science

Slingshot argument

Slingshot argument 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 Slingshot argument rather than just read about it. In short: In philosophical logic, a slingshot argument is one of a group of arguments claiming to show that all true sentences stand for the same thing. This type of argument was dubbed the "slingshot" by philosophers Jon Barwise and John Perry (1981) due to its disarming simplicity.

Key takeaways

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

Reference excerpt

In philosophical logic, a slingshot argument is one of a group of arguments claiming to show that all true sentences stand for the same thing. This type of argument was dubbed the "slingshot" by philosophers Jon Barwise and John Perry (1981) due to its disarming simplicity. It is usually said that versions of the slingshot argument have been given by Gottlob Frege, Alonzo Church, W. V. Quine, and Donald Davidson. However, it has been disputed by Lorenz Krüger (1995) that there is much unity in this tradition. Moreover, Krüger rejects Davidson's claim that the argument can refute the correspondence theory of truth. Stephen Neale (1995) claims, controversially, that the most compelling version was suggested by Kurt Gödel (1944). These arguments are sometimes modified to support the alternative, and evidently stronger, conclusion that there is only one fact, or one true proposition, state of affairs, truth condition, truthmaker, and so on.

The argument One version of the argument (Perry 1996) proceeds as follows. Assumptions:

Substitution. If two terms designate the same thing, then substituting one for another in a sentence does not change the designation of that sentence. Redistribution. Rearranging the parts of a sentence does not change the designation of that sentence, provided the truth conditions of the sentence do not change. Every sentence is equivalent to a sentence of the form F(a). In other words, every sentence has the same designation as some sentence that attributes a property to something. (For example, "All men are mortal" is equivalent to "The number 1 has the property of being such that all men are mortal".) For any two objects there is a relation that holds uniquely between them. (For example, if the objects in question are denoted by "a" and "b", the relation in question might be R(x, y), which is stipulated to hold just in case x = a and y = b.) Let S and T be arbitrary true sentences, designating Des(S) and Des(T), respectively. (No assumptions are made about what kinds of things Des(S) and Des(T) are.) It is now shown by a series of designation-preserving transformations that Des(S) = Des(T). Here, " ι x {\displaystyle \iota x} " can be read as "the x such that".

Note that (1)-(9) is not a derivation of T from S. Rather, it is a series of (allegedly) designation-preserving transformation steps.

Responses to the argument As Gödel (1944) observed, the slingshot argument does not go through if Bertrand Russell's famous account of definite descriptions is assumed. Russell claimed that the proper logical interpretation of a sentence of the form "The F is G" is:

Exactly one thing is F, and that thing is also G. Or, in the language of first-order logic:

∃ x ( ∀ y ( F ( y ) ↔ y = x ) ∧ G ( x ) ) {\displaystyle \exists x(\forall y(F(y)\leftrightarrow y=x)\land G(x))}

When the sentences above containing ι {\displaystyle \iota } -expressions are expanded out to their proper form, the steps involving substitution are seen to be illegitimate. Consider, for example, the move from (3) to (4). On Russell's account, (3) and (4) are shorthand for:

Clearly the substitution principle and assumption 4 do not license the move from (3') to (4'). Thus, one way to look at the slingshot is as simply another argument in favor of Russell's theory of definite descriptions. If one is not willing to accept Russell's theory, then it seems wise to challenge either substitution or redistribution, which seem to be the other weakest points in the argument. Perry (1996), for example, rejects both of these principles, proposing to replace them with certain weaker, qualified versions that do not allow the slingshot argument to go through.

See also Abstraction Logic of information Charles Sanders Peirce bibliography

References Barwise, K. J. & Perry, John (1981), "Semantic innocence and uncompromising situations", Midwest Studies in the Philosophy of Language, VI. Gödel, Kurt (1944), "Russell's mathematical logic", in Paul Arthur Schilpp (ed.), The Philosophy of Bertrand Russell, Evanston and Chicago: Northwestern University Press, pp. 125–53. Krüger, Lorenz (1995), "Has the correspondence theory of truth been refuted?", European Journal of Philosophy, vol. 3, 157–173, repr. in Lorenz Krüger, Why Does History Matter to Philosophy and the Sciences?, ed. by Thomas Sturm, Wolfgang Carl, and Lorraine Daston. Berlin: De Gruyter, 2005, pp. 201–217. Licata, Gaetano (2011), Truth and Facts: Rejection of the Slingshot Argument in Defence of the Correspondence Theory of Truth, Rome, Aracne. Neale, Stephen (1995), "The philosophical significance of Gödel's Slingshot", Mind, vol. 104, no. 416, pp. 761–825. Peirce, C. S. (1906), "Prolegomena to an Apology for Pragmaticism", The Monist, 16, 492–546 (1906). Reprinted, Collected Papers, CP 4.530–572. Eprint. Perry, John (1996), "Evading the slingshot", in Andy Clark et al. (eds.), Philosophy and Cognitive Science. PDF.

External links Stephen Neale's Facing Facts reviewed by John Macfarlane An Analysis of Davidson's Slingshot Argument

Worked examples

Example 1 — a first encounter with Slingshot argument

Start with the simplest possible case. Write down what Slingshot argument 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 Slingshot argument 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 Slingshot argument 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 Slingshot argument

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

Read the reference excerpt below once, without taking notes.
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Frequently asked questions

What is Slingshot argument in simple terms?

Why does Slingshot argument 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 Slingshot argument?

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 Slingshot argument.