Now we have to say a couple of words about the relation of closeness (or similarity) between possible worlds. Formally, it is a two-place relation relativised to the actual world: “world w1 is more similar to the actual world than world w2”, and it is assumed to possess standard properties, such as asymmetricity, transitivity and linearity, plus minimality (the actual world is closer to itself than any other world). But what properties of possible worlds should be taken into account when evaluating their relative similarity with respect to the actual world? Let us observe that two aspects of similarity can be taken into account: similarity with respect to individual facts and similarity with respect to laws. It may seem that the similarity with respect to laws should be seen as more important than the similarity with respect to individual facts, and consequently that a world with laws different than those in the actual world should be seen as more distant than any world with the same laws but different individual facts. But this assumption leads to unintuitive consequences, as Lewis points out. Suppose that we are working under the assumption of determinism, i.e. the assumption that the complete state of the world at a given moment t, together with the laws, uniquely determine all the later states. From this it follows that if we consider a world w which differs from the actual world at a moment t, and has all the actual laws, w would have to differ from the actual world at all moments preceding t. But this implies the following counterfactual: “If I sneezed now, the state of the universe would be different at any past moment t”. Counterfactuals for which the antecedent describes an event happening later than the event described by the conditional are called “backtracking”. Lewis maintains that backtracking counterfactuals are usually considered incorrect in standard discourse. In his approach backtracking counterfactuals come out false even under determinism, because possible worlds in which a small violation of laws (“a miracle”) makes it possible for the antecedent-event to occur are usually closer to the actual world than the worlds in which the differences in individual facts stretch infinitely into the past. The world in which we evaluate the counterfactual “If I sneezed at t, then ...” is exactly identical with the actual world up to moment t, when a small miracle occurs making it possible for me to sneeze.
Let us return to the analysis of causation done with the help of counterfactual conditionals. The elimination of backtracking counterfactuals advocated by Lewis solves the main problems affecting the regularity approach: the problem of mixing up causes and effects and the problem of how to distinguish causal relations from the common cause correlations. If an event x of type A causes an event y of type B, the counterfactual “If y had not happened, x would not have happened beforehand” is not (typically) true, because it is a backtracking counterfactual. To evaluate it, we take a possible world which is identical with the actual one up to the moment when y is supposed to occur, and in such a world x happens, but a small miracle prevents y from happening. Regarding the common cause case in which A causes B and then C, it is not true that if B hadn’t occur, C would not have occurred, because A would still be present, causing C to happen. The elimination of B is achieved again not by eliminating its cause A via a backtracking counterfactual (which would eliminate C as well), but by assuming a small miracle which happens just before B and makes it disappear.
But Lewis’s account of causation has its own share of troublesome cases. The identification of the causal relation with the relation of counterfactual dependence between distinct events leads to difficulties with the cases of pre-emption. Suzie’s throw is clearly a cause of the bottle’s shattering, and yet there is no counterfactual dependence between the two events, due to the presence of Billy and his stone. And the counterfactual “If Suzie hadn’t thrown her stone, Billy would have thrown his” is a normal, forward-looking counterfactual which does not require backtracking. Lewis’s response to this case is the following modification of the definition of causal relation. Event x is a cause of event y iff there are events x1, x2, ..., xn such that x1 is counterfactually dependent on x (meaning that if x hadn’t happened, x1 would not have happened), x2 is counterfactually dependent on x1, ..., and y is counterfactually dependent on xn. In the pre-emption case this modification works as follows. We pick an event X between the act of throwing the stone and the shattering such that at its moment Billy has already given up on his throw (this event may be that the stone is flying to its target at a certain speed). Now we can observe that X is counterfactually dependent on Suzie’s throw (if she hadn’t thrown, her stone would not have been flying towards the target), while the shattering is counterfactually dependent on X (if X hadn’t happened, the bottle would not have shattered). The crucial assumption is again that no backtracking is allowed, for we cannot accept that if Suzie’s stone hadn’t been flying, Billy would have thrown his stone). Lewis’s modification has one more advantage: it ensures that the causal relation is transitive (as we remember, the relation of counterfactual dependence is not transitive).
However, Lewis’s analysis faces more threats from modified cases of pre-emption. Suppose that in the Suzie and Billy case Billy has actually thrown his stone, but Suzie’s stone has reached the bottle first, thus pre-empting Billy’s throw. In this case, known as late pre-emption, Lewis’s improved analysis still gives the wrong answer, because there is no moment during the flight of Suzie’s stone at which we could say that if there had been no stone, the bottle would not have shattered. Another troublesome case is called “trumping pre-emption”. A major and a sergeant both shout the same order to a soldier. The soldier obeys, but given the military hierarchy it looks like it was the major’s order and not the sergeant’s which caused the soldier’s action. But there is no counterfactual dependence: if the major’s had not given the command, the soldier would have obeyed the sergeant’s order.
Lewis considered several possible corrections to his approach in order to deal with the problems of late pre-emption and trumping pre-emption. One possibility is to adopt a conception of events whose identity conditions are so strict that even a small modification produces a numerically distinct event (such events are called ‘fragile’). If the shattering of the bottle is a fragile event, then the shattering produced by Billy’s stone is numerically different from the shattering brought about by Suzie’s stone (the stones are flying from slightly different directions, with slightly different speeds, etc.). Thus it is true that if Suzie’s throw had not occurred, this particular shattering would not have occurred (although a similar one would have replaced it). Notice that the fragile character of events is supported in Kim’s conception, according to which events are differentiated by properties, and quantitative properties can be close in value and yet numerically distinct. But an undesirable consequence of this solution is that now plenty of insignificant background conditions will become causes of a given event. Even a gust of wind counts as a cause of the shattering, because it certainly, although minimally, affected the trajectory of the stone, so it is true that if there had been no gust of wind, there would have been no actual shattering, but a very similar yet numerically distinct one. On the other hand, the solution based on the assumption of fragility may be defended against this objection, if we observe that the purported cause (the gust of wind) is itself a fragile event. Hence, the counterfactual assumption that there was no gust of wind can be made true by assuming that the gust of wind was slightly different, and given that the dependence of the stone’s trajectory on the wind is very weak, it is natural to expect that a slight change of the strength of the wind would produce no discernible differences in the qualities of the shattering.
But even the fragility solution is unable to cope with the following counterexample. Suppose that at a point where the railway tracks split two terrorists plan an attack on a coming train. One of them operates the switch, sending the train on a dead end track and causing a train wreck. The second terrorist acts as a back-up, in case the first one does not carry out the sabotage. Clearly, there is no counterfactual dependence: if the first terrorist had not moved the switch, the second one would have acted and the train would have crashed. But the counterfactual dependence cannot be restored even if we assume that all events are fragile. The train wreck is identical regardless of which terrorist moves the switch, or when exactly the switch is moved, or how the switch is moved. The reason is that the characteristic of the train wreck depends solely on the properties of the train and its travel (speed, brakes, etc.), and not the manner in which the switch is moved.
Reading:
E.J. Lowe, Chapter 10, "Counterfactuals and event causation", A Survey of Metaphysics, pp. 174-191.
Showing posts with label Lewis David. Show all posts
Showing posts with label Lewis David. Show all posts
Wednesday, May 5, 2010
Monday, May 3, 2010
Causation and counterfactuals
Let us now consider the way Mackie characterizes sufficient and necessary conditions. Standard definitions of these notions are as follows:
A is a sufficient condition of B iff, if A occurs, B occurs
A is a necessary condition of B iff, if B occurs, A occurs (or, equivalently, if A doesn’t occur, B doesn’t occur).
But these definitions are correct only when A and B are general types of events, and not names of individual objects (in that case the right-hand sides of the equivalences have to be interpreted as general statements: “For all x, if x is A and x occurs, then there is a y such that y is B and y occurs”). If A and B are singular names, the aforementioned definitions wrongly imply that all actual events are sufficient and necessary conditions of each other. Mackie attempts to give a better analysis applicable to singular claims, not general ones. His analysis is presented with the help of following equivalences:
x is a sufficient condition of y iff since x occurred, y occurred
x is a necessary condition of y iff if x had not occurred, y would not have occurred.
Mackie stresses that the conditionals used in each explanans can’t be interpreted as material conditionals. But this creates an immediate problem for the regularity approach, as one of its main assumptions is that causation should be explicated without resorting to modal notions, such as necessity or possibility. Mackie suggests the following interpretations of the non-material conditionals used above. He treats them as “telescoped arguments” in which some premises are omitted. For instance, the statement “If the short circuit had not occurred, there would have been no fire” can be expanded into the statement that there are some true universal propositions which together with true statements about the conditions of the house and together with the supposition that the short circuit did not occur logically imply that there was no fire. A similar analysis can be given for the statement “Since x occurred, y occurred”.
One of the most serious challenges for any account of causation is presented by the so-called redundant causation. There are two main types of redundant causation: overdetermination and pre-emption. Overdetermination occurs when there is more than one acting cause, each of which is sufficient for the effect to occur. An example can be an execution by a firing squad, in which each bullet causes a lethal injury. Is each individual shot a cause of the death of the condemned man? In Mackie’s approach the answer is negative, because one of his characteristics of causation is that no alternative sufficient conditions are present (a cause is necessary post factum for the effect). Only the disjunction of all shots is necessary in this sense.
The case of pre-emption can be described using the following example. Two children, Billy and Suzie, are throwing stones at a bottle. Seeing that Suzie has thrown her stone and shattered the bottle, Billy does not hurl his stone, but if Suzie had not thrown, Billy would have thrown his stone. We call this pre-emption, because Suzie’s throw pre-empts Billy’s action which would otherwise have taken place. Any reasonable theory of causation should imply that Suzie’s throw was the actual cause of the shattering. But wasn’t her throw unnecessary, given that Billy was present as a backup? Are the conditions imposed by Mackie satisfied? It turns out that they are, in spite of our initial worries. According to Mackie’s definition, there has to be a set of conditions X such that together with Suzie’s throw (let’s call it A) they would constitute a sufficient condition for the shattering, and moreover no alternative sets of sufficient conditions can be present. We can reasonably believe that without A Bill’s throw together with its conditions would create a different sufficient condition for the shattering of the bottle, but this set is not present at the time of Suzie’s throw. Suzie’s throw is still a necessary part of its own set of conditions – without it this set would not be sufficient, although a different one would be. So Mackie’s definition gives the right answer in the case of pre-emption.
David Lewis has noted that all regularity theories of causation, including Mackie’s, have problems with distinguishing causes from effects, and direct causal links from correlations arising due to a common cause. If only events of type A can cause B, we can say that a given event B is a sufficient condition (or part of a sufficient condition) of A, and hence B is wrongly classified as a cause of A. Even if we artificially exclude this possibility by stipulating that a cause has to be earlier than its effect, still the problem remains. Suppose that an event A causes B and C in succession, and that B can be created only by events of type A. In such a case B is a sufficient condition (or, as in Mackie’s conception, a necessary part of a sufficient condition) of A, and A is in turn a sufficient condition of C, hence B comes out to be a cause of C.
Lewis suggests an alternative account of causation: a counterfactual analysis. The simplest version of such an analysis (the so-called naive counterfactual analysis) is as follows: x is a cause of y iff if x had not occurred, y would not have occurred. But this definition is in need of serious corrections. For instance, suppose that I shut the door by slamming it. If I hadn’t shut the door, I wouldn’t have slammed it (we assume that each slamming shuts the door), but the shutting of the door is not a cause of its slamming. Similarly, if I hadn’t written the letter “L”, I would not have written the word “Lewis”, but the first did not cause the second. To eliminate these counterexamples, we have to assume that x and y are distinct events (i.e. they are not identical, nor one is part of the other). But in order to further advance the counterfactual analysis, we have to understand better the meaning of counterfactual conditionals.
Counterfactual conditionals can be generally presented as statements of the form “If it were (had been) the case that p, then it would be (have been) the case that q”. It is well known that sentences of that form are not truth-functional, i.e. the truth value of the entire complex statement is not determined by the truth values of its components. To see this, it suffices to compare the following two statements: “If Rodin’s sculpture ‘The Thinker’ were made out of wood, it would float” and “If Rodin’s sculpture ‘The Thinker’ were made out of wood, it would fly”. In both cases the antecedent and the consequent are false, and yet the first conditional is true, while the second false. The counterfactual connective is considered to be a modal one, and it receives an interpretation in terms of possible worlds, similar to that of necessity and possibility. The most commonly accepted analysis stipulates that the conditional “If it were p, then it would be q” is true if and only if q is true in all possible worlds in which p is true and which are closest to the actual world of all p-worlds. Thus the statement “If I threw a stone at a window, it would shatter” is true if in the possible worlds in which I throw the stone and which otherwise are as similar to the actual world as the truth of the antecedent allows, the window shatters. And this is what we expect to get, because in such worlds the laws of nature and the properties of materials such as glass and rock will be the same as in our world. On the other hand, if we considered a far away world in which glass is tougher than rock, the consequent would not be true. This shows that for a counterfactual to be true, the consequent does not have to be true in all worlds in which the antecedent is true (this truth condition defines the so-called strict conditional).
Counterfactual conditionals follow a slightly different logic than material conditionals or strict conditionals. Let us consider the three following logical laws: the law of the strengthening of the antecedent, the law of transposition and the law of transitivity. The first one states that if p implies q, then the conjunction p and r also implies q. But consider the following example: If someone shot a gun pointed at my chest, I would be dead, but if someone shot at me and I was wearing a bulletproof vest, I would survive. Given that in the actual world I am not wearing a bulletproof vest now, both statements seem to be true, which shows that the law of the strengthening of the antecedent is violated for counterfactual conditionals. The reason behind this is that we choose different possible worlds to evaluate both statements: the first one is the world where I am being fired at, but I am not wearing any protection, and the second one is the one in which I am protected by a bulletproof vest.
The law of transposition states that if p implies q, not-q implies not-p. A counterexample to this law is as follows: it is true that if I didn’t come to my lecture, the building in which I am lecturing would still stand. But from this it does not follow that if the building collapsed (for instance because of an earthquake), I would still come to the lecture. Finally, the law of transitivity prescribes that if p implies q, and q implies r, then p implies r. We already presented a case which violates this law when we discussed the problem of the transitivity of the causal relation. In this case p = the bomb was not planted, q = the bomb was not defused, r = the politician was assassinated. We can also note that the violation of transitivity follows directly from the violation of the strengthening of the antecedent, given that it is a logical truth that if it were p and r, then it would be p. Now we can choose p, q and r such that it is true that if it were p, it would be q, but it’s false that if it were p and r, then it would be q, and the transitivity is violated.
Reading:
E.J. Lowe, Chapter 8 "Counterfactual conditionals", pp. 137-154, A Survey of Metaphysics.
A is a sufficient condition of B iff, if A occurs, B occurs
A is a necessary condition of B iff, if B occurs, A occurs (or, equivalently, if A doesn’t occur, B doesn’t occur).
But these definitions are correct only when A and B are general types of events, and not names of individual objects (in that case the right-hand sides of the equivalences have to be interpreted as general statements: “For all x, if x is A and x occurs, then there is a y such that y is B and y occurs”). If A and B are singular names, the aforementioned definitions wrongly imply that all actual events are sufficient and necessary conditions of each other. Mackie attempts to give a better analysis applicable to singular claims, not general ones. His analysis is presented with the help of following equivalences:
x is a sufficient condition of y iff since x occurred, y occurred
x is a necessary condition of y iff if x had not occurred, y would not have occurred.
Mackie stresses that the conditionals used in each explanans can’t be interpreted as material conditionals. But this creates an immediate problem for the regularity approach, as one of its main assumptions is that causation should be explicated without resorting to modal notions, such as necessity or possibility. Mackie suggests the following interpretations of the non-material conditionals used above. He treats them as “telescoped arguments” in which some premises are omitted. For instance, the statement “If the short circuit had not occurred, there would have been no fire” can be expanded into the statement that there are some true universal propositions which together with true statements about the conditions of the house and together with the supposition that the short circuit did not occur logically imply that there was no fire. A similar analysis can be given for the statement “Since x occurred, y occurred”.
One of the most serious challenges for any account of causation is presented by the so-called redundant causation. There are two main types of redundant causation: overdetermination and pre-emption. Overdetermination occurs when there is more than one acting cause, each of which is sufficient for the effect to occur. An example can be an execution by a firing squad, in which each bullet causes a lethal injury. Is each individual shot a cause of the death of the condemned man? In Mackie’s approach the answer is negative, because one of his characteristics of causation is that no alternative sufficient conditions are present (a cause is necessary post factum for the effect). Only the disjunction of all shots is necessary in this sense.
The case of pre-emption can be described using the following example. Two children, Billy and Suzie, are throwing stones at a bottle. Seeing that Suzie has thrown her stone and shattered the bottle, Billy does not hurl his stone, but if Suzie had not thrown, Billy would have thrown his stone. We call this pre-emption, because Suzie’s throw pre-empts Billy’s action which would otherwise have taken place. Any reasonable theory of causation should imply that Suzie’s throw was the actual cause of the shattering. But wasn’t her throw unnecessary, given that Billy was present as a backup? Are the conditions imposed by Mackie satisfied? It turns out that they are, in spite of our initial worries. According to Mackie’s definition, there has to be a set of conditions X such that together with Suzie’s throw (let’s call it A) they would constitute a sufficient condition for the shattering, and moreover no alternative sets of sufficient conditions can be present. We can reasonably believe that without A Bill’s throw together with its conditions would create a different sufficient condition for the shattering of the bottle, but this set is not present at the time of Suzie’s throw. Suzie’s throw is still a necessary part of its own set of conditions – without it this set would not be sufficient, although a different one would be. So Mackie’s definition gives the right answer in the case of pre-emption.
David Lewis has noted that all regularity theories of causation, including Mackie’s, have problems with distinguishing causes from effects, and direct causal links from correlations arising due to a common cause. If only events of type A can cause B, we can say that a given event B is a sufficient condition (or part of a sufficient condition) of A, and hence B is wrongly classified as a cause of A. Even if we artificially exclude this possibility by stipulating that a cause has to be earlier than its effect, still the problem remains. Suppose that an event A causes B and C in succession, and that B can be created only by events of type A. In such a case B is a sufficient condition (or, as in Mackie’s conception, a necessary part of a sufficient condition) of A, and A is in turn a sufficient condition of C, hence B comes out to be a cause of C.
Lewis suggests an alternative account of causation: a counterfactual analysis. The simplest version of such an analysis (the so-called naive counterfactual analysis) is as follows: x is a cause of y iff if x had not occurred, y would not have occurred. But this definition is in need of serious corrections. For instance, suppose that I shut the door by slamming it. If I hadn’t shut the door, I wouldn’t have slammed it (we assume that each slamming shuts the door), but the shutting of the door is not a cause of its slamming. Similarly, if I hadn’t written the letter “L”, I would not have written the word “Lewis”, but the first did not cause the second. To eliminate these counterexamples, we have to assume that x and y are distinct events (i.e. they are not identical, nor one is part of the other). But in order to further advance the counterfactual analysis, we have to understand better the meaning of counterfactual conditionals.
Counterfactual conditionals can be generally presented as statements of the form “If it were (had been) the case that p, then it would be (have been) the case that q”. It is well known that sentences of that form are not truth-functional, i.e. the truth value of the entire complex statement is not determined by the truth values of its components. To see this, it suffices to compare the following two statements: “If Rodin’s sculpture ‘The Thinker’ were made out of wood, it would float” and “If Rodin’s sculpture ‘The Thinker’ were made out of wood, it would fly”. In both cases the antecedent and the consequent are false, and yet the first conditional is true, while the second false. The counterfactual connective is considered to be a modal one, and it receives an interpretation in terms of possible worlds, similar to that of necessity and possibility. The most commonly accepted analysis stipulates that the conditional “If it were p, then it would be q” is true if and only if q is true in all possible worlds in which p is true and which are closest to the actual world of all p-worlds. Thus the statement “If I threw a stone at a window, it would shatter” is true if in the possible worlds in which I throw the stone and which otherwise are as similar to the actual world as the truth of the antecedent allows, the window shatters. And this is what we expect to get, because in such worlds the laws of nature and the properties of materials such as glass and rock will be the same as in our world. On the other hand, if we considered a far away world in which glass is tougher than rock, the consequent would not be true. This shows that for a counterfactual to be true, the consequent does not have to be true in all worlds in which the antecedent is true (this truth condition defines the so-called strict conditional).
Counterfactual conditionals follow a slightly different logic than material conditionals or strict conditionals. Let us consider the three following logical laws: the law of the strengthening of the antecedent, the law of transposition and the law of transitivity. The first one states that if p implies q, then the conjunction p and r also implies q. But consider the following example: If someone shot a gun pointed at my chest, I would be dead, but if someone shot at me and I was wearing a bulletproof vest, I would survive. Given that in the actual world I am not wearing a bulletproof vest now, both statements seem to be true, which shows that the law of the strengthening of the antecedent is violated for counterfactual conditionals. The reason behind this is that we choose different possible worlds to evaluate both statements: the first one is the world where I am being fired at, but I am not wearing any protection, and the second one is the one in which I am protected by a bulletproof vest.
The law of transposition states that if p implies q, not-q implies not-p. A counterexample to this law is as follows: it is true that if I didn’t come to my lecture, the building in which I am lecturing would still stand. But from this it does not follow that if the building collapsed (for instance because of an earthquake), I would still come to the lecture. Finally, the law of transitivity prescribes that if p implies q, and q implies r, then p implies r. We already presented a case which violates this law when we discussed the problem of the transitivity of the causal relation. In this case p = the bomb was not planted, q = the bomb was not defused, r = the politician was assassinated. We can also note that the violation of transitivity follows directly from the violation of the strengthening of the antecedent, given that it is a logical truth that if it were p and r, then it would be p. Now we can choose p, q and r such that it is true that if it were p, it would be q, but it’s false that if it were p and r, then it would be q, and the transitivity is violated.
Reading:
E.J. Lowe, Chapter 8 "Counterfactual conditionals", pp. 137-154, A Survey of Metaphysics.
Wednesday, January 20, 2010
Identity and possible worlds
Is the relation of numerical identity contingent or necessary? It seems that in many cases identity statements are contingent. Gottlob Frege explained how it is possible that true identity statements can be informative. We may understand the meanings of names “a” and “b” without knowing that they refer to one and the same object, hence the statement “a = b” tells us more than the trivial truth that an object is identical with itself. It is tempting to interpret Frege’s result as implying that the identity “a = b” could be false, i.e. that there is a possible world in which “a” and “b” refer to different objects while retaining their original meanings. Saul Kripke famously questioned that suggestion. Kripke claims that all identity statements are in fact necessarily true, and he presents a formal argument in support of his claim. The argument is based on two premises. (1) Every object is necessarily identical with itself (For all x, it is necessary that x = x). (2) If x has property P and y is identical with y, then y has P. Premise (2) is a variant of Leibniz’s law. We can now use the formula “It is necessary that x = x” and, given that x = y, we can substitute y for x, obtaining “It is necessary that x = y”. In conclusion, (1) and (2) lead to the statement: (3) For all x, y, if x = y, then it is necessary that x = y. From (3) it follows that if we take any proper names “a” and “b”, then if only it is true that a = b, it is necessarily so.
But how can we reconcile this formal result with the intuition expressed at the beginning of the previous paragraph? In the actual world the names “Hesperus” and “Phosphorus” refer to the same object: the planet Venus. But couldn’t it be the case that in some other possible world Hesperus and Phosphorus were different objects? Kripke explains away this intuition by pointing out that the possible situation in which we would be tempted to say that Hesperus is not identical with Phosphorus can be reinterpreted in such a way that the identity will be preserved. According to Kripke, terms “Hesperus” and “Phosphorus” are so-called rigid designators, i.e. terms that refer to the same object in all possible worlds in which they refer to anything at all. “Hesperus” is not synonymous with the description “The brightest star on the morning sky”, nor is “Phosphorus” synonymous with “The brightest star on the evening sky”. These descriptions are used contingently in the actual world to fix the reference of both names. In another world the descriptions may not pick the object which is the referent of both terms (i.e. the planet Venus), but if Venus exists in this world, both terms “Hesperus” and “Phosphorus” will continue referring to it.
It may be pointed out that when we restrict the thesis of the necessity of identity statements to rigid designators, its truth becomes quite trivial. However, Kripke claims that his thesis has non-trivial consequences regarding for instance the mind-body controversy. Without going into too much detail, let us consider the Identity Theory, according to which mental events are numerically identical with some physical events. The identity theorists maintain that their claim is true but only contingently, i.e. in some possible worlds there are beings that possess particular neurological states but lack mental states (so-called zombies), and in other possible worlds there may be disembodied minds. But according to Kripke’s analysis, if the statement “This pain is identical with this stimulation of the nervous system” is true, it is necessary, and hence neither zombies nor disembodied minds are possible. But couldn’t we explain away these possible scenarios in a similar way we have redescribed the Hesperus-Phosphorus case? Namely, couldn’t we just say that the rigid designators “this pain” and “this stimulation of the nervous system” are contingently associated with some descriptions, which fail to pick the same object in alternative possible worlds? Unfortunately, as Kripke points out, the terms referring to mental states have no associated descriptions, because their reference is fixed directly by the person that is in a given mental state. So the case of the mind-body identification is different from the case of the Hesperus-Phosphorus identity.
What is the ontological status of possible worlds? One radical answer to this question is known under the name of modal realism (possibilism), which has been proposed by David Lewis. Modal realism consists of several claims. One of them is that possible worlds are made up of concrete, spatiotemporal objects. Possible worlds are not fictions or abstract constructions, but real places with flesh-and-blood inhabitants. Things contained in other possible worlds exist in the same fundamental sense as things in the actual world. Thus it is legitimate to assume that the variables of the existential quantifier range over all possible worlds. For the sake of convenience we may want to relativise the notion of existence to a particular world (speaking about “existing-in-a-world”), but this relativisation does not imply any significant ontological difference. The second element of the doctrine of modal realism is that there is nothing fundamental and absolute about the notion of actual world. The term “actual” is indexical (analogously to terms such as “here”, “now”, “I”, whose meaning depends on the context of utterance), which means that each possible world is actual from the perspective of its inhabitants. Finally, modal realism assumes that possible worlds are spatiotemporally and causally separated from each other. One important consequence of these assumptions is that one object cannot exist in more than one world. Transworld identity is an empty notion in modal realism. But how can we interpret the modal statement “This two-metre high tree could be five metres high” without assuming that this tree can exist in other possible worlds? Lewis solves this problem by introducing the notion of a counterpart. This tree has many counterparts in other possible worlds – trees that are sufficiently similar to it, but not numerically identical. An object could have a given property, if one of its counterparts possesses this property in some possible world.
The main motivation for modal realism comes from its radically reductive character. Lewis subscribes to nominalism and he uses the concept of concrete possible worlds to give a reductive analysis of various abstract entities, such as properties, propositions or meanings. For instance a proposition is simply defined as a class of possible worlds (the proposition “Snow is white” is the class of possible worlds in which snow is white). According to this definition, proposition p is true in a world w, if w is an element of the class of worlds p. Properties, in turn, are defined as functions which assign a set of objects to each possible world. These sets are intuitively understood as consisting of objects that possess a given property in a particular world. This definition avoids the well-known difficulty resulting from the fact that two numerically distinct properties can nevertheless have the same extension in the actual world. The property of being an elephant and the property of being the largest land animal living on Earth now may have the same extensions in the actual world, but there are possible worlds in which elephants are not the largest living land animals. However, reductions offered by modal realists are often criticised as not entirely adequate. For instance, it is pointed out that all necessary true propositions become identical. But we believe that there is a difference between the statements “2+2 = 4” and “It is snowing or it is not snowing”. Similarly, it can be maintained that the property of being triangular and being trilateral are different, and yet in all possible worlds their extensions are identical.
Modal realism is often rejected on grounds of its extravagant ontology. An alternative position is offered in the form of actualism (moderate realism). Alvin Plantinga suggests that possible worlds are mere theoretical constructions which enable us to formulate non-reductive explanations of modal notions. The only genuine world is the actual world, and the quantification in our language should be restricted to objects in the actual world. Possible worlds different from the actual world can be defined as complete and consistent sets of propositions, or better as complete and consistent states of affairs (situations). Each proposition corresponds to a given state of affairs. All states of affairs are abstract objects which exist in the actual world, but only some of them obtain (those that correspond to true propositions). False propositions describe existing states of affairs which nevertheless don’t obtain. According to actualism, the expression “actual” has an absolute meaning: it refers to one and only world that truly exists.
One important difference between actualism and possibilism regards the notion of transworld identity. Actualism admits that one object can exist in many possible worlds. But how are we to understand this statement, if possible worlds do not exist literally, but are mere constructions out of abstract objects? Plantinga proposes the following solution. That an object a exists in a possible world w means that if w were actual, a would exist in it. Note that the explicans is a counterfactual conditional, but it cannot be interpreted in terms of possible worlds, since this would require an introduction of second-order possible worlds (a possible world in which another possible world would be actual). This fact shows that Plantinga’s conception does not offer a fully reductive analysis of modal notions, and that some modalities have to be taken as primitive.
Readings:
M.J. Loux, "The necesary and the possible", pp. 153-186, Metaphysics: A Contemporary Introduction.
E.J. Lowe, "Necessity and identity", pp. 84-95, "Possible worlds", pp. 120-133, A Survey of Metaphysics.
But how can we reconcile this formal result with the intuition expressed at the beginning of the previous paragraph? In the actual world the names “Hesperus” and “Phosphorus” refer to the same object: the planet Venus. But couldn’t it be the case that in some other possible world Hesperus and Phosphorus were different objects? Kripke explains away this intuition by pointing out that the possible situation in which we would be tempted to say that Hesperus is not identical with Phosphorus can be reinterpreted in such a way that the identity will be preserved. According to Kripke, terms “Hesperus” and “Phosphorus” are so-called rigid designators, i.e. terms that refer to the same object in all possible worlds in which they refer to anything at all. “Hesperus” is not synonymous with the description “The brightest star on the morning sky”, nor is “Phosphorus” synonymous with “The brightest star on the evening sky”. These descriptions are used contingently in the actual world to fix the reference of both names. In another world the descriptions may not pick the object which is the referent of both terms (i.e. the planet Venus), but if Venus exists in this world, both terms “Hesperus” and “Phosphorus” will continue referring to it.
It may be pointed out that when we restrict the thesis of the necessity of identity statements to rigid designators, its truth becomes quite trivial. However, Kripke claims that his thesis has non-trivial consequences regarding for instance the mind-body controversy. Without going into too much detail, let us consider the Identity Theory, according to which mental events are numerically identical with some physical events. The identity theorists maintain that their claim is true but only contingently, i.e. in some possible worlds there are beings that possess particular neurological states but lack mental states (so-called zombies), and in other possible worlds there may be disembodied minds. But according to Kripke’s analysis, if the statement “This pain is identical with this stimulation of the nervous system” is true, it is necessary, and hence neither zombies nor disembodied minds are possible. But couldn’t we explain away these possible scenarios in a similar way we have redescribed the Hesperus-Phosphorus case? Namely, couldn’t we just say that the rigid designators “this pain” and “this stimulation of the nervous system” are contingently associated with some descriptions, which fail to pick the same object in alternative possible worlds? Unfortunately, as Kripke points out, the terms referring to mental states have no associated descriptions, because their reference is fixed directly by the person that is in a given mental state. So the case of the mind-body identification is different from the case of the Hesperus-Phosphorus identity.
What is the ontological status of possible worlds? One radical answer to this question is known under the name of modal realism (possibilism), which has been proposed by David Lewis. Modal realism consists of several claims. One of them is that possible worlds are made up of concrete, spatiotemporal objects. Possible worlds are not fictions or abstract constructions, but real places with flesh-and-blood inhabitants. Things contained in other possible worlds exist in the same fundamental sense as things in the actual world. Thus it is legitimate to assume that the variables of the existential quantifier range over all possible worlds. For the sake of convenience we may want to relativise the notion of existence to a particular world (speaking about “existing-in-a-world”), but this relativisation does not imply any significant ontological difference. The second element of the doctrine of modal realism is that there is nothing fundamental and absolute about the notion of actual world. The term “actual” is indexical (analogously to terms such as “here”, “now”, “I”, whose meaning depends on the context of utterance), which means that each possible world is actual from the perspective of its inhabitants. Finally, modal realism assumes that possible worlds are spatiotemporally and causally separated from each other. One important consequence of these assumptions is that one object cannot exist in more than one world. Transworld identity is an empty notion in modal realism. But how can we interpret the modal statement “This two-metre high tree could be five metres high” without assuming that this tree can exist in other possible worlds? Lewis solves this problem by introducing the notion of a counterpart. This tree has many counterparts in other possible worlds – trees that are sufficiently similar to it, but not numerically identical. An object could have a given property, if one of its counterparts possesses this property in some possible world.
The main motivation for modal realism comes from its radically reductive character. Lewis subscribes to nominalism and he uses the concept of concrete possible worlds to give a reductive analysis of various abstract entities, such as properties, propositions or meanings. For instance a proposition is simply defined as a class of possible worlds (the proposition “Snow is white” is the class of possible worlds in which snow is white). According to this definition, proposition p is true in a world w, if w is an element of the class of worlds p. Properties, in turn, are defined as functions which assign a set of objects to each possible world. These sets are intuitively understood as consisting of objects that possess a given property in a particular world. This definition avoids the well-known difficulty resulting from the fact that two numerically distinct properties can nevertheless have the same extension in the actual world. The property of being an elephant and the property of being the largest land animal living on Earth now may have the same extensions in the actual world, but there are possible worlds in which elephants are not the largest living land animals. However, reductions offered by modal realists are often criticised as not entirely adequate. For instance, it is pointed out that all necessary true propositions become identical. But we believe that there is a difference between the statements “2+2 = 4” and “It is snowing or it is not snowing”. Similarly, it can be maintained that the property of being triangular and being trilateral are different, and yet in all possible worlds their extensions are identical.
Modal realism is often rejected on grounds of its extravagant ontology. An alternative position is offered in the form of actualism (moderate realism). Alvin Plantinga suggests that possible worlds are mere theoretical constructions which enable us to formulate non-reductive explanations of modal notions. The only genuine world is the actual world, and the quantification in our language should be restricted to objects in the actual world. Possible worlds different from the actual world can be defined as complete and consistent sets of propositions, or better as complete and consistent states of affairs (situations). Each proposition corresponds to a given state of affairs. All states of affairs are abstract objects which exist in the actual world, but only some of them obtain (those that correspond to true propositions). False propositions describe existing states of affairs which nevertheless don’t obtain. According to actualism, the expression “actual” has an absolute meaning: it refers to one and only world that truly exists.
One important difference between actualism and possibilism regards the notion of transworld identity. Actualism admits that one object can exist in many possible worlds. But how are we to understand this statement, if possible worlds do not exist literally, but are mere constructions out of abstract objects? Plantinga proposes the following solution. That an object a exists in a possible world w means that if w were actual, a would exist in it. Note that the explicans is a counterfactual conditional, but it cannot be interpreted in terms of possible worlds, since this would require an introduction of second-order possible worlds (a possible world in which another possible world would be actual). This fact shows that Plantinga’s conception does not offer a fully reductive analysis of modal notions, and that some modalities have to be taken as primitive.
Readings:
M.J. Loux, "The necesary and the possible", pp. 153-186, Metaphysics: A Contemporary Introduction.
E.J. Lowe, "Necessity and identity", pp. 84-95, "Possible worlds", pp. 120-133, A Survey of Metaphysics.
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