One way to approach a problem is by trying to construct a solution via some method that is reliably thought to produce true solutions. Or we can approach problems by simply proposing solutions and then rejecting them when they fail to meet the standards for a good solution. Of course, even if you formally adopt the second approach, practicality often requires some measure of the first as well, simply because it may take too long to consider absolutely all of the alternatives, and so we shorten the process by attempting to look at the best ones first. A good example of this is the scientific method. Technically the scientific method only concerns itself with rejecting bad hypothesis. But in science as it is actually conduced there are a number of methods scientists use to construct candidate theories, such as trying to extend existing theories to cover the phenomena. Scientists aren’t committed to the idea that these theories are necessarily better, the last theory left standing is the best theory, and that is almost the only judge. Rather it is just happens to be the case that theories produced by those methods often do well when they are actually evaluated, but no one is committed to the idea that this is must be the case, it could be revealed to be a coincidence and that would not affect which scientific theories are thought to be the best.
The method for philosophy that I favor also has such a nature, that we find a solution to philosophical problems by evaluating possible solutions by the quality of explanations they provide, with the philosophical theories that don’t fall down in explaining being the best. But there is no need to go into the details of that metaphilosophical theory here. We can consider instead a simpler version that states that we should reject theories if they are logically inconsistent; if a claim asserted as part of the theory is denied as a consequence. Allow me to illustrate how this works with a topical example:
P1. Let us suppose that conceivability is identical to possibility.
P2. And let us further suppose that possibility allows us to demonstrate that some disputed claim is the case.
1. If we can demonstrate that it is the case then clearly its negation is not the case.
2. If its negation is possible then our appeal to possibility has not demonstrated anything.
3. Thus its negation is demonstrated to be impossible.
4. But if it is impossible then it must not be conceivable, by the first supposition.
5. Thus possibility can only be used to demonstrate which was already thought to be the case, because the negation is inconceivable and thus no one would hold it to be the case.
6. And so what is conceivable cannot be used to assert anything of substance (which people are of divided opinion about), which is a contradiction of the second supposition.
∴ we must deny one of the premises: either conceivability is not identical to possibility, or it cannot be used demonstrate anything of interest.
Thus an identification of conceivability with possibility “implodes”, it simply cannot be the case. This contrasts to an approach that attempts to show something about the nature of conceivability or possibility, such as the fact that they come apart in certain cases, or that possibility can only prove certain kinds of claims. Such an approach “refutes” the position the conceivability is identical to possibility by developing claims about them that exclude that claim. The advantages of such an approach is that at the end we have actually made some positive claims, and that may be more effective at leading people to believe that they were wrong about the relationship between conceivability and possibility, because they have a new theory to endorse. But, on the other hand, it is also much easier to argue against the alternate theory that is developed about conceivability and possibility. Surely that theory has its own premises, and some may dispute them. In contrast implosion relies only on the premises of the theory being imploded, and so it is much harder to take a stand against it. In many ways then which approach is preferable depends on what you are trying to accomplish. Are you trying to understand the objects of discussion or are you simply trying to get a misleading theory off the table?
But comparing and contrasting imploding theories versus constructing competing theories is only a preliminary to my real interest. Consider how we investigate the philosophical method itself. One way to investigate the method of philosophy would be to proceed by some meta-method and from its principles construct the correct method for philosophy. But obviously that is an impossible approach. The meta-method is itself part of philosophy, and so we can’t decide on which meta-method we should use until we have first decided upon the method of philosophy. And so we can’t even get started. Such considerations led me to think that these problems blocked any further thinking about the method of philosophy itself, that we would simply be forced to choose a method on basically non-rational principles. However, while we may not be able to construct the proper method for philosophy from first principles there is nothing stopping us from imploding various philosophical methods until only a few are left. Ideally only one would remain and that would simply be the philosophical method. But I am not committed to that idea, indeed the number of methods which don’t implode may be numerous. Still, by imploding some of them we clear out the “space” of methods, there are many similar methods used by philosophers with similar goals, and it is reasonable to expect implosion to sweep away some of them, leaving the remaining options at least more distinct. Although we may be forced to make a non-rational choice about which of the remaining methods to pick at least we have improved our situation, so that when we are motivated to select a philosophical method because it produces a certain kind of results or proceeds in a certain kind of way there is a single un-imploded method that stands out as satisfying our criteria.
Obviously I can’t hope to implode any significant possibilities in the remainder of this post, so let me conclude by simply making a few remarks about how we might proceed in imploding methods. The best way is, of course, show that the method results in a philosophical position that denies the correctness of the method, but such an option may not always be available. More promising is the possibility of discovering hidden commitments in the nature of the method, and then demonstrating that the method fails to live up to those commitments. For example, a commitment to a logical method, one that condones contradiction, may be demonstrating an implicit commitment to truth, because it is the desire to have true theories that often underlies such rules (if you don’t care about truth then contradiction isn’t a problem). If the method in turn is actually unable to produce true theories (for example, it endorses a number of competing theories) then clearly the method is failing by its own standards because it isn’t ensuring the truth of the theories produced.