But that just seems wrong. It seems that of the following, 1 is true, but 2 is false:. So, the argument goes, we should replace the material conditional analysis with something else. Note also that the example isn't particularly bizarre. OK, 2 is a little bit bizarre, but that's to make it more obviously false -- obviously false statements tend to be a bit bizarre, since nobody is inclined to assert them. But you can replace 2 with other statements which are still just as false -- perhaps less obviously so.
Now, a potential counterexample to the foregoing might be as follows: If 'Oswald didn't kill Kennedy' is false, and we know that it is false, aren't the conditionals in the family above all a bit, well, bizarre? After all, how can I contemplate who else might have killed him given that I know that it was Oswald? In that case, why does it matter what truth conditions I assign to 1 and 2?
An answer concerns degrees of belief. There's a chance I'm wrong. In that case, it's worth me considering the conditionals 1 and 2 ; I want to know how to revise my beliefs if I were to find out that I were wrong. But the material conditional analysis, says that, since I have high certainty in the falsehood of the antecedent, should have a high certainty in the falsehood of the conditional as a whole.
Your second bolded question seems to suggest something like this. Why should we care about the semantics of natural language in general, especially if we can avoid ambiguity ourselves? Remark : There seems to be a presupposition that the reason we should care as philosophers about the truth conditions of sentences is so that we can be clear what we're saying when we say it. This is perhaps the case we want well-defined semantics of formal languages; it helps us be precise when we want to make a statement with particular truth conditions.
So, for example, if we assert a conditional 'if p then q' which gets different truth conditions on different accounts of the semantics of conditionals, this would be problematic. But, as you say, in such a case, we can always say something less ambiguous somehow or other. But why not ask about the semantics of natural language? It's a pretty good question.
Perhaps there is some demarcation to be done, such as whether this is philosophy or linguistics, but that, I take it, isn't the issue. And why particular bits of natural language? I think the only good answer here will have to be something like: 'because it's more interesting' -- it throws up more problems, interesting subquestions and so on. There's also no doubt an element of fashion involved. A link : There's a recent interview with John Searle in which he expresses what I take to be similar reservations to yours. Philosophy of language has a habit of looking at a pice of natural language and then suggesting all manner of formal models of it, supplying truth conditions.
In doing so, we can have a lot of fun, but it's easy to miss why we're doing it. Here's a relevant quote:. JS: Well, what has happened in the subject I started out with, the philosophy of language, is that, roughly speaking, formal modeling has replaced insight. My own conception is that the formal modeling by itself does not give us any insight into the function of language.
Any account of the philosophy of language ought to stick as closely as possible to the psychology of actual human speakers and hearers. What happens now is that many philosophers aim to build a formal model where they can map a puzzling element of language onto the formal model, and people think that gives you an insight.
He goes on to give theories of counterfactuals as an example, but indicative conditionals could easily be another example. Here's a link to the interview. One reason you might find this interesting is if we draw a distinction between Logic as a mathematical field of study and the philosophical study of the foundations of Argumentation. Whatever you might want to say about the apparent formal restrictiveness of the idea of an indicative conditional, there appears to be something incredibly potent about many of the old Aristotelian Syllogism rules that defies a purely formal account.
Specifically, I'm thinking about the convincing nature of Modus Ponens arguments; that is, arguments of the form:. Unless we think that the "if" here has some kind of mathematical or logical foundational interpretation, this following isn't a logical guarantee - indeed, as has been pointed out in the literature around Truth, Modus Ponens seems to struggle as a law if we think that "If" means material implication and where Truth is taken to be considered in terms of the rules that you can deduce that the sentence 'P' is true whenever P is the case and vice versa.
Yet it seems to capture the very point of what it means to say "if" in casual discussion - we want the conclusion to "follow from" the premise in an authoritative mode of assertion. What we are looking for is some notion of the idea of a Logical Consequence relation suited for argument and reasoning. Picking apart the foundations of Argumentation in some kind of methodical, logical framework that can function as a public standard requires certain modelling assumptions about what each of the supposedly logical terms we appeal to are taken to mean.
- If P Then Q Conditionals And The Foundations Of Reasoning.
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Other analytical philosophers have tried to do something similar by using tools in proof theory to represent how we transform statements or propositions in more combinatorial ways. This was a pretty live debate even fairly recently, though I'm not sure if any definitive consensus has been reached as to whether the consequence work has any useful philosophical applications.
One major challenge for this field has been to address Curry's Paradox , which, much like Godel's argument, seems to render a complete capture of a relation of consequence of a particular logical system inaccessible to that same logical system. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Ships in 7 to 10 business days.
If P, then Q: Conditionals and the Foundations of Reasoning
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