Counterfactual conditional

Counterfactual conditional clauses , also counterfactual implications or counterfactuals for short , are called statements of the form “If ... were the case, then would be ---” in philosophy .

Examples:

If soccer player X hadn't been sent off with a red card, Bayern would have won the game.
If Fritz had practiced more, he wouldn't have done so badly on dictation.

In the antecedent or antecedent, a situation is described that did not happen like this, but could have happened (see also counterfactuality ). Consequences are drawn from this description of the situation in the postscript or succession.

In grammar there is the name " Irrealis " for counterfactuals , more precisely "Irrealis of the past". But since in philosophy, especially in the theory of science and logic, counterfactuals are examined from their own points of view and interests, a name of their own has become established for them there.

Relevance of the counterfactuals for the philosophy of science

Clarification of the concept of natural laws

Nelson Goodman has investigated in his work "Fact, Fiction, Prediction" how counterfactuals can help to clarify the nature of the laws of nature . There is the following close connection between counterfactuals and natural laws: Let the general statement “All F are G” be a natural law (or a statement that follows from natural laws). Then the counterfactual applies “If a were an F, then a would be a G”. However, if the universal statement does not have the character of a law of nature, then the counterfactual typically does not apply.

example

We start from the statement:

All matches that are lit (under suitable conditions) will ignite.

Suitable conditions mean that there is enough oxygen in the room, that the match is dry, etc. This statement expresses a natural law. Therefore the corresponding counterfactual is:

If the match had been struck, it would have ignited.

true, assuming that s is a match for which the above suitable conditions exist.

On the other hand: Let us consider the general statement:

All coins that were in my pocket at time t are made of silver.

This statement is not a natural law, but an accidental truth (we assume that the statement is true). Therefore the following counterfactual, predicated of a copper coin k, is wrong:

If k had been in my pocket at time t, k would have been made of silver.

Instead, the following counterfactual applies:

If k had been in my pocket at time t, not all of the coins in my pocket would have been made of silver.

Clarification of the concept of causality

David Lewis uses counterfactuals to explain the concept of causality . A simplified version of its definition is as follows:

The event a causes the event b if and only if:

If a had not occurred, b would not have occurred

Behind this definition is the observation that we often use counterfactuals to talk about causal processes. For example we can say:

If the glass hadn't been knocked off the table, it wouldn't have broken

to express that the breakage of the glass was caused by the impact. An important limitation here is that the counterfactual must relate events such as a shock or a break. In the sentence:

If Frank weren't my uncle, his daughter wouldn't be my cousin.

there is no causal relationship expressed: The fact that Frank is my uncle does not mean that his daughter is my cousin, but this is not an event (i.e. not an occurrence), but rather a condition.

Instead of the simple definition presented above, Lewis uses a more complex one. The reason for this lies in the transitivity of the causal relation: if an event a causes an event b and b in turn causes c, then a also causes c. In contrast to the causal relation, however, counterfactuals are not always transitive (see also below). To ensure the transitivity of the relation, Lewis uses the following, more complex definition:

The event caused a precisely then the event b if: There are events , ..., such that:

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If a had not occurred, and would not have occurred

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if it had not occurred, would not have occurred and ... and

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if it had not occurred, b would not have occurred.

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A formal semantic for counterfactuals

Formal semantics for counterfactuals were developed by David Lewis (after preliminary work by Robert Stalnaker ). The semantics make use of the concept of the “ possible world ”. We can imagine our world as being different from what it actually is; this world of ideas is then a possible world.

Lewis now assumes that these possible worlds are ordered by a similarity relation , i. H. the possible worlds are more or less similar to the real world. A counterfactual “If a, then b would be” is true according to Lewis if there is a possible world in which a and b hold, and if this world is more similar to the actual world than all worlds in which a is also true, but not b. So the phrase "if the match had been struck, it would have lit" is true if the possible world in which the match was struck and ignited is more like the real world than any world in which it was also struck but did not ignite.

By pouring these intuitions into mathematically precise terms, Lewis arrives at formal semantics for counterfactuals. The similarity relation is modeled as a relation for every world w, whereby it can be read as: “ is w at least as similar as ”. It is required that of every two worlds one w is at least as similar as the other or vice versa, so that all worlds must be comparable. (The intuitively obvious requirement of negative transitivity , which would result in a “ strict weak order ”, is not required to derive the properties of the counterfactual.) It can then be shown that the properties of the counterfactuals formulated above are valid under this definition. Lewis also makes the demand that no world can be so similar to a world as it is, that there is none with . As a result, counterfactuals with a true antecedent have the same truth conditions as a material implication with a true antecedent, i.e. H. they are true if the consequence is true, otherwise false. ${\ displaystyle R_ {w}}$ ${\ displaystyle w_ {1} R_ {w} w_ {2}}$ ${\ displaystyle w_ {1}}$ ${\ displaystyle w_ {2}}$ ${\ displaystyle R_ {w}}$ ${\ displaystyle w_ {1}}$ ${\ displaystyle w_ {1} R_ {w} w}$

literature

Nelson Goodman: Fact, Fiction, Prediction . Suhrkamp 1988. ISBN 3-518-28332-4
David Lewis: Counterfactuals , 2nd ed., Basil Blackwell, Oxford 1984
Robert Stalnaker: A Theory of Conditionals . In: Ernest Sosa (Ed.): Causation and Conditionals . Oxford 1975, ISBN 0198750307 . p. 165-179.

Web links

Horacio Arlo-Costa: The Logic of Conditionals. In: Edward N. Zalta (Ed.): Stanford Encyclopedia of Philosophy .
Dorothy Edgington: Conditionals. In: Edward N. Zalta (Ed.): Stanford Encyclopedia of Philosophy .
William Starr: Counterfactuals. In: Edward N. Zalta (Ed.): Stanford Encyclopedia of Philosophy .