Counterfactual conditional

Counterfactual conditionals, also counterfactual implications or short Kontrafaktuale be in philosophy statements of the form "If ... were the case, then --- would be" called.

Examples:

• If football player X would not have been sent off with a red card, Bayern have won the game.
• If Fritz had practiced more, he would dictate the not so badly.

In the antecedent antecedent or so describes a situation that is not so happen, but could have been done (see counterfactuality ). In the postscript or consequent conclusions are drawn from this description of the situation.

In the grammar exists for Kontrafaktuale the name " subjunctive ", more precisely " Irrealis the past." However, as in philosophy, particularly in the philosophy of science and logic Kontrafaktuale under their own points of view and interests are studied, including a separate name for it has become naturalized there.

Relevance of Kontrafaktuale for the Philosophy of Science

Clarification of the concept of natural law

Nelson Goodman has "Fact, Fiction, forecasting " investigates in his work, as can contribute Kontrafaktuale to clarify the nature of the laws of nature. There are following close relationship between Kontrafaktualen and laws of nature: Be the universal statement " All F are G" a law of nature (or a statement that follows from the laws of nature ). Then the counterfactual is true " If a were an F, then a would be a G". Has the universal statement but not in the nature of a natural law, then the counterfactual typically does not apply.

Example

We start from the statement of:

With suitable conditions, it is meant that there is enough oxygen in the room is that the match is dry, etc. This statement expresses a natural law of. Therefore, the appropriate counterfactual:

True, and we assume that s is a match for the present the appropriate above-mentioned conditions.

On the other hand, we consider the universal statement:

This statement is not a natural law, but a random truth ( we assume that the statement is true). Therefore, the following counterfactual, testified by a copper coin k, wrong:

Rather Instead, the following shall apply counterfactual:

Clarification of the concept of causality

David Lewis Kontrafaktuale used to explain the concept of causality. A simplified version of his definition is as follows:

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

To express that the breaking of the glass is caused by the collision. An important limitation is that the counterfactual events, such as a shock or a breakup, you have to relate. In the sentence:

Namely expressed no causal link: that Frank is my uncle, does not cause his daughter is my cousin, but this is also not an event (ie not happening ), but rather a condition.

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

Logical properties of Kontrafaktuale

From the literature, a number of properties of counterfactual conditionals are known.

• A counterfactual follows from a corresponding " strict implication ". For example, the following sentence required is: " If Frank is my uncle, so his daughter is my cousin ." Therefore, the following counterfactual must be true: "If my uncle Frank, his daughter would be my cousin ."

• Kontrafaktuale are not transitive. From "If a, then b would " and " would be b, then c would be " so does not always follow " would be a, then c would be". For example, the following two Kontrafaktuale apply: " carbon Had resigned in 1992, he would have the federal election not won in 1994 ," and " If carbon the federal election not won in 1994, the SPD had in 1994 taken over the government. " But it is not necessarily true: "If carbon resigned in 1992, the SPD had taken over the government in 1994 "because the CDU would be taken up with another candidate for chancellor and would have then had quite chances to win the election.

• Non- validity of the premise gain. For most implications ( eg in the " material implication " ) can always reinforce assumptions, that is, from "If a, then b " follows " If a and c, then b". (This property is called monotony. ) This applies to Kontrafaktualen not, as the following example shows: From "If Fritz had gone on vacation, we could settle us in his house" does not follow "If Fritz went on holiday and his wife would have stayed here, we could settle us in his house. "

A formal semantics for Kontrafaktuale

A formal semantics for Kontrafaktuale was developed by David Lewis ( building on work done by Robert Stalnaker ). The semantics makes use of the notion of " possible world ," We can think of our world that they would be different than it actually is, in this world of imagination then there is a possible world.

Lewis is now expected that these possible worlds are ordered by a similarity relation, that is, the possible worlds are the real world more or less similar. A counterfactual "If a, then b would be " according to Lewis is true if there is a possible world in which a and b are, and if this world to the actual world is more similar than all the worlds in which a does also, but not b. The sentence " If the match had been painted, would it ignites " is true so if the possible world in which the match was painted and it is inflamed, the real world is more similar than all the worlds in which it was also painted, but has not ignited.

By Lewis pours these intuitions in mathematically precise terms, he is taken to a formal semantics for Kontrafaktuale. The similarity relation is modeled as a relation for every world w, where to read as: "w is at least as similar to ". It is postulated that of two worlds, the one w at least as similar to the other or vice versa, all the worlds must therefore be comparable. ( The intuitively obvious requirement of negative transitivity, which would make it a " strict weak ordering " is not needed to derive the properties of the Kontrafaktuals. ) It can be shown then that the above formulated properties of Kontrafaktuale are valid under this definition. Lewis is still on the requirement that no world a world can be so similar to themselves, so that there are not that. This Kontrafaktuale have a true antecedent same truth-conditions as a material implication with true antecedent, that is, they are true if the consequent is true, otherwise false.