<!DOCTYPE html><HTML lang="en"> <head><meta charset="utf-8"> <title>Jackson (Frank) - Grue (Theo Todman's Book Collection - Paper Abstracts) </title> <link href="../../TheosStyle.css" rel="stylesheet" type="text/css"><link rel="shortcut icon" href="../../TT_ICO.png" /></head> <BODY> <CENTER> <div id="header"><HR><h1>Theo Todman's Web Page - Paper Abstracts</h1><HR></div><A name="Top"></A> <TABLE class = "Bridge" WIDTH=950> <tr><th><A HREF = "../../PaperSummaries/PaperSummary_00/PaperSummary_255.htm">Grue</A></th></tr> <tr><th><A HREF = "../../Authors/J/Author_Jackson (Frank).htm">Jackson (Frank)</a></th></tr> <tr><th>Source: Journal of Philosophy 72.5, Mar. 1975, pp. 113-131</th></tr> <tr><th>Paper - Abstract</th></tr> </TABLE> </CENTER> <P><CENTER><TABLE class = "Bridge" WIDTH=800><tr><td><A HREF = "../../PaperSummaries/PaperSummary_00/PaperSummary_255.htm">Paper Summary</A></td><td><A HREF = "../../PaperSummaries/PaperSummary_00/PaperCitings_255.htm">Books / Papers Citing this Paper</A></td><td><A HREF = "../../PaperSummaries/PaperSummary_00/PapersToNotes_255.htm">Notes Citing this Paper</A></td><td><A HREF = "../../Notes/Notes_12/Notes_1206.htm">Link to Latest Write-Up Note</A></td></tr></TABLE></CENTER></P> <hr><P><FONT COLOR = "0000FF"><U>Philosophers Index Abstract</U><FONT COLOR = "800080"><ol type="1"><li>Since Nelson Goodman's 1946 paper, it has been almost universally supposed that the inductive rule: certain fs being g supports other fs being g, needs to be restricted to "projectible" predicates and hypotheses. </li><li>I argue against this view, and suggest three sources of it: <ol type="i"><li>a tendency to conflate three different ways of defining 'grue'; </li><li>a lack of precision about just how, in detail, the 'grue' paradox is supposed to arise; and </li><li>a failure to note a counterfactual condition which governs the vast majority of our applications of the <U><A HREF="#On-Page_Link_P255_1">SR</A></U><SUB>1</SUB><a name="On-Page_Return_P255_1"></A>. </ol></li></ol></FONT><hr><FONT COLOR = "0000FF"><B>Comment: </B><BR><BR>For a prcis, see the <a name="1"></a><A HREF="../../Notes/Notes_12/Notes_1206.htm">Note</A><SUP>2</SUP>.<BR><FONT COLOR = "0000FF"><hr><br><B><u><U><A HREF="#On-Page_Link_P255_3">Write-up</A></U><SUB>3</SUB><a name="On-Page_Return_P255_3"></A></u> (as at 04/01/2018 13:36:29): Jackson - Grue</B><BR><br>This note provides my detailed review of <a name="2"></a>"<A HREF = "../../Abstracts/Abstract_00/Abstract_255.htm">Jackson (Frank) - Grue</A>". <BR><BR>Currently, this write-up is only available as a PDF. For a prcis, click <a href="../../JacksonGrue.pdf" target = "_top">File Note (PDF)</a>. I am in the process of converting this to Note, as below:- <BR><BR><hr><BR><u><b>Detailed analysis</b></u><BR><BR><u><b>Introduction</b></u><ul type="disc"><li>The paper is concerned with one aspect of describing or specifying rational inductive practices. </li><li>One common inductive practice taken as rational is to project common properties from samples to populations, arguing from certain Fs being G to other Fs being G. This can be specified in semi-formal terms in several ways, including :- <ol type="a"><li> Fa&Ga confirms  "x[Fx " Gx] </li><li> All examined As are B supports  All unexamined As are B </li><li> Fa<sub>1</sub> && & Fa<sub>n</sub> gives a good reason for  Fa<sub>n+1</sub> . </li></ol>The precise formulation of this inductive pattern isn t important & Jackson refers to it as the <em>straight rule</em> (SR). The discussion considers the simplest case where the <em>whole</em> sample, rather than a percentage, has the property under consideration. </li><li>To say that the SR is a common inductive argument considered rational isn t to claim it as the most fundamental, important to science or the one that will show that induction is justified. The paper isn t concerned with the relative merits of the SR as against hypothetico-deduction. It is merely concerned with acknowledging that we all treat it as rational & use it occasionally and <em>describes</em> those applications of the SR we consider to be rational. </li><li>Since Goodman s 1946 <a name="3"></a>"<A HREF = "../../Abstracts/Abstract_23/Abstract_23059.htm">Goodman (Nelson) - A Query on Confirmation</A>", developed in <a name="5"></a>"<A HREF = "../../BookSummaries/BookSummary_00/BookPaperAbstracts/BookPaperAbstracts_532.htm">Goodman (Nelson) - Fact, Fiction and Forecast</A>", it has been supposed that the above formulations of the SR requires the insertion of a substantial proviso to the effect that the properties / predicates / hypotheses involved be <em><U><A HREF="#On-Page_Link_P255_4">projectible</A></U><SUB>4</SUB><a name="On-Page_Return_P255_4"></A></em>. The SR is taken to be manifestly true of some properties, manifestly false of others. </li><li>Thus arises Goodman s new riddle in inductive logic  that of demarcating projectible from non-projectible properties. The <em>extension</em> of the problem has not been as controversial as its intension. That is, <ol type="a"><li>we re agreed that <em>green</em> and <em>round</em> are projectible while <em>grue</em> and <em>sampled</em> aren t but </li><li>there s enormous controversy about the <em>rationale</em> for this division. </li></ol>It has proved difficult, to say the least, to provide a non-arbitrary account of projectibility other than the useless and circular one that projectible predicates are just those to which the SR applies. </li><li>Jackson thinks we can resolve this problem by challenging its foundation; by arguing that <em>all</em> consistent predicates are projectible so that there is no  new riddle of induction and no paradox arising from grue and the like. </li><li>Jackson thinks the popularity of the non-projectible thesis arises from three sources; <ol type="1"><li>the conflation of three ways of defining grue </li><li>imprecision about how the in detail the <em>grue paradox</em> is supposed to arise </li><li>a failure to note a counterfactual condition that governs the vast majority of our applications of the SR. </li></ol></li><li>Jackson considers these in turn. </li></ul><BR><u><b>I. The Three Ways of defining  Grue </u></b><ul type="disc"><li>Of the three ways of defining grue, Jackson considers that the first two pose not even a prima facie problem for the SR.</li><li>Typical examples of the three definitions are:- <ol type="1"><li>D<SUB>1</SUB>. x is grue iff x is green before T and blue thereafter. <U><A HREF="#On-Page_Link_P255_5">Note</A></U><SUB>5</SUB><a name="On-Page_Return_P255_5"></A>.</li><li>D<SUB>2</SUB>. x is grue at t iff (x is green at t < T) or (x is blue at t e" T). <U><A HREF="#On-Page_Link_P255_6">Note</A></U><SUB>6</SUB><a name="On-Page_Return_P255_6"></A>.</li><li>D<SUB>3</SUB>. x is grue at t iff (x is examined by T and x is green at t) or (x is not examined by T and x is blue at). <U><A HREF="#On-Page_Link_P255_7">Note</A></U><SUB>7</SUB><a name="On-Page_Return_P255_7"></A>. </li></ol>Where T is a chosen time in the future. </li></ul><BR><u><b>Discussion of D<SUB>1</SUB></u></b> <ul type="disc"><li><em>D<SUB>1</SUB>. x is grue iff x is green before T and blue thereafter. </em></li><li>Jackson points out that for D<SUB>1</SUB>, x is <em>grue</em> or not once and for all, rather than grue at one time and not grue at another. It is atemporal and so differs from <em><U><A HREF="#On-Page_Link_P255_8">green</A></U><SUB>8</SUB><a name="On-Page_Return_P255_8"></A></em>. </li><li>Jackson claims that we cannot make out that grue<sub>1</sub> is non-projectible, for if we found that all emeralds so far examined have this property (of being green up to T and then turning blue), there s no reason why, ceteris paribus, we shouldn t suppose all unexamined emeralds have it. At least we d count the hypothesis as supported by our observations. </li><li>We would doubtless think that emeralds were like tomatoes and change colour dramatically during their life-cycles, seeking some rational explanation as to why the change occurs at time T. Jackson suggests hypothetically that the greenness of emeralds could be due to a critical level of radiation that will drop below the threshold at time T. </li><li>Jackson points out that this example is based on a curious blunder. Since, before T, we don t know, and wouldn t believe, that emeralds will turn blue at T, all we can say is that all emeralds examined before T have been green, not <U><A HREF="#On-Page_Link_P255_9">grue</A></U><SUB>9</SUB><a name="On-Page_Return_P255_9"></A>. </li></ul><BR><u><b>Discussion of D<SUB>2</SUB></u></b> <ul type="disc"><li><em>D<SUB>2</SUB>. x is grue at t iff (x is green at t < T) or (x is blue at t e" T) </em></li><li>Jackson says that according to D<SUB>2</SUB>, grue<sub>2</sub> is like  green in being <em>temporal</em>; an object can be grue<sub>2</sub> at one time and not-grue<sub>2</sub> at <U><A HREF="#On-Page_Link_P255_10">another</A></U><SUB>10</SUB><a name="On-Page_Return_P255_10"></A>.</li><li>Jackson notes a <U><A HREF="#On-Page_Link_P255_11">tendency</A></U><SUB>11</SUB><a name="On-Page_Return_P255_11"></A> to slip from D<SUB>1</SUB> to D<SUB>2</SUB>, and puts this down to the theorem<BR> x is grue<sub>1</sub> a" "t(x is grue<sub>2</sub> at t) .</li><li>D<SUB>2</SUB> is <U><A HREF="#On-Page_Link_P255_12">sometimes</A></U><SUB>12</SUB><a name="On-Page_Return_P255_12"></A> (mis-)read as saying that :-<BR><em>D<SUB>2.1</SUB>.  x is grue means  x is green before T and  x is blue afterwards. </em><BR>Jackson says that this is a case of  ambiguity and that consequently it raises no problems for the SR; for, when we understand the SR as warranting the projection of a common predicate, we assume the predicate has the same meaning throughout (ie. is <U><A HREF="#On-Page_Link_P255_13">unambiguous</A></U><SUB>13</SUB><a name="On-Page_Return_P255_13"></A>). </li><li>However, Jackson correctly points out that D<SUB>2</SUB> and D<SUB>2.1</SUB> are <u>not</u> equivalent, as is apparent if we re explicit about time in D<SUB>2.1</SUB>. We rewrite D<SUB>2.1</SUB> as:- <BR><em>D<SUB>2.1.1</SUB>.  x is grue at t means  x is green at t before T and  x is blue at t afterwards. </em> </li><li>Consider t<sub>1</sub> < T. Is a green emerald grue at t<sub>1</sub> ? According to D<SUB>2</SUB>, yes, but according to D<SUB>2.1.1</SUB>, the answer depends on when the question is asked. If before T, the answer is yes, because  x is grue<sub>2.1</sub> at t <em>means</em>  x is green at t , which, at t<sub>1</sub> the emerald is. However, if the question is asked after T, because  x is grue<sub>2.1</sub> at t means  x is blue at t , and the emerald wasn t blue at t<sub>1</sub> < T, the answer is no. So, D<SUB>2</SUB> and D<SUB>2.1</SUB> are not equivalent because the time we consider the question of the emerald s grueness is important for D<SUB>2.1</SUB>, but unimportant for D<SUB>2</SUB>; for on D<SUB>2</SUB>, the time at which the object is blue or green is relevant, not the time we consider the matter. </li><li>Jackson thinks that D<SUB>2</SUB>, is perfectly respectable as a definition and does not give rise to  new riddles in conjunction with the SR, so grue<sub>2</sub> cannot be used as the prime example of a non-projectible predicate, whose existence therefore remains to be proved. </li><li>Jackson diagnoses the genesis of the contrary view as being from a confusion over the application of the SR / grue<sub>2</sub> to objects considered <ol type="a"><li>as 4-dimensional (as enduring through time) or </li><li>as 3-dimensionsional time-slices of 4-dimensional objects at times. </li></ol></li><li>If we consider 4-dimensional objects, ie. those enduring through time, they aren t (assumed monochrome at a particular time) one colour <em>simpliciter</em> but may change colour over time. A tomato isn t red and green, but green in the early part of its life-history and red later. </li><li>So, if we take the SR as applying to enduring objects and licensing projections of common predicates from samples to populations, we have to include a temporal factor   predicate at time t . The paradox only arises for projections across T, and the explanation is forgetting the foregoing point. Take a sample of emeralds green and therefore grue<sub>2</sub> at t<sub>1</sub> < T. So the SR will support the compatible claims that  all emeralds are green at t<sub>1</sub> and  all emeralds are grue<sub>2</sub> at t<sub>1</sub> . However, we shouldn t be led to use the SR to project the incompatible claims that  all emeralds are green at t<sub>2</sub> and  all emeralds are grue<sub>2</sub> at t<sub>2</sub> for t<sub>2</sub> e" T, since it is impossible for a sample of emeralds to be both green and grue<sub>2</sub> at t<sub>2</sub>. </li><li>We only run into problems and apparent paradox when we slide from t<sub>1</sub> < T d" t<sub>2</sub> and take emeralds being both green and grue<sub>2</sub> at t<sub>1</sub> to imply that they will be both green and grue<sub>2</sub> at t<sub>2</sub>. </li><li>An objection to this diagnosis is that the role of the SR is that its role is unfairly restricted by insisting on the temporal distinctions  x is grue<sub>2</sub> (green) at t<sub>1</sub> and  x is grue<sub>2</sub> (green) at t<sub>2</sub> . The SR is used in two ways, firstly (as above) to project on the greenness of emeralds now, but also secondly to project on the greenness of emeralds in the future, which would seem to require us to ignore the t<sub>1</sub> / t<sub>2</sub> distinction. </li><li>Jackson s response is to say that the SR is best viewed, rather than as applying to enduring objects, as applying <em>simpliciter</em> to time-slices of objects. We think of the SR as being true of the temporal part at time t of an emerald, rather than to the enduring emerald. When making future projections, we should not fudge the distinction between being green now and being green in the future. The projected property should be regarded as a tenseless characteristic of present emerald temporal-parts which the SR allows us to project to future emerald temporal-parts. </li><li>Jackson notes that, if D<SUB>2</SUB> is recast as being about temporal-parts rather than enduring objects, we end up essentially with a definition analogous to D<SUB>3</SUB> as far as grue paradoxes are concerned, so no separate treatment is required. </li></ul><BR><u><b>Introductory discussion of D<SUB>3</SUB></u></b> <ul type="disc"><li>D<SUB>3</SUB>. <em>x is grue at t iff (x is examined by T and x is green at t) or (x is not examined by T and x is blue at t)</em></li><li>Jackson notes that D<SUB>1</SUB> and D<SUB>2</SUB>, while prominent features of the grue literary landscape, are not the kinds of predicates that Goodman intended. The form of Goodman s predicate is  (x is green and x) v (x is blue and x) , where x is chosen so that its extension includes all the emeralds from we are projecting, and x those we re projecting on ( =  sampled ,  observed , & ). Goodman s usual, though not invariable, procedure is to introduce a temporal element into , and the above definition D<SUB>3</SUB> is <U><A HREF="#On-Page_Link_P255_14">close</A></U><SUB>14</SUB><a name="On-Page_Return_P255_14"></A> to the one adopted in FFF. </li><li>D<SUB>3</SUB> is for enduring objects, as is indicated by the  at t . To simplify the prose, Jackson from now on drops the  at t and the  at T , with the discussion in the editorial present and T taken as a moment in the near future, so we re talking about things examined or unexamined  to date . Being grue<sub>3</sub> can be simply characterised as being green and examined or blue and unexamined. Jackson says that we will see that the paradox apparently resulting is not essentially time- linked, so that there s no problem simplifying with respect to time. We don t need to consider all the sampled emeralds at one time and the others at another in order to arrive at apparent paradox. </li><li>According to Jackson, grue<sub>3</sub>, as well as being Goodman s definition, is the only one that leads to apparent paradox, so hereafter, grue refers to grue<sub>3</sub>. </li></ul><BR><u><b>II. What is the Grue Paradox?</b></u> <ul type="disc"><li>The grue paradox is that, choosing our predicates carefully, starting from the same evidence we can use the SR to predict contradictory events. In particular, using green and grue as predicates for emeralds and using the SR to predict their future colour. </li><li>Jackson spells out the problem. Imagine {a<sub>1</sub>, & ., a<sub>n</sub>, a<sub>n+1</sub>} are emeralds where the first n have been examined as green and a<sub>n+1</sub> is the one that has not been examined yet and whose colour we wish to determine. How does the SR provide incompatible projections ? </li><li>Using obvious terminology, Gux = (Grx & Ex) v (Bx & Ex), from D<SUB>3</SUB>, and also <ol type="1"><li>Gra<sub>1</sub> & & & Gra<sub>n</sub> and </li><li>Gua<sub>1</sub> & & . Gua<sub>n</sub>. </li></ol></li><li>Jackson notes that, <ol type="a"><li>since (1) and (2) are not <U><A HREF="#On-Page_Link_P255_15">equivalent</A></U><SUB>15</SUB><a name="On-Page_Return_P255_15"></A>, there is no objection to the SR giving different <U><A HREF="#On-Page_Link_P255_16">predictions</A></U><SUB>16</SUB><a name="On-Page_Return_P255_16"></A>, Gra<sub>n+1</sub> & Gua<sub>n+1</sub>, regarding a<sub>n+1</sub> </li><li>that the predictions are not inconsistent as neither entails the denial of the other and </li><li>neither (1) nor (2) embodies our total evidence. </li></ol></li><li>In response to (c) Jackson says that our total evidence is actually (3) Gra<sub>1</sub> & Ea<sub>1</sub> & & & Gra<sub>n</sub> & Ea<sub>n</sub>, which is  of course <U><A HREF="#On-Page_Link_P255_17">equivalent</A></U><SUB>17</SUB><a name="On-Page_Return_P255_17"></A> to (4) Gua<sub>1</sub> & Ea<sub>1</sub> & & & Gua<sub>n</sub> & Ea<sub>n</sub>, </li><li>Jackson now says that (3) & (4) support, via the SR, (5) Gra<sub>n+1</sub> & Ea<sub>n+1</sub>, and (6) Gua<sub>n+1</sub> & Ea<sub>n+1</sub>, which  far from being incompatible are equivalent . </li><li>However, he agrees that (5) entails (7) Ea<sub>n+1</sub> " Gra<sub>n+1</sub> and that (6) entails (8) Ea<sub>n+1</sub> " Gua<sub>n+1</sub> which is itself equivalent to Ea<sub>n+1</sub> " Ba<sub>n+1</sub>. He thinks it will be argued that (7) and (9) entail that if a<sub>n+1</sub> is not examined it is both green and blue and that consequently incompatible predictions have derived from the (allegedly) equivalent bases (3) & (4). </li><li>Jackson rejects this conclusion by saying that it is like the argument B " (W " B), ie. that our projection that an unobserved raven will be black supports the prediction that white ravens are <U><A HREF="#On-Page_Link_P255_18">black</A></U><SUB>18</SUB><a name="On-Page_Return_P255_18"></A>. </li><li>Jackson claims that the obvious fallacy in the above argument is that the reason we have support for W " B is that we have support for the falsity of the antecedent (ie. for W). He claims that similarly the support of (3) & (4) for (7) & (8) only because their antecedents (ie. Ea<sub>n+1</sub>) are false (ie. Ea<sub>n+1</sub>, that a<sub>n+1</sub> has been examined). The counter-argument (he says) is that we don t have support for this falsity, because  Ex is not projectible, but Jackson s response is that this argument both (a) assumes there are non-projectible properties in the middle of an argument that s trying to prove there are such beasts and (b) Jackson intends to prove in IV that being examined is a projectible <U><A HREF="#On-Page_Link_P255_19">property</A></U><SUB>19</SUB><a name="On-Page_Return_P255_19"></A>. </li></ul><BR><u><b>III. The Counterfactual Condition</b></u> <ul type="disc"><li>Jackson has not yet used the known fact Ea<sub>n+1</sub> (a<sub>n+1</sub> <U><A HREF="#On-Page_Link_P255_20">is</A></U><SUB>20</SUB><a name="On-Page_Return_P255_20"></A> not examined), and he takes the existence of unexamined emeralds to be central to Goodman s argument (and quotes him from <U><A HREF="#On-Page_Link_P255_21">FFF</A></U><SUB>21</SUB><a name="On-Page_Return_P255_21"></A> to that effect). </li><li>Jackson asks how we are to use this information and suggest that an argument of the following form may be in mind. (1) our evidence supports a<sub>n+1</sub> being green and examined (2) we know independently that a<sub>n+1</sub> is not examined, so our overall evidence supports a<sub>n+1</sub> being green and not <U><A HREF="#On-Page_Link_P255_22">examined</A></U><SUB>22</SUB><a name="On-Page_Return_P255_22"></A>. But the SR also supports a<sub>n+1</sub> being grue and examined, hence grue and not examined, hence not green. </li><li>Jackson claims that, while we have genuine contradictory categorical predictions, the pattern of argument is  quite plainly invalid . </li><li>He points out that this argument is of the form : if p supports (q&r) and we know that p is true and, independently, that r is false, that we have independent support for (q&r) and so for anything this entails. </li><li>He now proves this invalid, noting that since (1) ([(q&r) v (q&r)] & r) a" (q&r) and (2) ([(q&r) v (q&r)] & r) a" (q&r), by (1) p supports (q&r) iff p supports [(q&r) v (q&r)] & r). But, by the above argument pattern, if I know independently that r is false, I have overall support equally for (q&r) and for what it entails, namely, ([(q&r) v (q&r)] & r) which, by (2), is (q&r). So, we have equal support for inconsistent conclusions (q&r) and (q&r). </li><li>Jackson says we can demonstrate the same thing by a horse-racing example. If I m told that a certain horse won the race by a certain margin, and independently that a horse won by a different margin, can I conclude that my horse won by this ne3w margin ? Maybe, but the evidence is ambiguous  it may imply either that my first informant was wrong about the horse that won, or that he wasn t interested in the margin. </li><li>We have hear an example of the defeasibility of inductive support, which is often overlooked in arguments about grue. It is sometimes argued that, given any n object at all, the SR supports the n+1 th object being G, for <em>any</em> <U><A HREF="#On-Page_Link_P255_23">G</A></U><SUB>23</SUB><a name="On-Page_Return_P255_23"></A>. The proof (eg. as in Skyrms) is simple. For any n+1 objects there is some property F that applies to the first n but not the last. So, (Fx v Gx) is true of the first n and the SR supports it being true for the n+1 th object. Since Fx is false for this object, Gx must be true, whatever G is! Jackson s diagnosis is that arguments such as  If p supports q, then (p&r) supports (q&r) are not valid, and so information that the n+1 th is not F cannot be simply <U><A HREF="#On-Page_Link_P255_24">incorporated</A></U><SUB>24</SUB><a name="On-Page_Return_P255_24"></A>. </li><li>Hence we must be very careful before incorporating the information that a<sub>n+1</sub> is unexamined, and see things in context, as follows. </li><li>The context is that we have {a<sub>1</sub>, & a<sub>n</sub>} each of whose members has two properties   being <U><A HREF="#On-Page_Link_P255_25">examined</A></U><SUB>25</SUB><a name="On-Page_Return_P255_25"></A> and the one of interest  being green (or grue)  and that the former is false of a<sub>n+1</sub>. This situation occurs almost whenever we use the SR, as does the situation of some universal property of the sample not being a property of all or any members of the external population. Some common properties are disregarded as trivial, such as being a member of {a<sub>1</sub>, & a<sub>n</sub>} or being sampled (before & ), but others cannot be. Jackson gives an example of diamonds glinting in the light. All so far examined have glinted and this gives us reason to believe that the next one will  unless it has not been polished. Indeed, had the others not been polished, they would not have glinted. This detail makes it unreasonable to expect the next diamond to glint. Our expanded evidence (rightly) does <em>not</em> support an unpolished diamond glinting. </li><li>Similarly, I do not have good evidence to expect the next lobster I observe to be red, despite that fact that all I ve seen hitherto have been red, because the reason for this is that they have been cooked, and had they not been cooked they would not have been red. </li><li>This generalises to say that while some Fs being G supports by the SR other Fs being G, certain Fs that are H being G does not support other Fs that are not H being G, the reason being the <em>counterfactual condition</em> - that the Fs in the first class would not have been G if they had not been H. Jackson cannot prove this other than by way of illustration, but thinks it will be commonly accepted. He also expresses the claim more formally: (Certain Fs which are H being G) and (these Fs being such that if they had been H would not have been G) does not support (other non-H Fs being G). </li><li>Having got this out of the way, Jackson is in a position to discuss the incorporation of the additional information that a<sub>n+1</sub> is unexamined. Unsurprisingly, in the above analysis we replace F by <em>emerald</em>, G by <em>green</em> and H by <em>examined</em>. We would be wrong to predict that the next emerald will be green if the counter-factual condition applies; that had the other emeralds not been examined they would not have been green. However, our knowledge of emeralds chemical composition and crystalline structure assures us that their greenness is due to this rather than to their being examined, so the condition <U><A HREF="#On-Page_Link_P255_26">fails</A></U><SUB>26</SUB><a name="On-Page_Return_P255_26"></A> and our predictions are correct. </li><li>However, the opposite is the case with grue. Jackson s definition of grue was that <U><A HREF="#On-Page_Link_P255_27">x is grue iff</A></U><SUB>27</SUB><a name="On-Page_Return_P255_27"></A> (x is examined and x is green) or (x is not examined and x is blue). If the emerald had not been examined it would have been green, hence not blue, hence not grue. Hence projecting that a<sub>n+1</sub> will be grue violates the counterfactual condition. </li><li>Jackson replays the argument to show the importance of the counterfactual condition. If we take note of it, no inconsistency arises because if the {a<sub>1</sub>, & a<sub>n</sub>} had not been examined, they would not have been grue and we therefore couldn t project that a<sub>n+1</sub> would be grue. An inconsistency <em>cannot</em> arise on the standard logic of counterfactuals because we can t have both  if X had not been H, it would not have been G and  if X had not been H it would have been G . </li><li>Jackson has discussed the SR in terms of constants, {ai}, rather than universals, and thinks that the counterfactual condition shows that it can be misleading to characterise the SR as   All examined As are B supports  All unexamined As are B  . </li><li>This concern is illustrated by reference to the disturbing effect of examination in elementary particle physics when we know that unexamined particles would not have the properties that examined ones do. </li><li>The grue situation is similar to this, in that unexamined objects do not have the properties of examined ones. Unexamined emeralds aren't grue; it is a mistake to argue from  all examined emeralds are grue to  all unexamined emeralds are grue , but the reason is <em>not</em> that grueness is unprojectible but because the counterfactual condition has been violated. </li><li>Jackson notes that similar arguments apply to the <U><A HREF="#On-Page_Link_P255_28">functor</A></U><SUB>28</SUB><a name="On-Page_Return_P255_28"></A> expression of the SR as   All examined as are B supports  The first unexamined A is a B  . The equivalence of the claims to greenness and grueness of all examined emeralds appears to support the inconsistent claims to both greenness and grueness of the first unexamined emerald, as Quine does in <U><A HREF="#On-Page_Link_P255_29"><em>Natural Kinds</em></A></U><SUB>29</SUB><a name="On-Page_Return_P255_29"></A>. But, since being B is not independent of being examined, it is unreasonable to use this version of the SR in this case. </li><li>Jackson makes an important point that we should distinguish what is the case, and what supports what, from what we (come to) <em>know</em>. He thinks it is unfortunate that the SR is so often expressed with references to examination embedded in it. The SR is intended with whether p supports q irrespective of whether p is known. Our knowing that certain As are Bs is a separate issue from the <em>relational</em> principle of these As being B supporting other As being B. Any support is provided by <em>what</em> we come to know, not the fact that we come to know it. </li><li>It might not have been the case that unexamined emeralds would still have been green. It might have been the case that unexamined emeralds are blue (and that we would know this from their structure), but where the act of examining them turns them green, so that all examined emeralds are green. In such a world, we ought to believe that all unexamined emeralds are blue and that all emeralds are grue. This is consistent with out counterfactual condition, because we know that, in such a world, not only are all examined emeralds grue, but had the unexamined emeralds been examined, they would also have been grue (ie. blue and not green). </li></ul> <BR><u><b>IV. The Projectibility of Being Sampled</u></b> <ul type="disc"><li>Richard Jeffrey says that, while we might doubt whether or not being grue is projectible, it is beyond question that properties of the kind of membership of a set or being examined are not projectible. </li><li>The reason is that when we sample marbles from a barrel, finding them all red supports the others being red, not sampled. </li><li>However, I might be trying to determine whether they have all already been sampled by someone else by checking for finger-prints. In this case, being sampled is <U><A HREF="#On-Page_Link_P255_30">projectible</A></U><SUB>30</SUB><a name="On-Page_Return_P255_30"></A>, in that finding finger-prints on all to date entitles me to be more confident of finding finger-prints on them all. </li><li>Jackson thinks it s a mistake to diagnose the distinction by saying that being <em>sampled by me now</em> is not projectible whereas <em>being sampled by Jones in the past</em> is projectible. Say I am Jones, sample a set of marbles, go for a coffee and return, at which time I m confronted by a set of sampled-in-the-past-by-Jones marbles. Clearly, the expectation of the remaining marbles being sampled is not increased, and the property distinction of projectibility doesn t help explain this (and this is just the sort of situation in which we would expect that it should). </li><li>Jackson claims that it is the counterfactual condition that explains the difference. We know that a marble is sampled-by-me if it is out of the barrel. If it was not out of the barrel it would not have been sampled-by me, so we can have no expectation of sampled-by-me-ness of those marbles still in the barrel. The situation for sampled-by-Jones (where Jones is not me) is different because the marbles locations have no bearing on whether or not Jones has sampled them in the past, so the counterfactual condition is not violated. </li><li>So, there is nothing intrinsically non-projectible about being sampled. Where we cannot project it, this has to do with violation of the counterfactual condition rather than with the nature of meaning of the predicate. Jackson takes it as read that the same applies to the property of being examined and now shows it also applies to the property of membership of a set. </li><li>Jackson s examples are (1) finding that all cat-burglaries in a neighbourhood have been committed by Tom, Dick or Harry leads me to believe that the next burglary will be committed by a member of this set. (2) If I find each marble I withdraw from a barrel is marked a<sub>1</sub>, & , a<sub>n</sub>, I m entitled to believe that the next marble withdrawn will belong to this <U><A HREF="#On-Page_Link_P255_31">set</A></U><SUB>31</SUB><a name="On-Page_Return_P255_31"></A>. Jackson points that after withdrawing n marbles without replacement, I m no longer entitled to my expectation, but claims this has nothing to do with non-projectibility but the role of additional negative evidence; namely, that n+1 things cannot be identical to n things. </li><li>By contrast, giving the marbles names on withdrawal means that I have no expectation of subsequent marbles belonging to the range. Again, this is because of counterfactual conditional violation  withdrawn marbles don t have the same names as they would have had unwithdrawn. </li><li>Whenever we apply the SR, we know too much. We don t project recent exposure to light or being in my hand to unsampled marbles; but, again, the reason is not non-projectibility but the counterfactual condition. We know that had these marbles not been sampled, they would have been in the barrel and therefore would not have had these properties. </li><li>Jackson foresees two objections to his use of counterfactuals. The first is that counterfactuals raise some of philosophy s most difficult problems, but Jackson counters this by saying that in some cases we know with certainty that particular counterfactuals are true, despite any problems analysing just what it is we know and how we know it. </li><li>The second objection is one of circularity  that we know that our examined emeralds would have been green, rather than grue, had they not been examined just because we know that unexamined emeralds are green. So, we cannot appeal to the fact that examined emeralds would have been green had they been examined to explain why the SR predicts that unexamined emeralds are green. </li><li>Jackson points out that this knowledge is about examined emeralds, not unexamined ones, and is such that we might have even were there no emeralds left unexamined. Even if our supply of unexamined emeralds was exhausted, this wouldn t affect the fact that if an examined emerald had not been examined, it would still have been green. Also, were we suddenly to discover a source of red emeralds, this still wouldn t undermine the claim that, had so-far examined emeralds been left unexamined, they would have been <U><A HREF="#On-Page_Link_P255_32">green</A></U><SUB>32</SUB><a name="On-Page_Return_P255_32"></A>. </li><li>Jackson claims that consequently there is no tacit knowledge that unexamined emeralds are green underwriting our knowledge that examined emeralds would have been green even if not examined. We would still have this knowledge about the colour of previously examined emeralds, had they not been examined, even if there were no emeralds left to examine, or all currently unexamined emeralds were red. Hence we can appeal to this knowledge without circularity in explaining why the SR correctly supports us in believing unexamined emeralds to be green rather than <U><A HREF="#On-Page_Link_P255_33">grue</A></U><SUB>33</SUB><a name="On-Page_Return_P255_33"></A>. </li><li>In the marble-barrel case, I know that the red marbles I ve drawn out would have been red even if I d not drawn them out even if I don t know the colours of the other marbles (as, in general, I don t). Knowing the counterfactual is a consequence of knowing the lack of connection between something being of a particular colour and it having been examined. Should there be such a connection (say heat-sensitive paint), then I know the marbles would not have been red unless drawn out and so I have no expectation that the undrawn marbles are red, and I need have no knowledge of the colour of the undrawn marbles to be wary of making a prediction. Hence no <U><A HREF="#On-Page_Link_P255_34">circularity</A></U><SUB>34</SUB><a name="On-Page_Return_P255_34"></A>. </li></ul><BR><u><b>V. Summary</u></b> <ul type="disc"><li>Jackson concludes that the SR  certain Fs being G supporting other Fs being G  does not lead to incompatible predictions for grue and like predicates. </li><li>When we usually use the SR, our argument is usually of the form that certain Fs that are H being G supports other Fs that are not H being G, on condition that it is not the case that the Fs which were H would not have been G had they not been H (where H is  examined , etc.). This condition guarantees that we can never be led by the same evidence to contradictory predictions concerning the non-H Fs. The reason is that, if we define G* = (Hx & Gx) v (Hx & Gx), that even though Fs are H and G iff they are H and G*, we cannot be led to deduce that non-H Fs are both G and G* (ie. G) because it cannot be the case that both the following counterfactuals are true. That is, both that (1) the Fs that are H and G would have been G if they had not been H and (2) they would have been G* if they had not been H, for this would imply a non-H F would have been both G and G (as G* is G if H). </li><li>To arrive at counterfactuals of the required form we require knowledge of the world, and it is very controversial just <em>which</em> knowledge. But this knowledge is not that required in applying the SR, so we don t have circularity. Nor is it controversial that applying the SR requires use of knowledge gained from other applications, since even knowing that certain Fs are G requires trusting one s senses, memory, reference books and so on. While this may raise problems along the lines of the old problem of induction, this has not been Jackson s concern in this paper. His aim has been to describe circumstances in which the SR can be used without dividing predicates into the projectible and the non-projectible. </li></ul><BR><HR><BR><U><B>In-Page Footnotes</U></B><a name="On-Page_Link_P255_1"></A><BR><BR><U><A HREF="#On-Page_Return_P255_1"><B>Footnote 1</A></B></U>: Straight Rule. <a name="On-Page_Link_P255_3"></A><BR><BR><U><A HREF="#On-Page_Return_P255_3"><B>Footnote 3</A></B></U>: <ul type="disc"><li>This is the write-up as it was when this Abstract was last output, with text as at the timestamp indicated (04/01/2018 13:36:29). </li><li><A HREF = "../../Notes/Notes_12/Notes_1206.htm">Link to Latest Write-Up Note</A>. </li></ul><a name="On-Page_Link_P255_4"></A><U><A HREF="#On-Page_Return_P255_4"><B>Footnote 4</A></B></U>: Jackson talks primarily of properties rather than of hypotheses; so follows <em>A Query</em> rather than <em>FFF</em>.<a name="On-Page_Link_P255_5"></A><BR><BR><U><A HREF="#On-Page_Return_P255_5"><B>Footnote 5</A></B></U>: Supported by Kyburg, Hacking and Barker. <a name="On-Page_Link_P255_6"></A><BR><BR><U><A HREF="#On-Page_Return_P255_6"><B>Footnote 6</A></B></U>: Supported by Kyburg & Nagel, Achinstein & Barker and Skyrms (Jackson explains Kyburg and Barker s support for both D<SUB>1</SUB> and D<SUB>2</SUB> under the discussion of D<SUB>2</SUB>). <a name="On-Page_Link_P255_7"></A><BR><BR><U><A HREF="#On-Page_Return_P255_7"><B>Footnote 7</A></B></U>: Jackson claims this as Goodman s own definition in FFF, but I find that itself ambiguous  need to check the wording against Goodman s, as well as ascertain that Jackson hasn t missed any ambiguities.<a name="On-Page_Link_P255_8"></A><BR><BR><U><A HREF="#On-Page_Return_P255_8"><B>Footnote 8</A></B></U>: This is a very odd definition that seems to apply only to objects that are blue before T, then change to green and stay green. Hence their colour-history is mapped out for them and they can t change colour like a green object can. <a name="On-Page_Link_P255_9"></A><BR><BR><U><A HREF="#On-Page_Return_P255_9"><B>Footnote 9</A></B></U>: Jackson doesn t discuss the case of emeralds examined after T. If they were all blue, and that we knew those examined before T had been green, then we could happily project that all emeralds are grue. So, he is correct that, where coherent, grue<sub>1</sub> is perfectly projectible. <a name="On-Page_Link_P255_10"></A><BR><BR><U><A HREF="#On-Page_Return_P255_10"><B>Footnote 10</A></B></U>: I have to admit to not understanding what he means here.<a name="On-Page_Link_P255_11"></A><BR><BR><U><A HREF="#On-Page_Return_P255_11"><B>Footnote 11</A></B></U>: Eg. by Kyburg and Barker, as noted above.<a name="On-Page_Link_P255_12"></A><BR><BR><U><A HREF="#On-Page_Return_P255_12"><B>Footnote 12</A></B></U>: Kelly gets the credit for this.<a name="On-Page_Link_P255_13"></A><BR><BR><U><A HREF="#On-Page_Return_P255_13"><B>Footnote 13</A></B></U>: Jackson may expatiate on this later  if not, and in any case, change this footnote!<a name="On-Page_Link_P255_14"></A><BR><BR><U><A HREF="#On-Page_Return_P255_14"><B>Footnote 14</A></B></U>: His actual wording is  grue applies to all things examined before t just in case they are green and to all other things just in case they are blue .<a name="On-Page_Link_P255_15"></A><BR><BR><U><A HREF="#On-Page_Return_P255_15"><B>Footnote 15</A></B></U>: In what sense? Formally? Both predicates imply that a<sub>1</sub>, & ., a<sub>n</sub>, are green.<a name="On-Page_Link_P255_16"></A><BR><BR><U><A HREF="#On-Page_Return_P255_16"><B>Footnote 16</A></B></U>: What prediction is? Ie, what colour are we to expect a<sub>n+1</sub> to be? According to Jackson s atemporal definition, once a<sub>n+1</sub> has been examined, to be grue it has to be green, which it is. Is this why Jackson sees no problem? The paradox is supposed to arise because after T, to be grue an emerald has to be blue.<a name="On-Page_Link_P255_17"></A><BR><BR><U><A HREF="#On-Page_Return_P255_17"><B>Footnote 17</A></B></U>: What does equivalence mean  that all have been equally examined are found to be equally green. Why, if (1) & (2) were not equivalent are (3) & (4) obviously equivalent?<a name="On-Page_Link_P255_18"></A><BR><BR><U><A HREF="#On-Page_Return_P255_18"><B>Footnote 18</A></B></U>: I seem to remember reading somewhere recently that support for a proposition doesn t lend support for propositions entailed by that proposition. Check this out!<a name="On-Page_Link_P255_19"></A><BR><BR><U><A HREF="#On-Page_Return_P255_19"><B>Footnote 19</A></B></U>: What s this extraordinary claim supposed to mean? That because I ve examined the one card that accidentally fell out of my opponent s hand that I have examined (or even  will examine ) them all? <a name="On-Page_Link_P255_20"></A><BR><BR><U><A HREF="#On-Page_Return_P255_20"><B>Footnote 20</A></B></U>: Dodgy: ignoring of tenses again?<a name="On-Page_Link_P255_21"></A><BR><BR><U><A HREF="#On-Page_Return_P255_21"><B>Footnote 21</A></B></U>: Check my analysis of FFF to see whether I even note this point!<a name="On-Page_Link_P255_22"></A><BR><BR><U><A HREF="#On-Page_Return_P255_22"><B>Footnote 22</A></B></U>: But this contradicts it s being green and examined.<a name="On-Page_Link_P255_23"></A><BR><BR><U><A HREF="#On-Page_Return_P255_23"><B>Footnote 23</A></B></U>: NB: it is unimportant whether a<sub>1</sub> & a<sub>n</sub> are G.<a name="On-Page_Link_P255_24"></A><BR><BR><U><A HREF="#On-Page_Return_P255_24"><B>Footnote 24</A></B></U>: But the  diagnosis contains conjunctions rather than disjunctions?<a name="On-Page_Link_P255_25"></A><BR><BR><U><A HREF="#On-Page_Return_P255_25"><B>Footnote 25</A></B></U>: There is something fishy about treating this as a property like any other  almost like treating existence in this way.<a name="On-Page_Link_P255_26"></A><BR><BR><U><A HREF="#On-Page_Return_P255_26"><B>Footnote 26</A></B></U>: Jackson has recast the counterfactual condition into a positive form (& would have been & ) at this stage, so regards the condition as satisfied, which comes to the same thing.<a name="On-Page_Link_P255_27"></A><BR><BR><U><A HREF="#On-Page_Return_P255_27"><B>Footnote 27</A></B></U>: He takes t to be now and T in the very near futures such that any further examinations will be after T. <em>Examined</em> means <em>examined by now</em>.<a name="On-Page_Link_P255_28"></A><BR><BR><U><A HREF="#On-Page_Return_P255_28"><B>Footnote 28</A></B></U>: Check this out in Dretske (?)<a name="On-Page_Link_P255_29"></A><BR><BR><U><A HREF="#On-Page_Return_P255_29"><B>Footnote 29</A></B></U>: <a name="4"></a>"<A HREF = "../../Abstracts/Abstract_02/Abstract_2117.htm">Quine (W.V.) - Natural Kinds</A>", in <a name="6"></a>"<A HREF = "../../BookSummaries/BookSummary_00/BookPaperAbstracts/BookPaperAbstracts_43.htm">Quine (W.V.) - Ontological Relativity</A>". Look this up sometime!<a name="On-Page_Link_P255_30"></A><BR><BR><U><A HREF="#On-Page_Return_P255_30"><B>Footnote 30</A></B></U>: But, we normally take  sampled as  sampled by me , or even if we take it more widely, we don t expect that all emeralds, say, have already been sampled by someone.<a name="On-Page_Link_P255_31"></A><BR><BR><U><A HREF="#On-Page_Return_P255_31"><B>Footnote 31</A></B></U>: This seems a bizarre notion. After drawing two marbles they belong in a range, but this doesn t entitle me to believe the next one will lie in the middle. <a name="On-Page_Link_P255_32"></A><BR><BR><U><A HREF="#On-Page_Return_P255_32"><B>Footnote 32</A></B></U>: Presumably only if we had just discovered this source.<a name="On-Page_Link_P255_33"></A><BR><BR><U><A HREF="#On-Page_Return_P255_33"><B>Footnote 33</A></B></U>: Of course, the SR would be wrong in the case of all unexamined emeralds in fact being red! <a name="On-Page_Link_P255_34"></A><BR><BR><U><A HREF="#On-Page_Return_P255_34"><B>Footnote 34</A></B></U>: Jackson refers to Goodman s appeal to the entrenchment of predicates, saying it s not circular but excessively anthropocentric. <BR><BR><FONT COLOR = "0000FF"><HR></P><a name="ColourConventions"></a><p><b>Text Colour Conventions (see <A HREF="../../Notes/Notes_10/Notes_1025.htm">disclaimer</a>)</b></p><OL TYPE="1"><LI><FONT COLOR = "0000FF">Blue</FONT>: Text by me; &copy; Theo Todman, 2018</li><LI><FONT COLOR = "800080">Mauve</FONT>: Text by correspondent(s) or other author(s); &copy; the author(s)</li></OL> <BR><HR><BR><CENTER> <TABLE class = "Bridge" WIDTH=950> <TR><TD WIDTH="30%">&copy; Theo Todman, June 2007 - August 2018.</TD> <TD WIDTH="40%">Please address any comments on this page to <A HREF="mailto:theo@theotodman.com">theo@theotodman.com</A>.</TD> <TD WIDTH="30%">File output: <time datetime="2018-08-13T13:16" pubdate>13/08/2018 13:16:58</time> <br><A HREF="../../Notes/Notes_10/Notes_1010.htm">Website Maintenance Dashboard</A></TD></TR> <TD WIDTH="30%"><A HREF="#Top">Return to Top of this Page</A></TD> <TD WIDTH="40%"><A HREF="../../Notes/Notes_11/Notes_1140.htm">Return to Theo Todman's Philosophy Page</A></TD> <TD WIDTH="30%"><A HREF="../../index.htm">Return to Theo Todman's Home Page</A></TD> </TR></TABLE></CENTER><HR> </BODY> </HTML>