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Sven Ove Hansson |
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Professor and Head of
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2. What example(s) from your work illustrates the role formal methods can play in philosophy? I would like to give three examples that can hopefully illustrate more general points about formal models in philosophy. The first example is the interdefinability of some of the central terms of moral discourse. There are two major proposals in the literature on how to define “good” in terms of “better”. One is Brogan’s proposal to equate “good” with “better than its negation”. The other proposal was put forward by Chisholm and Sosa. They define “good” as “better than X”, where X is some indifferent state of affairs. Since both these definitions are intuitively reasonable, an obvious question is under what conditions they are equivalent. This is a question that can be asked informally, but only answered with formal methods. It turned out that they are only equivalent under what I would consider to be rather special conditions. A similar and even more interesting issue concerns the interrelations between values and norms. Too little attention has been paid to the distinction between these two categories. A value statement does not have the inherent action-guiding or action-motivating force that a normative statement has. So the two categories are distinct. Nevertheless, they are not unconnected. It would be strange to say to someone what is the worst thing that she can do in a certain situation, and then go on to tell her that she ought to do it. To make a long story short, I am convinced that George Moore was right when he said that norms and values can be extensionally but not intensionally equivalent. I believe that the essential (extensional) connection can be best expressed in the form of a very simple principle on the negative side of the value-scale: “What is worse than something forbidden is itself forbidden.” Note that this is not equivalent to the idea that what is better than something obligatory is itself obligatory. It is morally obligatory for me to offer a starving fellow-being a nourishing meal. Arguably, it is also morally better for me to offer a meal that is both nourishing and delicious. It does not seem to follow that it is obligatory for me to offer the latter type of meal. The very simple principle I referred to, “What is worse than something forbidden is itself forbidden,” is sufficient for building a deontic logic in which we get rid of all the standard paradoxes of deontic logic. These paradoxes are, by the way, clear examples of issues of the third type that I just referred to. The second example is the specification of alternative sets. Again, a very simple insight can be used to clarify important philosophical issues. Again this insight has its full force only in a formalized treatment. The insight I refer to is that preferences are not sufficiently precise unless the set of alternatives is specified. Consider for instance the money-pumps that are so popular in decision theory. A money-pump is a hypothetical construction, obtained by appending monetary rewards to the alternatives in a decision that did not originally contain these rewards. Much confusion can be avoided by just explicitly constructing the new alternative set instead of performing the analysis in the original alternative set that contains no monetary rewards. However, instead of going into details about that I would like to mention how the same basic insight can be applied in the analysis of social decisions. Richard Wollheim's democratic paradox is illustrative. Wollheim asks us to consider an individual who endorses the democratic procedure, or “democratic machine”. This person prefers a certain social state p to its negation ¬p, but as a democrat she also wants the democratic decision on p to be respected. It turns out that a democratic decision is made in favour of ¬p. Now, how should our democrat react? Since she wants the majority's will to be respected, she prefers ¬p to p. But she regrets the majority's position for the simple reason that she in fact prefers p to ¬p. How can she both prefer p to ¬p and ¬p to p? This problem can be solved if we use an adequate description of the states of affairs that her preferences refer to. These states include not only p and its negation, but also information about what the “democratic machine” has decided. We can use the predicate D to denote democratic decisions. Thus Dp means: “A valid democratic decision in favour of p has been made.” Comparisons should then not be made between p and ¬p but between the four states of affairs Dp &p, Dp &¬p, D¬p &p, and D¬p &¬p. A democrat who voted for p may nevertheless prefer D¬p &¬p to D¬p &p. That she prefers p to ¬p, in the sense mentioned by Wollheim, can be expressed as a preference that refers only to alternatives in which the democratic decision is respected, i.e. she prefers Dp &p to D¬p &¬p. That she prefers ¬p to p can be expressed as a preference restricted to cases in which D¬p holds, i.e. she prefers D¬p &¬p to D¬p &p. More importantly, this insight about alternative sets can be applied in the formal study of social choices and decisions, in the tradition that was developed by Kenneth Arrow. In the standard social choice formalism, the individuals who take part in a voting procedure are assumed to have preferences that refer to the alternatives on which they vote. This is quite a natural starting-point. If we are going to vote on the alternatives x, y, and z, it is reasonable to assume that we all come to the meeting with preferences over the set consisting of these three alternatives, and vote accordingly. However, as participants in collective decision procedures we often have preferences that do not refer exclusively to these options (decision-alternatives). Besides wanting the outcome to be as good as possible (according to your own standard), you may for instance prefer the decision to be taken by as large a majority as possible. Such preferences often lead a committee member to vote for her second or third best alternative in order to contribute to unanimity. Or you may prefer to be yourself part of the winning coalition, etc. I started to work in this area with the conviction that we need a representation of individual preferences that is capable of representing these types of procedural preferences. It turned out that this can be done surprisingly well with a very simple construction: The set of preference-alternatives (comparison classes) is equal to the set of possible voting patterns, i.e. the set of complete descriptions of how all participants vote. Consider three persons who vote, according to the simple majority rule, between the alternatives x, y, and z. Voting patterns can be represented by vectors, such that for instance <y,x,x> represents the voting pattern in which the first participant votes for y and the two others for x. In Arrow’s framework, each of the three participants has a preference ordering over the set consisting of x, y, and z. In the modified framework, each of them has a preference ordering over the set of voting patterns. This makes it possibly to express procedural references like the ones I just mentioned. Suppose for instance that, informally speaking, one of the voters is in favour of x but is also in favour of unanimity, and that she gives higher priority to unanimity than to the difference between her preferred x and her second-best z. Such a person may prefer <x,x,x> to <z,z,z> and <z,z,z> to <x,z,z>. Needless to say, a multitude of issues concerning strategic voting, coalition formation etc. can be expressed and analyzed game-theoretically in this framework. My third example concerns the definition of epistemic coherentism. According to the standard view, “all beliefs” in a coherentist system are capable of contributing to the justification of other beliefs. In studies of belief revision I was led to pay attention to beliefs that we have as “mere logical consequences” of other beliefs. For a simple example, since I believe that Paris is the site of the French foreign ministry (p) I also believe that either Paris or Quito is the site of the French foreign ministry (p∨q). However, this latter belief does not have an independent standing; it stands or falls with the former. What role can such merely derived beliefs have in relation to coherentism? I hope to have shown that a coherence theory that includes all such beliefs has quite implausible consequences and that therefore, we have to revise coherentism. If I am right, then coherentists will have to recognize that certain beliefs (the merely derived beliefs) are mere epiphenomena in the sense that they do not contribute to the justification of other beliefs. However, the rest of the beliefs, those that are not merely derived in this sense, do not correspond to the basic beliefs referred to in foundationalist epistemology. The relationship between coherentism and foundationalism seems to be different from what we have previously believed. Issues like this can only be investigated if we take the decisive step from the semi-formal style that has dominated in epistemology to a fully formalized framework. |
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