Nietzsche, F. “First Essay: ‘Good and Bad,’ ‘Good and Evil'” in On the Genealogy of Morals.

The following entry is a summary that was given by Mary Salvaggio during a graduate pro-seminar session at Columbia University on March 5, 2008. Mary Salvaggio is currently a Ph.D. student of philosophy at Columbia University. Many thanks for the entry, Mary.

SUMMARY:

In this essay, Nietzsche wants to explain the origins of our moral concepts. He focuses on the difference between the dichotomies of good and bad and good and evil. The ‘English Psychologists’ claim that “good” was originally used to refer to unegoistic useful actions by those that benefited from those actions. Nietzsche thinks that this is historically inaccurate and the utilitarian use of “good” has only arisen relatively recently. He suggests that in order to discover the true origins of the concept “good” we should look at the etymology of words we use to express this concept. I’m not going to discuss his claims about word origins, but he comes to the conclusion that goodness was first associated with nobility and that badness is associated with simpleness and the common man.

These results inspire Nietzsche to tell his own story about the origins of morality. His main idea is that “good” was first used by the noble classes to designate themselves and their actions. “Bad” was used to denote the opposite, namely, the lower classes. Those suffering under the noble class came up with the concept of “evil” to refer to their rulers. Our modern concept of “good” is not the original one used by the noble class, but comes about as a contrast to this idea of “evil”. Anything good in this sense is what is opposite to nobility. He calls the morals of the noble class a master morality and the morals of the lower classes is the slave morality. He then goes on to describe the origins and natures of both these moralities in more detail.

Noble men are powerful, healthy, and courageous. Their powerful natures are kept in check among themselves by the ties of tradition, custom, and mutual respect. However, when they are among foreigners, they feel completely free to murder, rape, and pillage. Nietzsche conceded that it is with some fairness that those encountering these men only as foreigners refer to them as barbaric. The noble man is ruled mostly by instinct and Nietzsche refers to them as predatory ‘blond beasts’. Examples of these nobles include the ancient Greeks and Romans as well as the Goths and Vikings.

Slave morality originated among the priestly class. They use the word “pure” to refer to themselves. In the beginning this only means following certain rules for cleanliness and diet. Priests are in general weak and unhealthy so they devise these customs to protect themselves against the dangers that noble men take on without a second thought. This favors a turning away from action and focusing inward instead. He thinks that Jews are the prime examples of a priestly class. When the priests have conflicts with the noble warrior class the priests obviously cannot win relying on physical strength alone. They must become clever and inventive in exacting revenge against the conquering warriors. This new emphasis on cleverness gives humanity depth. It also marks the first time that mankind becomes capable of evil. Nietzsche admits that without this development human history would be uninteresting and that humans would not be so different from other animals.

The revenge of these priests is the inversion of the value system of the noble class. All the qualities associated with goodness according to the master morality become evil to the slave moralist. Slave morality then redefines “good” to be that which is not evil. Resentment is the reactive nature of those with a slave morality. Since they lack the strength for the kind of true action and self affirmation that lead the nobles to claim goodness for themselves, the common man first requires an ‘evil’ external world to derive the concept of good as a secondary notion. It’s interesting that the first people capable of true evil use that term to describe their enemies. When in reality the noble class is as unmindful of evil as animals are. The ruling class can be guilty of misunderstanding or even contempt towards the lower classes, but this is nothing compared with the demonization of the nobles that is perpetrated by the priests.

Nietzsche thinks that this conception of the nobles as evil arises in part from a linguistic confusion. Since our sentences contain a subject and a predicate, we think that there are not only actions, but a subject that performs those actions and has an existence apart from the actions. According to Nietzsche there is only willing, and not some soul-like subject that does the willing. This confusion leads us to assume that the powerful man can choose to act with strength or with weakness and so can be blamed for acting with strength. The example of the lambs and the birds of prey illustrates this idea. It’s a mistake to call the birds of prey evil for eating little lambs. The birds of prey cannot become lambs any more than the lambs can become birds of prey. Similarly, the powerful cannot be blamed for acting from strength any more than the weak can be blamed for failing to be strong.

While Christianity appears at first glance to be a movement against the Jews, it is actually slave morality’s greatest victory. It is accomplished via the image of God crucified for the sake of all of mankind. This is the ultimate illustration of the subject/predicate mistake just mentioned. Here God becomes humble and weak as if it were possible that an all-powerful God could express itself as anything but strength. This idea is just absurd to someone with views like Nietzsche’s. The striking image of a humbled God helps spread slave morality throughout the word. For all of Christianity’s talk about love, it is a love born out of the hatred of the priests and an extension of that hatred. To see this, one only needs to notice the immense pleasure that Christians take from the idea of watching the strong suffer for all eternity. What kind of love is this?

Since the weak are forced to submit to the strong in this world, they imagine a new world, a ‘Kingdom of God’. Here the first shall become last and the meek will inherit the earth. Finally the common man will be rewarded for his lowness and the noble man will be punished for his power. The desire for a mystical union with God is merely a desire for nothingness. This desire for nothingness is the last resort for a will that has been thwarted in its other attempts at expression.

It is obvious which morality is currently winning. The mistake of most of Nietzsche’s contemporaries is a lack of historical insight that lead them to see the slave morality’s system of values as the only one that there has ever been. Nietzsche thinks of slave morality as a poison. It celebrates all that is weak and sickly about humanity while choking out all the qualities that made us proud to be human.

 

Lewis, David K. “Counterfactual Dependence and Time’s Arrow.” Nous, Vol. 13, No. 4, Special Issue on Counterfactuals and Laws. (Nov., 1979), pp. 455-476.

NOTE for the Reader: When and wherever one encounters “tA”, “tC”, “w0″, “w1″, “w2″, “w3″, and “w4″ in the summary below, one should keep in mind that Lewis writes “A”, “C”, “0”,”1″, “2”, “3”, and “4” as subscripts in the original article.

The Asymmetry of Counterfactual Dependence

The future depends counterfactually on the way the present is. That is, if the present were different, the future would be different. Likewise, the present depends counterfactually on the past. The reverse is seldom the case: “Seldom, if ever, can we find a clearly true counterfactual about how the past would be different if the present were somehow different.” (Lewis 455)

We ordinarily assume that facts about the past are counterfactually independent of a counterfactual supposition about the present and such facts are freely used as auxiliary premises. On the other hand, we sometimes encounter back-tracking arguments. These arguments assume dependence of past facts on the present; such arguments have the following upshot: if the present were different, the past would also need to be different as well, since there are a causal connections by which the present conditions are determined by their past causes.

Lewis suggests that we sometimes do not, and sometimes do, assume dependence of past facts on the present due to the following features of counterfactuals and reasoning about counterfactuals: (1) vagueness of counterfactuals require us to resolve the vagueness differently in different contexts. (2) We ordinarily resolve the vagueness of counterfactuals in such a way that counterfactual dependence is asymmetric. “Under this standard resolution, back-tracking arguments are mistaken: if the present were different the past would be the same, but the same past causes would fail somehow to cause the same present effects.” (Lewis 457) (3) Special contexts favor a different resolution of vagueness, one under which the past depends counterfactually on the present and under which some back-tracking arguments are considered correct. (Partners in conversation may favor such a resolution in order to give the speaker, who is giving a back-tracking argument, a chance to be correct. However, after this special resolution of vagueness comes to an end, the standard resolution returns.) (4) Although we favor the standard resolution, we also charitably tend to favor a resolution which gives the sentence under consideration a chance of truth. (Definition. A counterfactual which (i) states that the past would be different if the present were different, (ii) may come out true under the special resolution of vagueness, but (iii) is false under the standard resolution, is a back-tracking counterfactual. Back-tracking counterfactuls, used in a context that favors their truth, are marked by a syntactic peculiarity: the usual subjunctive construction is replaced by more complicated constructions: “If it were that…then it would have to be that…”.)

Only counterfactuals under the standard resolution preserve a clear-cut asymmetry of counterfactual dependence between past and present, present and future. Lewis is not interested in discussing back-tracking counterfactuals further in this paper (he introduced them for the sake of distinguishing them from those counterfactuals read under the standard resolution).

In summary, Lewis claims the following in this section: “Consider those counterfactuals of the form “If it were that A, then it would be that C” in which the supposition A is indeed false, and in which A and C are entirely about the states of affairs at two times tA and tC respectively. Many such counterfactuals are true in which C also is false and in which tC is later than tA. These are counterfactuals that say how the way things are later depends on the way things were earlier. But if tC is earlier than tA, then such counterfactuals are true if and only if C is true. These are the counterfactuals that tell us how the way things are earlier does not depend on the way things will be later.” (Lewis 458)

Asymmetries of Causation and Openness

Lewis believes that counterfactual dependence serves to explain more familiar asymmetries, specifically, the asymmetry of causation and the asymmetry of openness. Typically, causes precede their effects. Lewis advocates a counterfactual analysis of causation: (1) the relation of cause to effect consists in their being linked by a causal chain; (2) a causal chain is a certain kind of chain of counterfactual dependences; and (3) the counterfactuals involved are to be taken under the standard resolution of vagueness. According to this analysis backward causation is possible if the past is counterfactually dependent on the present. (Lewis 459)

The asymmetry of openness is “the obscure contrast we draw between the ‘open future’ and the ‘fixed past.'” (Lewis 459) What accounts for this contrast and why does the contrast seem to be a genuine one between past and future? Lewis considers the following hypotheses that are offered as explanations of the asymmetry of openness, finding each to but the final hypothesis unsatisfactory.

Hypothesis 1: Asymmetry of Epistemic Possibility. According to this hypothesis, the asymmetry of openness is accounted for by the asymmetry of our knowledge of the past and future, i.e., we know more about the past but not the future (that is why the future seems to be “open” while the past is not because the future is richer in epistemic possibilities). Problem with Hyp. 1: The epistemic contrast here is a difference of degree, not a difference in kind. We have knowledge of the future (Lewis claims), and we lack knowledge of many facts about the past. Ignorance of history, however, does not make us think that the past is “open”; by analogy neither should a lack of knowledge of facts about the future make us conclude that it is “open”. Hyp. 1 cannot be the right explanation.

Hypothesis 2: Asymmetry of Multiple Actuality. Is it that all our possible futures are equally actual whereas possible pasts are not? Elsewhere Lewis argues for: (1) Any inhabitant of any possible world may truly call his own world actual; (2) we ourselves inhabit this world only, and are not identical with our other-worldly counterparts. If (1) is true and (2) is false, then we cannot preserve asymmetry: in some sufficiently broad sense of possibility, we have alternative possible pasts as well as alternative possible futures, all of which are equally actual.

Hypothesis 3: Asymmetry of Indeterminism. Is it that we think of our world as governed by indeterministic laws of nature, so that the actual past and present are nomically compossible with various alternative future continuations? Problems: First, it is not certain that our world is indeterministic. Secondly, if we believe in indeterminism then we have reason to believe that the laws of nature are indeterministic in both directions, so that the actual future and present are nomically compossible with various alternative pasts. Again no asymmetry is preserved.

Lewis believes that indeterminism is neither necessary nor sufficient for the asymmetries that are the topic of discussion. He, therefore, ignores the possibility of indeterminism in the remainder of the paper, and focuses on seeing how the asymmetries might arise under strict determinism. DEFINITION: “A deterministic system of laws is one such that, whenever two possible worlds both obey the laws perfectly, then either they are exactly alike throughout all of time, or else they are not exactly alike through out any stretch of time.” (Lewis 460) Lewis assumes for the remainder of the paper that the laws of the actual world are deterministic in this sense.

Hypothesis 4: Asymmetry of Mutability. Is it that we can change the future, but not the past? Problem: Lewis claims that the actual past, present, and future are all alike immutable. Therefore, we cannot change the actual past, present, or future as it is.

Final Hypothesis: Asymmetry of Counterfactual Dependence. However, what we can do by way of “changing the future” (so to speak) is to bring it about that the future is the way it actually is, rather than any of the other ways it would have been if we acted differently in the present. This “is not literally change, since the difference we make is between actuality and other possibilities, not between successive actualities. The literal truth is just that the future depends counterfactually on the present. […] Likewise something we ordinarily cannot do by way of ‘changing the past’ is to bring it about that the past is the way it actually was, rather than some other way it would have been if we acted differently in the present. The past would be the same, however we acted now. The past does not at all depend on what we do now. It is counterfactually independent of the present.” (Lewis 461-462)

Lewis concludes that the Final Hypothesis is correct: the mysterious asymmetry between open future and fixed past is the asymmetry of counterfactual dependence. “The forking paths into the future–the actual one and all the rest–are the many alternative futures that would come about under various counterfactual suppositions about the present. The one actual, fixed past is the one past that would remain actual under the same range of suppositions.” (Lewis 462)

Two Analyses of Counterfactuals

The previous section had the task of convincing the reader that there is an asymmetry of counterfactual dependence and that it has important consequences. Any satisfactory semantic analysis of counterfactual conditionals ought to explain this asymmetry and in the rest of the paper Lewis is occupied in considering how that explanation ought to work.

Analyses of counterfactuals. Analysis 1. (In this analysis the asymmetry of counterfactual dependence is built in by fiat.) “Consider a counterfactual ‘If it were that A, then it would be that C’ where A is entirely about affairs in a stretch of time tA. Consider all those possible worlds w such that:

(1) A is true at w;

(2) w is exactly like our actual world at all times before a transition period beginning shortly before tA;

(3) w conforms to the actual laws of nature at all times after tA; and (4) during tA and the preceding transition period, w differs no more from our actual world than it must to permit A to hold.The counterfactual is true if and only if C holds at every such world w.” (Lewis 463)It is important that we do not require that w be exactly like our actual world at all times before tA. Doing so would make for abrupt discontinuities: e.g., suppose at a time t in the actual world a match is a foot from a surface that would ignite the match if struck against the surface. Suppose we want to consider a counterfactual situation in which the match is struck at t. Not allowing there to be a transition period would require that the match travel a foot instantaneously at any world, w, where the counterfactual situation holds. So, we better allow for transition periods during which w diverges from the actual world.The need for transition periods brings along a worry of there being a definite dependence of the transition period on the supposed, proceeding counterfactual affairs at time t. If this dependence is really definite, which Lewis hopes it is not, then it is difficult for Lewis to say why some of this dependence of the transition period on the proceeding counterfactual states of affairs should not be (wrongly)interpreted as backward causation over short intervals of time. On the other hand, if the immediate past depends on the counterfactual present in a non-definite way, such that there are a variety of ways the transition period can go, then there is room for Lewis to resist the conclusion that there is backward causation between the present counterfactual states of affairs and its immediate past. (Lewis 462)For the following two reasons, analysis 1 is not accepted by Lewis as completely satisfactory. (1) Analysis 1 requires a supposition about a particular time. Analysis 1 is not built to handle suppositions such as “If kangaroos had no tails…” and “If gravity went by the inverse cube of distance…” which are not about particular times. (2) Analysis 1 gives us more asymmetry than we want. Since asymmetry was built in by fiat, analysis 1 rules out, a priori, the possibility of special exceptions to the normal asymmetry of counterfactual dependence.Analysis 1 covers instances of counterfactuals in which we have the right sort of supposition, the standard resolution of vagueness, and no extraordinary circumstances. The correct analysis of counterfactuals, however, needs to be more general and flexible than analysis 1.

In Lewis’s opinion, analysis 2 is correct.

Analysis 2. A counterfactual “If it were that A, then it would be that C” is (non-vacuously) true if and only if some (accessible) world where both A and C are true is more similar to our actual world, overall, than is any world where A is true but C is false. (Lewis 465)

Analysis 2 is only a skeleton, which must be fleshed out with an account of the appropriate similarity relation, and this relation will differ from context to context. The task at hand now is to see what sort of similarity relation can be combined with analysis 2 to yield what Lewis has called the standard resolution of vagueness: that is, the task at hand is to find what sort of similarity relation combined with Analysis 2 (1) invalidates back-tracking arguments, (2) yields asymmetry of counterfactual dependence, (3) does not rule our special cases of the failure of asymmetry a priori, and (4) agrees with Analysis 1 wherever this analysis is correct.

Two cautionary notes: (1) Not every similarity between worlds will be relevant when assessing the truth value of a counterfactual. The context of a counterfactual will determine which similarities are taken to be relevant and which are taken to be negligible. (For instance, when comparing what is similar between Wittgenstein’s and Heidegger’s philosophical writings some similarities, say philosophical assumptions made in these writings, are relevant while other similarities are negligible, e.g., the ratio of vowels to consonants.) (2) “It is all too easy to make offhand similarity judgments and then assume that they will do for all purposes. But if we respect the extreme shiftiness and context-dependences of similarity, we will not set much story by offhand judgments. We will be prepared to distinguish between the similarity relations that guide our offhand explicit judgments and those that govern our counterfactuals in various contexts.” (E.g., One may assert, “If A, the world would be very different; but if A and B, the world would not be very different.” “Only if the similarity relation governing counterfactuals disagrees with that governing explicit judgments of what is ‘very different’ can such a pair be true under Analysis 2.”) (Lewis 463)

According to Lewis, we should not try to start deciding on what we think about similarity of worlds, so that we can afterward use these decisions to test analysis 2. Doing this would be to test of the combination of analysis 2 with a “foolish denial of the shiftiness of similarity. Rather, we must use what we know about the truth and falsity of counterfactuals to see if we can find some sort of similarity relation–not necessarily the first one that springs to mind–that combines with Analysis 2 to yield the proper truth conditions. It is this combination that can be tested against our knowledge of counterfactuals, not Analysis 2 by itself. In looking for a combination that will stand up to the test, we must use what we know about counterfactuals to find out about the appropriate similarity relation–not the other way around.” (Lewis 466-467)

The Future Similarity Objection

A serious objection to Analysis 2 has been raised. Kit Fine states it as follows.

“The counterfactual ‘If Nixon had pressed the button there would have been a nuclear holocaust’ is true or can be imagined to be so. Now suppose that there never will be a nuclear holocaust. Then that counterfactual is, on Lewis’s analysis, very likely false. For given any world in which antecedent and consequent are both true it will be easy to imagine a closer world in which the antecedent is true and the consequent false. For we need only imagine a change that prevents the holocaust but that does not require such great divergence from reality. (Lewis 467)

Lewis’s response. In response to the preceding objection Lewis stipulates a world w0, a world in which Nixon did not press the button but in which our worst fantasies about the button are true: there is a button, it is fully functional, everything else is in faultless working order, there is no way for anyone to stop the attack, and so on. Given all this, Lewis agrees that Fine’s counterfactual is true at w0. There are other worlds to consider though: worlds in which Nixon (or rather, a counterpart of Nixon) presses the button at t. We must consider which class of these worlds differs the least, under the appropriate similarity relation, from w0.

A first class consists of worlds like w1: Until shortly before t, w1 is exactly like w0. The two match perfectly in every detail of particular fact. Shortly before t, the spatio-temporal region of perfect match comes to an end and w1 and w0 begin to diverge. The deterministic laws of w0 are violated at w1 in some simple, localized, inconspicuous way. A tiny miracle takes place and as a result of this miracle Nixon presses the button. With no further miracles events take their lawful course and the two worlds w1 and w0 go their separate ways. In w1 the Holocaust and all its effects take place. (NOTE: By a miracle occurring at w1, Lewis means that the laws of w0 break down in w1. The laws that “break down” cannot be laws of w1 because laws are exceptionless regularities.) (Lewis 469)

A second class of worlds consists of worlds like w2: w2 is a world completely free of miracle; the deterministic laws of w0 are obeyed perfectly in w2. “However, w2 differs from w0 in that Nixon presses the button. By definition of determinism, w2 and w0 are alike always or alike never, and they are not alike always; therefore, they are never alike.” (Lewis 469)

Worlds in the class typified by w1 should turn out to be more similar to w0 than worlds in the class typified by w2. The lesson learned from comparing w1 and w2 is that a lot of perfect match in particular fact is worth a little miracle.

The third class of candidates is typified by w3: w3 is a world that begins like w1. “Until shortly before t, w3 is exactly alike w0. Then a tiny miracle takes place, permitting divergence. Nixon presses the button at t. But there is no holocaust, because soon after t a second tiny miracle takes place, just as simple and localized and inconspicuous as the first. The fatal signal vanishes on its way from the button to rockets.” (Lewis 469) Thereafter events at w3 take their lawful course and, so, w0 and w3 are no longer exactly alike in particular fact (e.g., the button in w3 has Nixon’s fingerprint, the photons bumping off of his finger in w3 when he presses the button at t will differ from the way the photons bounce off of his finger at t in w0, etc.).

If Analysis 2 is to succeed, worlds such as w3 must not turn out to be the most similar to w0 where Nixon presses the button. The lesson learned from comparing w1 and w3 is that under the similarity relation we seek, close but approximate match of particular fact is not worth even a little miracle. Taking this lesson along with the previous lesson learned from comparing w1 and w2 we learn that “perfect match of particular facts counts for much more than imperfect match, even if the imperfect match is good enough to give us similarity in respects that matters very much to us.” (Lewis 470)

A fourth class of worlds is typified by w4: w4 begins like w1 and w3. “There is perfect match with w0 until shortly before t, there is a tiny divergence miracle, the button is pressed. But there is a widespread and complicated and diverse second miracle after t. It not only prevents the holocaust but also removes all traces of Nixon’s button-pressing.” (Lewis 470) In w4, the cover-up is miraculously perfect. After this second miracle w0 and w4 reconverge.

The lesson that is learned from comparing w1 and w4 is that under the similarity relation we seek, perfect match of particular fact even through the entire future is not worth a big, widespread, diverse miracle. Taking this lesson and the lesson of w2 together, we learn that avoidance of big miracles counts for much more than avoidance of little miracles. ‘This concludes the different classes of worlds that Lewis deems fit to consider (he also briefly mentions worlds where Nixon presses the button but the Holocaust does not follow because something prior to t has happened that prevents the button from triggering the Holocaust: e.g., Haig disconnected the button before t.)

“Under the similarity relation we seek, w1 must count as closer to w0 than any of w2, w3, and w4. That means that a similarity relation that combines with Analysis 2 to give the correct truth conditions for counterfactuals such as the one we have considered, taken under the standard resolution of vagueness, must be governed by the following system of weights or priorities.

(1) It is of the first importance to avoid big, widespread, diverse violations of law.

(2) It is of the second importance to maximize the spatiotemporal region throughout which perfect match of particular fact prevails.

(3) It is of the third importance to avoid even small, localized, simple violations of law.

(4) It is of little or no importance to secure approximate similarity of particular fact, even in matters that concern us greatly.” (Lewis 472)

This concludes Lewis’s response to Fine’s objection.

The Asymmetry of Miracles

What explains the asymmetry of counterfactual dependence in the Nixon-case? (The asymmetry is that: If Nixon had pressed the button, the future would be of the sort found at w1: a future very different in matters of particular fact, from that of w0. The past, however, would have been of the sort found at w1: a past exactly like that of w0 until shortly before t.) The asymmetry neither comes from Analysis 2, nor the standards of similarity that were deemed fit to combine with Analysis 2 (i.e., (1)-(4) in the previous section). Instead, the asymmetry is accounted for by an asymmetry in the range of candidates. “We considered worlds where a small miracle permitted approximate convergence to w0 and worlds where a big miracle permitted approximate convergence to w0 and worlds where a big miracle permitted perfect convergence to w0. But we did not consider any worlds where a small miracle permitted perfect convergence to w0. If we had, our symmetric standards of similarity would have favored such worlds no less than w1.” (Lewis 473) However, there are no such worlds–it requires much more than a little miracle for a world where Nixon pressed the button to converge perfectly with w0 in particular matters of fact (other than the fact about Nixon pressing the button). Divergence from w0 is easier to achieve than perfect convergence (for reasons given in the next section). Thus, the asymmetry of counterfactual dependence arises in the Nixon case because the appropriate standards of similarity, themselves symmetric, respond to this asymmetry of miracles (i.e., it takes a much larger miracle to achieve perfect convergence than to achieve divergence from w0; this is the asymmetry of miracles being referred to here). (Lewis 473) NOTE: The asymmetry of miracles is not general or universal. In a world, W*, with only one atom the asymmetry breaks down since it would presumably take miracles of equal proportion to get another possible world with one atom to converge or diverge with W*. “The asymmetry of miracles, and hence of counterfactual dependence, rests on a feature of worlds like w0 which very simple worlds cannot share.” (Lewis 473)

Asymmetry of Overdetermination

In a deterministic world, every fact of that world is predetermined throughout the past and postdetermined throughout the future. At any time, past or future, it has at least one determinant: a minimal set of conditions jointly sufficient, given the laws of nature, for the fact in question. Members of such a set may be causes of the fact, or traces of the fact, or neither. At a given time a fact may have only one determinant, or it may have more than one determinant. In the latter cases, the fact is overdetermined at that time. Overdetermination holds in degrees: the more determinants of a fact at a time, the greater the overdetermination of that fact at that time.

Lewis claims that the reason why it takes a much larger miracle to achieve convergence as opposed to divergence, in a world like w0, is due to an asymmetry of overdetermination at such a world. w0, it was assumed, is deterministic. In order to break the link between any determinant and that which it determines one needs a miracle. “To diverge from w0, a world where Nixon presses the button need only break the links whereby certain past conditions determine that he does not press it. To converge to w0, a world where Nixon presses the button must break the links whereby a varied multitude of future conditions vastly overdetermine that he does not press it. The more overdetermination, the more links need breaking and the more widespread and diverse must a miracle be if it is to break them all.” (Lewis 474-475)

Taking stock of Lewis’s reasoning about the asymmetry of counterfactual dependence in the Nixon-case we find that Lewis is claiming that the asymmetry of overdetermination is responsible for the asymmetry of miracles, and the asymmetry of miracles is responsible for the asymmetry of counterfactual dependence in the Nixon-case.

Word of Caution: The asymmetry of overdetermination is a contingent, de facto matter. The asymmetry of overdetermination may also be a local matter holding near here but not in remote parts of time and space. If the latter is true, then all that rests on it, such as asymmetries of miracles, of counterfactual dependence, of causation and openness, may also be local and subject to exceptions.

In the final paragraph, Lewis regrets to inform the reader that he is unable to connect the asymmetries he has so far discussed with the asymmetry of entropy.

 

Stalnaker, Robert. “On Logics of Knowledge and Belief.” Philosophical Studies (2006) 128: 169-199.

The aim in “On Logics of Knowledge and Belief” is to bring out some of the connections between issues that arise in the development and application of formal semantics for knowledge and belief and more traditional substantive issues in epistemology. The paper is structured as follows: Stalnaker first gives a brief sketch of Jaakko Hintikka’s basic logic of knowledge; in section 2, Stalnaker discusses the S5 epistemic models that were developed and applied by theoretical computer scientists and game theorists, and argues that these models conflate knowledge and belief. In section 3, he discusses a basic theory that distinguishes knowledge from belief and that remains relatively noncommital about substantive questions about knowledge, but provides a definition of belief in terms of knowledge. This theory validates an S4.2 logic of knowledge. In the remaining four sections, Stalnaker considers some alternative ways of adding constraints on the relation between knowledge and belief that go beyond the basic theory: in section 4, he considers the S5 partition models as a special case of the basic theory; in section 5, he discusses the upper and lower bounds to an extension of the semantics of belief to a semantics for knowledge; in section 6, he discusses a version of the defeasibility analysis of knowledge, and in section 7, a simplified version of a causal theory.

 

Grim, Patrick. “There Is No Set of All Truths”. Analysis, Vol. 44, No. 4. (Oct., 1984), pp. 206-208.

Patrick Grim gives an argument against the existence of a set of all truths: Suppose, for argument by contradiction, that there is a set, S, of all truths. Consider all subsets of S. That is, consider all elements of the power set of S. Denote the power set of S by ‘P(S)’. Let S* be a variable that ranges over elements of P(S). Suppose that x is a variable that only takes values which will yield a true particular instance of: For any S*, for some x, x is a member of S*; an example of what I mean by a true particular instance is the truth “b is a member of B” such that b= “If its snowing and its not snowing, then its sunny out”, b is a member of B, and B is a singleton in P(S). There are at least as many true particular instances as there are elements in P(S) – { }. Given b, “b is not a member of the empty set” is a corresponding truth to the empty set. So, there are at least as many truths as elements in P(S). By Cantor’s power set theorem, P(S) has more elements than S. Thus, the set of truths whose members are the corresponding truths to members of P(S) has a greater cardinality than S. Therefore, S cannot be a set of all truths. This contradicts our initial assumption. Therefore, there is no set of all truths. Grim makes note that this argument can be extended as an argument against the view that possible worlds are maximally consistent sets of propositions. Maximally consistent sets of propositions are “proposition-saturated sets to which no further proposition can be added without incurring inconsistency…”. (Grim 207) Here’s a gloss on the argument: Assume for the sake of deriving a contradiction that there is a maximally consistent set of propositions; call it S. Take the power set of S. Corresponding to each element in the power set of S is a truth. By Cantor’s power set theorem, P(S) has more members than S. So, the cardinality of the set of all truths whose members are truths corresponding to elements in P(S) is greater than the cardinality of S. Truths corresponding to elements in P(S) that are not in S can be added to S without precipitating inconsistency. Thus, S is not a maximally consistent set. This contradicts our initial assumption that there is a maximally consistent set. Therefore, there is no maximally consistent set of propositions. It follows from the latter conclusion that there can be no possible worlds which are maximally consistent sets of propositions. Thus, on the view that possible worlds are maximally consistent sets of propositions, there is no actual world. In the final section of the paper, Grim makes note of the compatibility of his “Cantorian” result(s) and Lindenbaum’s Lemma.