-called picture theory of the proposition.

See also Bradley's regress Third man argument

References

Bibliography

External links The Identity Theory of Truth The Nature and Unity of the Proposition Joachim's The Nature of Truth - contains a discussion of the problem Selection from Russell including a discussion of the problem

Worked examples

Example 1 — a first encounter with Unity of the proposition

Start with the simplest possible case. Write down what Unity of the proposition 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 Unity of the proposition 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 Unity of the proposition 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 Unity of the proposition

In research: Unity of the proposition 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 Unity of the proposition 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: Unity of the proposition is common in secondary-school and first-year university syllabi. It links to neighbouring topics Philosophy of language, Propositions, so understanding it makes those chapters shorter.
In everyday life: Look for Unity of the proposition 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 Unity of the proposition in 20 minutes

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

Frequently asked questions

What is Unity of the proposition in simple terms?

In philosophy, the unity of the proposition is the problem of explaining how a sentence in the indicative mood expresses more than just what a list of proper names expresses. History The problem was discussed under this name by Bertrand Russell, but can be traced back to Plato.

Why does Unity of the proposition 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 Unity of the proposition?

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 Unity of the proposition.