Slingshot argument
Encyclopedia
In logic
, a slingshot argument is one of a group of arguments claiming to show that all true
sentence
s 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. Versions of the slingshot argument have been given by Gottlob Frege
, Alonzo Church
, W. V. Quine, and Donald Davidson
. 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
, states of affairs
, truth condition
, truthmaker
, and so on.
Assumptions:
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, "
" 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-preservating transformation steps.
's famous account of definite description
s is assumed. Russell claimed that the proper logical interpretation of a sentence of the form "The F is G" is:
Or, in the language of first-order logic
:
When the sentences above containing
-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.
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
, a slingshot argument is one of a group of arguments claiming to show that all true
True
True may refer to:* Truth, the state of being in accord with fact or reality-Music:* True , 1996* True , 2002* True , 1983** "True"...
sentence
Sentence (linguistics)
In the field of linguistics, a sentence is an expression in natural language, and often defined to indicate a grammatical unit consisting of one or more words that generally bear minimal syntactic relation to the words that precede or follow it...
s stand for the same thing.
This type of argument was dubbed the "slingshot
Slingshot
A slingshot, shanghai, flip, bean shooter or catapult is a small hand-powered projectile weapon. The classic form consists of a Y-shaped frame held in the off hand, with two rubber strips attached to the uprights. The other ends of the strips lead back to a pocket which holds the projectile...
" by philosophers Jon Barwise
Jon Barwise
Kenneth Jon Barwise was an American mathematician, philosopher and logician who proposed some fundamental revisions to the way that logic is understood and used....
and John Perry
John Perry (philosopher)
John R. Perry is Henry Waldgrave Stuart Professor of Philosophy at Stanford University. He has made significant contributions to areas of philosophy, including logic, philosophy of language, metaphysics, and philosophy of mind...
(1981) due to its disarming simplicity. Versions of the slingshot argument have been given by Gottlob Frege
Gottlob Frege
Friedrich Ludwig Gottlob Frege was a German mathematician, logician and philosopher. He is considered to be one of the founders of modern logic, and made major contributions to the foundations of mathematics. He is generally considered to be the father of analytic philosophy, for his writings on...
, Alonzo Church
Alonzo Church
Alonzo Church was an American mathematician and logician who made major contributions to mathematical logic and the foundations of theoretical computer science. He is best known for the lambda calculus, Church–Turing thesis, Frege–Church ontology, and the Church–Rosser theorem.-Life:Alonzo Church...
, W. V. Quine, and Donald Davidson
Donald Davidson (philosopher)
Donald Herbert Davidson was an American philosopher born in Springfield, Massachusetts, who served as Slusser Professor of Philosophy at the University of California, Berkeley from 1981 to 2003 after having also held teaching appointments at Stanford University, Rockefeller University, Princeton...
. Stephen Neale
Stephen Neale
Stephen Roy Albert Neale is Distinguished Professor of Philosophy and Linguistics and holder of the John H. Kornblith Family Chair in the Philosophy of Science and Values at the Graduate Center, City University of New York...
(1995) claims, controversially, that the most compelling version was suggested by Kurt Gödel
Kurt Gödel
Kurt Friedrich Gödel was an Austrian logician, mathematician and philosopher. Later in his life he emigrated to the United States to escape the effects of World War II. One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the...
(1944).
These arguments are sometimes modified to support the alternative, and evidently stronger, conclusion that there is only one fact
Fact
A fact is something that has really occurred or is actually the case. The usual test for a statement of fact is verifiability, that is whether it can be shown to correspond to experience. Standard reference works are often used to check facts...
, or one true proposition
Proposition
In logic and philosophy, the term proposition refers to either the "content" or "meaning" of a meaningful declarative sentence or the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence...
, states of affairs
State of affairs
The state of affairs is that combination of circumstances applying within a society or group at a particular time. The current state of affairs may be considered acceptable by many observers, but not necessarily by all. The state of affairs may present a challenge, or be complicated, or contain a...
, truth condition
Truth condition
In semantics, truth conditions are what obtain precisely when a sentence is true. For example, "It is snowing in Nebraska" is true precisely when it is snowing in Nebraska....
, truthmaker
Truthmaker
A truthmaker for a truthbearer is that entity in virtue of which the truthbearer is true. Philosophers have speculated on the question whether every truthbearer requires a truthmaker. Parmenides' classic claim that what does not exist cannot be thought about has been read as a claim that every...
, 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, "
" can be read as "the x such that".| 1. |  | |
| 2. |  | assumption 3 |
| 3. |  | redistribution |
| 4. |  | substitution, assumption 4 |
| 5. |  | redistribution |
| 6. |  | redistribution |
| 7. |  | substitution, assumption 3 |
| 8. |  | redistribution |
| 9. |  | assumption 3 |
Note that (1)-(9) is not a derivation of T from S. Rather, it is a series of (allegedly) designation-preservating transformation steps.
Responses to the argument
As Gödel (1944) observed, the slingshot argument does not go through if Bertrand RussellBertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...
's famous account of definite description
Definite description
A definite description is a denoting phrase in the form of "the X" where X is a noun-phrase or a singular common noun. The definite description is proper if X applies to a unique individual or object. For example: "the first person in space" and "the 42nd President of the United States of...
s 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
First-order logic
First-order logic is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic...
:
When the sentences above containing
-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:| 3'. |  |
| 4'. |  |
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.