Don't have an account? The difference between the two kinds of conditionals is explained in terms of different constraints imposed on the contexts relative to which the different forms of conditionals are interpreted. A pragmatic concept of reasonable inference is defined and contrasted with semantic entailment. This concept is then used to explain why certain inferences involving indicative conditionals are compelling, and to diagnose a fallacy in a familiar argument for fatalism. Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service.
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A is called the antecedent, C the consequent. These are adequate synonyms. But we want more than synonyms. A theory of conditionals aims to give an account of the conditional construction which explains when conditional judgements are acceptable, which inferences involving conditionals are good inferences, and why this linguistic construction is so important. Despite intensive work of great ingenuity, this remains a highly controversial subject. First let us delimit our field.
Counterfactuals will be the subject of a separate entry, and theories addressing them will not be discussed here. You look sceptical but stay outside, when there is large crash as the roof collapses.
I told you so. It is controversial how best to classify conditionals. See Gibbard , pp. Bennett changed his mind. Jackson defends the traditional view.
Still, straightforward statements about the past, present or future, to which a conditional clause is attached — the traditional class of indicative conditionals — do in my view constitute a single semantic kind.
The theories to be discussed do not fare better or worse when restricted to a particular subspecies. As well as conditional statements, there are conditional commands, promises, offers, questions, etc.. As well as conditional beliefs, there are conditional desires, hopes, fears, etc..
Our focus will be on conditional statements and what they express — conditional beliefs; but we will consider which of the theories we have examined extends most naturally to these other kinds of conditional. Three kinds of theory will be discussed. On development, it appears to be incompatible with construing conditionals as statements with truth conditions. The generally most fruitful, and time-honoured, approach to specifying the meaning of a complex sentence in terms of the meanings of its parts, is to specify the truth conditions of the complex sentence, in terms of the truth conditions of its parts.
A semantics of this kind yields an account of the validity of arguments involving the complex sentence, given the conception of validity as necessary preservation of truth. Throughout this section we assume that this approach to conditionals is correct. The truth-functional theory of the conditional was integral to Frege's new logic It is the first theory of conditionals which students encounter. Typically, it does not strike students as obviously correct. It is logic's first surprise. Yet, as the textbooks testify, it does a creditable job in many circumstances.
And it has many defenders. Assuming truth-functionality — that the truth value of the conditional is determined by the truth values of its parts — it follows that a conditional is always true when its components have these combinations of truth values. Some do not, demanding a further relation between the facts that A and that B see Read You don't touch it.
Was my remark true or false? According to the non-truth-functionalist, it depends on whether the wire is live or dead, on whether you are insulated, and so forth. Robert Stalnaker's account is of this type: consider a possible situation in which you touch the wire, and which otherwise differs minimally from the actual situation.
Let A and B be two logically independent propositions. The four lines below represent the four incompatible logical possibilities for the truth values of A and B. The main argument points to the fact that minimal knowledge that the truth-functional truth condition is satisfied is enough for knowledge that if A , B.
Suppose there are two balls in a bag, labelled x and y. All you know about their colour is that at least one of them is red.
That's enough to know that if x isn't red, y is red. Or: all you know is that they are not both red. That's enough to know that if x is red, y is not red. Suppose you start off with no information about which of the four possible combinations of truth values for A and B obtains.
You then acquire compelling reason to think that either A or B is true. You don't have any stronger belief about the matter. In particular, you have no firm belief as to whether A is true or not. You have ruled out line 4. The other possibilities remain open. Look at the possibilities for A and B on the left.
You have eliminated the possibility that both A and B are false. So if A is false, only one possibility remains: B is true. The truth-functionalist call him Hook gets this right. Look at column ii. The non-truth-functionalist call her Arrow gets this wrong. Look at column v. Eliminate line 4 and line 4 only, and some possibility of falsity remains in other cases which have not been ruled out. The same point can be made with negated conjunctions.
In particular, you don't know whether A. You rule out line 1, nothing more. Hook gets this right. Arrow gets this wrong. Here is a second argument in favour of Hook, in the style of Natural Deduction.
Look at the last two lines of column i. Hook might respond as follows. How do we test our intuitions about the validity of an inference? The direct way is to imagine that we know for sure that the premise is true, and to consider what we would then think about the conclusion. In this circumstance conditionals have no role to play, and we have no practice in assessing them.
If our smoothest, simplest, generally satisfactory theory has the consequence that it does follow, perhaps we should learn to live with that consequence. There may, of course, be further consequences of this feature of Hook's theory which jar with intuition.
That needs investigating. We have seen that rival theories also have counterintuitive consequences. Natural language is a fluid affair, and we cannot expect our theories to achieve better than approximate fit. This was no doubt Frege's attitude. Frege's primary concern was to construct a system of logic, formulated in an idealized language, which was adequate for mathematical reasoning.
For the purpose of doing mathematics, Frege's judgement was probably correct. There are some peculiarities, but as long as we are aware of them, they can be lived with. And arguably, the gain in simplicity and clarity more than offsets the oddities. The oddities are harder to tolerate when we consider conditional judgements about empirical matters. The difference is this: in thinking about the empirical world, we often accept and reject propositions with degrees of confidence less than certainty.
We can, perhaps, ignore as unimportant the use of indicative conditionals in circumstances in which we are certain that the antecedent is false. But we cannot ignore our use of conditionals whose antecedent we think is likely to be false. We use them often, accepting some, rejecting others. Hook's theory has the unhappy consequence that all conditionals with unlikely antecedents are likely to be true. According to Hook, this person has grossly inconsistent opinions. Not only does Hook's theory fit badly the patterns of thought of competent, intelligent people.
On the contrary, we would be intellectually disabled: we would not have the power to discriminate between believable and unbelievable conditionals whose antecedent we think is likely to be false.
Arrow does not have this problem. This is perhaps less obviously unacceptable: if I'm sure that B , and treat A as an epistemic possibility, I must be sure that if A , B. Again the problem becomes vivid when we consider the case when I'm only nearly sure, but not quite sure, that B.
I think B may be false, and will be false if certain, in my view unlikely, circumstances obtain. For example, I think Sue is giving a lecture right now. I don't think that if she was seriously injured on her way to work, she is giving a lecture right now.
I reject that conditional. But on Hook's account, the conditional is false only if the consequent is false. I think the consequent is true: I think a sufficient condition for the truth of the conditional obtains. There are many ways of speaking the truth yet misleading your audience, given the standard to which you are expected to conform in conversational exchange.
One way is to say something weaker than some other relevant thing you are in a position to say. Consider disjunctions.
A is called the antecedent, C the consequent. These are adequate synonyms. But we want more than synonyms. A theory of conditionals aims to give an account of the conditional construction which explains when conditional judgements are acceptable, which inferences involving conditionals are good inferences, and why this linguistic construction is so important.
The Logic of Conditionals