Classification of Conditionals

Philosophers divide conditionals into categories that are in part based on linguistic distinctions and in part based on conceptual differences among the kinds of concepts that are expressed by conditionals. The broadest category distinction is between indicative on the one hand and subjunctive and counterfactual conditionals on the other.

A standard example showing that there is a difference between indicatives and subjunctives is the following:

Philosophers typically treat both kinds of conditionals as a connective joining two propositions.

There are different symbolizations of the conditionals. In all the material in this guide, the indicative is symbolized with a single arrow, A→C, and the subjunctive or counterfactual is symbolized with what is called the corner connective, A>C.

Recently, there has been a lot of research discussing whether fundamentally there is just one kind of conditional that is just used in different ways, depending on the tense of the conditional, and another debate about which category should contain conditionals wholly about the future.

A Y-shaped analysis is a general analysis of conditionals that attributes common feature to indicative and subjunctive conditionals and then explains where the two types of conditionals differ or diverge.

After independently considering analyses of indicative and subjunctive conditionals, many philosophers are left wondering if the two are only loosely connected at best. Others have attempted to give a more unified theory of the two, explaining how the analyses converge and diverge, that is, a Y-shaped analysis. Wayne Davis and Robert Stalnaker give two such accounts with similar formats.

The Davis Account

According to Davis, the proper analysis of subjunctive conditionals is as follows: A>C is true iff at the A-world most like the actual world in terms of world states up to the time of the antecedent, C is true. To make this more vivid, let's take an example: If Booth had not shot Lincoln in 1865, someone else would have. That conditional is true iff at the world most like the actual world (in terms of world states) until Lincoln's 1865 death, someone else shoots him.

The analysis of indicatives is as follows: A→C is true iff at the A-world most like the actual world in terms of all world states, C is true. Lets look at the indicative version of our previous conditional: If Booth didn't shoot Lincoln in 1865, someone else did. That conditional is true iff at the closest A-world to the actual world in terms of all world states, C is also true.

The analysis forms a general Y-shape. Here is how: In order to assess the truth of any conditional, you must determine whether at the closest world to the actual world (in terms of similarity with respect to all world states) at which the antecedent is true, the consequent is true. The subjunctive and indicative branch off because in the subjunctive case you need only consider the world most similar to the actual world up to the time of the antecedent whereas in the indicative case you must consider the world most similar to the actual world at all times.

Problems

One obvious thing to note about Davis's account is that it presupposes that indicative conditionals have truth-values. The analysis also fails to give any account for the importance of the Ramsey test to the indicative conditional.

Further, the manner in which Davis recommends for evaluating subjunctives, that is, considering similarity between all world slices up to the time of the antecedent seems to lead to "bumps": large violations of the laws in the candidate worlds for the evaluation for the conditional. Consider the conditional, "If I were in Russia today, I would see the Hermitage." On Davis's analysis, it appears that the world to look at when evaluating the conditional, is one in which I was where I actually was, and did what I actually did until today (And that doesn't include making any travel plans or flying in a plane), and then miraculously appeared in Russia. In that world, it is not even clear that the conditional is true (though it seems perfectly reasonable), since I might spend my time in Russia confused and desperate to figure out how I got there.

Perhaps these remarks are uncharitable and the Davis analysis is only intended to give a rough sketch of the way conditionals function. Nonetheless, the analysis is not widely accepted.

The Stalnaker Account

Robert Stalnaker offers another approach for explaining the common features of indicative and subjunctive conditionals. He suggests that whenever someone asserts a conditional, he asserts that C is true at some A-world picked out by a selection function. The idea of the "most similar world" will always be a part of the selection function, but, the selection function will vary with the context of the utterance.

In any given context, Stalnaker observes, there is a certain set of propositions the truth of which everyone takes for granted. Stalnaker calls the class of worlds at which all of those propositions are true the context set. Worlds in the context set, because all assumed propositions are true at them, are candidates for the actual world.

When someone asserts a conditional, unless he indicates otherwise, we are entitled to take it for granted that he is using a selection function that will pick out a world in the context set. Signals that indicate that we cannot take this for granted include the markers of the subjunctive conditional, like the use of the word 'would'. When a speaker utters a subjunctive conditional, his selection function might pick out a world which everyone is convinced is non-actual.

Again, the analysis takes a Y-shape. When someone asserts any kind of conditional he asserts that C is true at an A-world determined by his selection function. Indicatives and subjunctives divide in that, in the indicative case the selection function picks out a world in the context set (a candidate for actuality), whereas in the subjunctive case, the selection function may very well pick out a world outside the context set.