<!DOCTYPE html><HTML lang="en"> <head><meta charset="utf-8"> <title>Williamson (Timothy) - Vagueness, Identity and Leibniz's Law (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_11/PaperSummary_11611.htm">Vagueness, Identity and Leibniz's Law</A></th></tr> <tr><th><A HREF = "../../Authors/W/Author_Williamson (Timothy).htm">Williamson (Timothy)</a></th></tr> <tr><th>Source: Bottani - Individuals, Essence and Identity, 2002</th></tr> <tr><th>Paper - Abstract</th></tr> </TABLE> </CENTER> <P><CENTER><TABLE class = "Bridge" WIDTH=800><tr><td><A HREF = "../../PaperSummaries/PaperSummary_11/PaperSummary_11611.htm">Paper Summary</A></td><td><A HREF = "../../PaperSummaries/PaperSummary_11/PaperCitings_11611.htm">Books / Papers Citing this Paper</A></td><td><A HREF = "../../PaperSummaries/PaperSummary_11/PapersToNotes_11611.htm">Notes Citing this Paper</A></td><td><A HREF="#ColourConventions">Text Colour-Conventions</a></td></tr></TABLE></CENTER></P> <hr><P><FONT COLOR = "0000FF"><U>Author s Introduction</U><FONT COLOR = "800080"><ol type="1"><li>When we reflect on the <a name="1"></a><A HREF="../../Notes/Notes_0/Notes_77.htm">individuation</A><SUP>1</SUP> of objects, we soon encounter hard cases. We are presented with pairs of objects the grounds for classifying which as identical look no better and no worse than the grounds for classifying them as distinct; we have no idea how to decide the question. For instance, the diachronic identify of the <a name="2"></a><A HREF="../../Notes/Notes_0/Notes_44.htm">ship of Theseus</A><SUP>2</SUP> was already a matter of philosophical debate when Plutarch wrote, and has still not been settled: <ul type="disc">The thirty-oared galley in which <a name="3"></a><A HREF="../../Notes/Notes_0/Notes_44.htm">Theseus</A><SUP>3</SUP> sailed with the youths and returned safely was preserved by the Athenians down to the time of Demetrius of Phalerum. At intervals, they removed the old timbers and replaced them with sound ones, so that the ship became a classic illustration for the philosophers of the disputed question of growth and change, some of them arguing that it remained the same, and others that it became a different vessel. (Plutarch, 'Life of Theseus' 23, Scott Kilvert (trans.) [I960]) </ul>If the name 'S1' is conferred by ostension at the time of <a name="4"></a><A HREF="../../Notes/Notes_0/Notes_44.htm">Theseus</A><SUP>4</SUP> on the ship then present, and the name 'S2' is conferred by ostension at the time of Demetrius of Phalerum on the ship present at that later time, then it seems unclear whether S1 = S2; S1 and S2 are apparently neither clearly identical nor clearly distinct. Examples of this kind abound. </li><li>Someone might describe the case thus: <ul type="disc">There are objects of which it is vague whether they are identical. Such vagueness concerns the objects themselves, not their names. When the name 'S1' was introduced, it was clear which ship was being pointed at; likewise when the name 'S2' was introduced. Thus there are objects (the ships S1 and S2) and a relation (identity) such that it is vague whether those objects stand in that relation. That amounts to vagueness in reality itself, not merely in our mental or linguistic representations of reality. </ul>Such a description contradicts the usual understanding of vagueness as located only in representations. </li><li>We might doubt whether ships are perfectly representation-independent objects, for they are artefacts, individuated at least partly in accord with the intentions of their makers or users; intentions involve mental representations. But similar identity puzzles arise for natural objects, such as planets, many of which (idealists notwithstanding) would have had the same existence and nature even if beings capable of forming representations had never evolved. </li><li>Cases of vague identity have also been claimed to occur in quantum mechanics (Lowe [1994]). However, no theory of vagueness has made any serious contribution to the understanding of problems in quantum mechanics. It is not as though we understand what is physically happening in such cases but need a theory of vagueness to describe it clearly. Quantum mechanics in its present mystifying state has no obvious morals for the theory of vagueness. </li><li>Many philosophers conceive vagueness as a kind of indeterminacy. On such a view, if it is vague whether objects are identical then it is indeterminate whether they are identical, in roughly the sense that there is no right answer to the question 'Are they identical?'. Thus reality itself would be indeterminate. That would explain our prolonged failure to resolve philosophical disputes about identity. Yet Gareth Evans [1978] and Nathan Salmon [1982] (pp.243-5), have argued formally that it cannot be indeterminate whether objects are identical. Very roughly: if it is indeterminate whether x is identical with y, then x has a property that y lacks, because it is determinate that x is self-identical, and therefore determinate whether x is identical with x, thus x is distinct from y, by <a name="5"></a><A HREF="../../Notes/Notes_0/Notes_81.htm">Leibniz's Law</A><SUP>5</SUP> of the <a name="6"></a><A HREF="../../Notes/Notes_0/Notes_81.htm">indiscernibility of identicals</A><SUP>6</SUP>, so it is after all not indeterminate whether they are identical. The claim of vague identity is self-refuting. In response, numerous attempts have been made to construct a coherent account of vague identity within a framework of many-valued logic. </li><li><ul type="disc"><li>Section 1 of this paper argues, on grounds independent of those adduced by Evans and Salmon, that many-valued logic is unpromising as a context for an account of vague identity. </li><li>Section 2 makes some more general methodological comments on non-classical treatments of vague identity. </li><li>Section 3 traces objections to the Evans argument to a significant difficulty in formulating an appropriate version of <a name="7"></a><A HREF="../../Notes/Notes_0/Notes_81.htm">Leibniz's Law</A><SUP>7</SUP> to govern the logic of identity; but the difficulty can be finessed in a way which vindicates the spirit of the Evans argument. </li><li>Section 4 shows how to make sense of a modest sort of vague identity while respecting that argument, by using an epistemic account of vagueness. </li></ul> </li></ol> </FONT><hr><FONT COLOR = "0000FF"><B>Comment: </B><BR><BR>See <a name="8"></a>"<A HREF = "../../Abstracts/Abstract_11/Abstract_11678.htm">Edgington (Dorothy) - Williamson on Vagueness, Identity and Leibniz's Law</A>" for a response.<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="2018-08-02T07:36" pubdate>02/08/2018 07:36:29</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>