This condition is clearly false: the degree of Bill Gates has nothing to do with whether Elvis is still alive. However, the direct encoding of this formula in classical logic using material implication lead to:
This formula is true because a formula is true whenever the antecedent is false. Hence, this formula is not an adequate translation of the original sentence. Strict conditions are encodings of implications in modal logic attempting A different encoding is:
In modal logic, this formula means (roughly) that, in every possible world in which Bill Gates graduated in Medicine, Elvis never died. Since one can easily imagine a world where Bill Gates is a Medicine graduate and Elvis is dead, this formula is false. Hence, this formula seems a correct translation of the original sentence.
Although the strict conditional is much closer to being able to express natural language conditionals than the material conditional, it has its own problems. The following sentence, for example, is not correctly formalized by a strict conditional:
Using strict conditionals, this sentence is expressed as:
In modal logic, this formula means that, in every possible world where Bill Gates graduated in medicine, it holds that 2 + 2 = 4. Since 2 + 2 is equal to 4 in all possible worlds, this formula is true. While it is clearly not the case that 2 + 2 = 4 if Bill Gates graduated in medicine, the corresponding strict material statement is true.
To avoid the paradoxes of strict implication, some logicians have created counterfactual conditionals. Others, such as Paul Grice, have used conversational implicature to argue that, despite apparent difficulties, the material conditional is just fine as a translation for the natural language 'if...then...'. Others still have turned to relevant logic to supply a connection between the antecedent and consequent of provable conditionals.
In logic, the corresponding conditional of an argument (or derivation) is a logical implication whose antecedent is the conjunction of the argument's (or derivation's) premises and whose consequent is the argument's conclusion. An argument is valid if and only if its corresponding conditional is a necessary truth. It follows that an argument is valid if and only if the negation of its corresponding conditional is a contradiction.
Consider the following argument,
This argument's corresponding conditional may be stated as a conjunction of the premises that implies the conclusion,
For an introduction to non-classical logic as an attempt to find a better translation of the conditional, see:
For an extended philosophical discussion of the issues mentioned in this article, see:
Strict conditionals: a negative result.(PHILOSOPHICAL ABSTRACTS)(C.I. Lewis and Jonathan Lowe's work on implication)(Brief article)
Dec 01, 2006; Jonathan Lowe has argued that a particular variation on C.I. Lewis' notion of strict implication avoids the paradoxes of strict...