<!DOCTYPE html><HTML lang="en"> <head><meta charset="utf-8"> <title>What is a Law of Nature? (Armstrong (David)) - Theo Todman's Book Collection (Book-Paper Abstracts)</title> <link href="../../../TheosStyle.css" rel="stylesheet" type="text/css"><link rel="shortcut icon" href="../../../TT_ICO.png" /> </head> <a name="Top"></a> <BODY> <div id="header"> <HR><H1>Theo Todman's Book Collection (Book-Paper Abstracts)</H1></div> <hr><CENTER><TABLE class = "Bridge" WIDTH=950><tr><td colspan =2><A HREF = "../BookSummary_1192.htm">What is a Law of Nature?</A></td></tr><tr><td colspan =2><A HREF = "../../../Authors/A/Author_Armstrong (David).htm">Armstrong (David)</a></td></tr><tr><td colspan =2>This Page provides (where held) the <b>Abstract</b> of the above <b>Book</b> and those of all the <b>Papers</b> contained in it.</td></tr><tr><td><A HREF="#ColourConventions">Text Colour-Conventions</a></td><td><A HREF = "../BookCitings_1192.htm">Books / Papers Citing this Book</A></td></tr></tr></TABLE></CENTER><hr> <P ALIGN = "Justify"><FONT Size = 2 FACE="Arial"><FONT COLOR = "0000FF"><B>BOOK ABSTRACT: </B><BR><BR><U>Amazon Book Description</U><FONT COLOR = "800080"><ol type="1"><li>This is a study of a crucial and controversial topic in metaphysics and the philosophy of science: the status of the laws of nature. D. M. Armstrong works out clearly and in comprehensive detail a largely original view that laws are relations between properties or <a name="1"></a><A HREF="../../../Notes/Notes_10/Notes_1008.htm">universals</A><SUP>1</SUP>. The theory is continuous with the views on <U><A HREF="#On-Page_Link_B1192_2">universals</A></U><SUB>2</SUB><a name="On-Page_Return_B1192_2"></A> and more generally with the scientific realism that Professor Armstrong has advanced in earlier publications. </li><li>He begins here by mounting an attack on the orthodox and sceptical view deriving from Hume that laws assert no more than a regularity of coincidence between instances of properties. In doing so he presents what may become the definitive statement of the case against this position. </li><li>Professor Armstrong then goes on to establish his own theory in a systematic manner defending it against the most likely objections, and extending both it and the related theory of <a name="2"></a><A HREF="../../../Notes/Notes_10/Notes_1008.htm">universals</A><SUP>3</SUP> to cover functional and statistical laws. </li><li>This treatment of the subject is refreshingly concise and vivid: it will both stimulate vigorous professional debate and make an excellent student text.</li></ol></FONT><BR><U>Chapters</U><FONT COLOR = "800080"><ol type="I">Acknowledgements  x<li>PART I  A critique of the Regularity theory  1 <ol type="1"><li>Introductory  3</li><li>Critique of the Regularity theory (1): The problem of accidental uniformities  11</li><li>Critique of the Regularity theory (2)  24</li><li>Critique of the Regularity theory (3)  39</li><li>Can the Regularity theory be sophisticated?  60</li></ol></li><li>PART II  Laws of nature as relations between <a name="3"></a><A HREF="../../../Notes/Notes_10/Notes_1008.htm">universals</A><SUP>4</SUP>  75<ol start = "6" type="1"><li>Laws of nature as relations between <a name="4"></a><A HREF="../../../Notes/Notes_10/Notes_1008.htm">universals</A><SUP>5</SUP>  77</li><li>Functional laws  111</li><li>Uninstantiated laws  117</li><li>Probabilistic laws  128</li><li>Further considerations concerning the form of laws  137</li><li>Are the laws of nature necessary or contingent?  158 </li></ol><BR>Conclusions  172 <BR>Works cited  174 <BR>Index  177 </li></ol></FONT><BR><HR><BR><U><B>In-Page Footnotes</U> (<a name="5"></a>"<A HREF = "../../../BookSummaries/BookSummary_01/BookPaperAbstracts/BookPaperAbstracts_1192.htm">Armstrong (David) - What is a Law of Nature?</A>")</B><a name="On-Page_Link_B1192_2"></A><BR><BR><U><A HREF="#On-Page_Return_B1192_2"><B>Footnote 2</B></A></U>: See <a name="6"></a>"<A HREF = "../../../BookSummaries/BookSummary_00/BookPaperAbstracts/BookPaperAbstracts_275.htm">Armstrong (David) - Universals and Scientific Realism (Vol. 1: Nominalism and Realism)</A>" & <a name="7"></a>"<A HREF = "../../../BookSummaries/BookSummary_00/BookPaperAbstracts/BookPaperAbstracts_276.htm">Armstrong (David) - Universals and Scientific Realism (Vol. 2: A Theory of Universals)</A>". <BR><BR><FONT COLOR = "0000FF"><HR><B>BOOK COMMENT: </B><ul type="disc"><li>CUP, 1985 </li><li>Photocopy of complete book; </li><li>filed in <a name="8"></a>"<A HREF = "../../../BookSummaries/BookSummary_01/BookPaperAbstracts/BookPaperAbstracts_1190.htm">Various - Papers on Logic & Metaphysics Boxes: Vol 1 (Coursework & A-E)</A>". </li></ul></P> <P ALIGN = "Justify"><FONT Size = 2 FACE="Arial"><FONT COLOR = "0000FF"><HR><BR>"<B><A HREF = "../../../PaperSummaries/PaperSummary_00/PaperSummary_163.htm">Dretske (Fred) - Review of Armstrong's 'What is a Law of Nature'</A></B>"<BR><BR><B>Source</B>: British Journal for the Philosophy of Science 36.1, March 1985, pp. 79-81<BR><BR><FONT COLOR = "0000FF"><B>COMMENT: </B>Review of "<A HREF = "../../../BookSummaries/BookSummary_01/BookPaperAbstracts/BookPaperAbstracts_1192.htm">Armstrong (David) - What is a Law of Nature?</A>".</P> <P ALIGN = "Justify"><FONT Size = 2 FACE="Arial"><FONT COLOR = "0000FF"><HR><BR>"<B><A HREF = "../../../PaperSummaries/PaperSummary_00/PaperSummary_424.htm">Wilson (Mark) - Review of David Armstrong's 'What is a Law of Nature?'</A></B>"<BR><BR><B>Source</B>: Philosophical Review 96.3, July 1987, pp. 435-441<BR><BR><FONT COLOR = "0000FF"><B>COMMENT: </B>Review of "<A HREF = "../../../BookSummaries/BookSummary_01/BookPaperAbstracts/BookPaperAbstracts_1192.htm">Armstrong (David) - What is a Law of Nature?</A>".</P> <P ALIGN = "Justify"><FONT Size = 2 FACE="Arial"><FONT COLOR = "0000FF"><HR><BR>"<B><A HREF = "../../../PaperSummaries/PaperSummary_00/PaperSummary_522.htm">Armstrong (David) - What is a Law of Nature? Introductory</A></B>"<BR><BR><B>Source</B>: Armstrong - What is a Law of Nature? Chapter 1<BR><FONT COLOR = "0000FF"><BR><BR><U>Sections</U><FONT COLOR = "800080"><ol type="1"><li>The importance of our topic  3</li><li>A possible difficulty in investigating our topic  5</li><li>Assumptions  7</li><li>The Regularity theory  9 </li></ol></FONT></P> <P ALIGN = "Justify"><FONT Size = 2 FACE="Arial"><FONT COLOR = "0000FF"><HR><BR>"<B><A HREF = "../../../PaperSummaries/PaperSummary_21/PaperSummary_21603.htm">Armstrong (David) - Critique of the Regularity theory (1): The problem of accidental uniformities</A></B>"<BR><BR><B>Source</B>: Armstrong - What is a Law of Nature? Chapter 2<BR><FONT COLOR = "0000FF"><BR><BR><U>Sections</U><FONT COLOR = "800080"><ol type="1"><li>The Naive Regularity theory of law  11</li><li>Classification of criticisms of the Regularity theory  12</li><li>Single-case uniformities  13</li><li>How to pass from single-case uniformities to multi-case uniformities  15</li><li>How to pass from local uniformities to Humean uniformities  17</li><li>Unrealized physical possibilities  17</li><li>Humean uniformities with non-existent subjects  19 </li></ol></FONT></P> <P ALIGN = "Justify"><FONT Size = 2 FACE="Arial"><FONT COLOR = "0000FF"><HR><BR>"<B><A HREF = "../../../PaperSummaries/PaperSummary_21/PaperSummary_21604.htm">Armstrong (David) - Critique of the Regularity theory (2)</A></B>"<BR><BR><B>Source</B>: Armstrong - What is a Law of Nature? Chapter 3<BR><FONT COLOR = "0000FF"><BR><BR><U>Sections</U><FONT COLOR = "800080"><ol type="1"><li>Spatio-temporally limited laws  24</li><li>Local uniformities as laws  26</li><li>Infinitely qualified laws  27</li><li>Probabilistic laws  29</li><li>Probabilistic laws: the retreat to Positivism  35</li><li>Functional laws  37 </li></ol></FONT></P> <P ALIGN = "Justify"><FONT Size = 2 FACE="Arial"><FONT COLOR = "0000FF"><HR><BR>"<B><A HREF = "../../../PaperSummaries/PaperSummary_21/PaperSummary_21605.htm">Armstrong (David) - Critique of the Regularity theory (3)</A></B>"<BR><BR><B>Source</B>: Armstrong - What is a Law of Nature? Chapter 4<BR><FONT COLOR = "0000FF"><BR><BR><U>Sections</U><FONT COLOR = "800080"><ol type="1"><li>Lack of inner connection  39</li><li>Laws of nature as Principles of Explanation  40</li><li>The Paradoxes of Confirmation  41</li><li>The problem of counterfactuals  46</li><li>The Problem of Induction  52 </li></ol></FONT></P> <P ALIGN = "Justify"><FONT Size = 2 FACE="Arial"><FONT COLOR = "0000FF"><HR><BR>"<B><A HREF = "../../../PaperSummaries/PaperSummary_21/PaperSummary_21606.htm">Armstrong (David) - Can the Regularity theory be sophisticated?</A></B>"<BR><BR><B>Source</B>: Armstrong - What is a Law of Nature? Chapter 5<BR><FONT COLOR = "0000FF"><BR><BR><U>Sections</U><FONT COLOR = "800080"><ol type="1"><li>Preliminary  60</li><li>Epistemic restriction upon uniformities  61</li><li>The Resiliency solution  64</li><li>Systematic restrictions upon uniformities  66 </li></ol></FONT></P> <P ALIGN = "Justify"><FONT Size = 2 FACE="Arial"><FONT COLOR = "0000FF"><HR><BR>"<B><A HREF = "../../../PaperSummaries/PaperSummary_21/PaperSummary_21607.htm">Armstrong (David) - Laws of nature as relations between universals</A></B>"<BR><BR><B>Source</B>: Armstrong - What is a Law of Nature? Chapter 6<BR><FONT COLOR = "0000FF"><BR><BR><U>Sections</U><FONT COLOR = "800080"><ol type="1"><li>The need for <A HREF="../../../Notes/Notes_10/Notes_1008.htm">universals</A><SUP>1</SUP>  77</li><li>The theory of <A HREF="../../../Notes/Notes_10/Notes_1008.htm">universals</A><SUP>2</SUP>  81</li><li>A first formulation  85</li><li>Laws as <A HREF="../../../Notes/Notes_10/Notes_1008.htm">universals</A><SUP>3</SUP>  88</li><li><A HREF="../../../Notes/Notes_0/Notes_39.htm">Causation</A><SUP>4</SUP> as a relation between particulars  93</li><li>Necessitation, <A HREF="../../../Notes/Notes_10/Notes_1008.htm">universals</A><SUP>5</SUP> and laws  96</li><li>Advantages and some disadvantages of conceiving of laws of nature as relations between <A HREF="../../../Notes/Notes_10/Notes_1008.htm">universals</A><SUP>6</SUP>  99</li><li>Braithwaite's and Popper's argument  107</li></ol></FONT></P> <P ALIGN = "Justify"><FONT Size = 2 FACE="Arial"><FONT COLOR = "0000FF"><HR><BR>"<B><A HREF = "../../../PaperSummaries/PaperSummary_21/PaperSummary_21608.htm">Armstrong (David) - Functional laws</A></B>"<BR><BR><B>Source</B>: Armstrong - What is a Law of Nature? Chapter 7<BR></P> <P ALIGN = "Justify"><FONT Size = 2 FACE="Arial"><FONT COLOR = "0000FF"><HR><BR>"<B><A HREF = "../../../PaperSummaries/PaperSummary_21/PaperSummary_21609.htm">Armstrong (David) - Uninstantiated laws</A></B>"<BR><BR><B>Source</B>: Armstrong - What is a Law of Nature? Chapter 8<BR><FONT COLOR = "0000FF"><BR><BR><U>Sections</U><FONT COLOR = "800080"><ol type="1"><li>Tooley's cases  117</li><li>Tooley's conclusions  118</li><li>Tooley's cases solved by the introduction of powers?  121</li><li>A sceptical treatment of Tooley's cases  123</li><li>Uninstantiated laws with nomically impossible antecedents  126 </li></ol></FONT></P> <P ALIGN = "Justify"><FONT Size = 2 FACE="Arial"><FONT COLOR = "0000FF"><HR><BR>"<B><A HREF = "../../../PaperSummaries/PaperSummary_21/PaperSummary_21610.htm">Armstrong (David) - Probabilistic laws</A></B>"<BR><BR><B>Source</B>: Armstrong - What is a Law of Nature? Chapter 9<BR><FONT COLOR = "0000FF"><BR><BR><U>Sections</U><FONT COLOR = "800080"><ol type="1"><li>The form of probabilistic laws  128</li><li>Probabilistic laws as probabilities of necessitation  131</li><li>Other types of probabilistic laws  135 </li></ol></FONT></P> <P ALIGN = "Justify"><FONT Size = 2 FACE="Arial"><FONT COLOR = "0000FF"><HR><BR>"<B><A HREF = "../../../PaperSummaries/PaperSummary_21/PaperSummary_21611.htm">Armstrong (David) - Further considerations concerning the form of laws</A></B>"<BR><BR><B>Source</B>: Armstrong - What is a Law of Nature? Chapter 10<BR><FONT COLOR = "0000FF"><BR><BR><U>Sections</U><FONT COLOR = "800080"><ol type="1"><li>Scientific identification  137</li><li>Laws with universal scope  140</li><li>Are there any Exclusion laws?  143</li><li>Iron laws and Oaken laws  147</li><li>Disjunctive laws  150 </li><li>Do laws always link the properties of the same object?  153 </li><li>Formal properties of Necessitation  155 </li></ol></FONT></P> <P ALIGN = "Justify"><FONT Size = 2 FACE="Arial"><FONT COLOR = "0000FF"><HR><BR>"<B><A HREF = "../../../PaperSummaries/PaperSummary_21/PaperSummary_21612.htm">Armstrong (David) - Are the laws of nature necessary or contingent?</A></B>"<BR><BR><B>Source</B>: Armstrong - What is a Law of Nature? Chapter 11<BR><FONT COLOR = "0000FF"><BR><BR><U>Sections</U><FONT COLOR = "800080"><ol type="1"><li>Arguments for the necessity of laws  159 </li><li>Strong Necessity  163 </li><li>Weak Necessity  166 </li><li>Uninstantiated laws  169 </li></ol></FONT></P> <P ALIGN = "Justify"><FONT Size = 2 FACE="Arial"><FONT COLOR = "0000FF"><HR><BR>"<B><A HREF = "../../../PaperSummaries/PaperSummary_11/PaperSummary_11264.htm">Armstrong (David) - What is a Law of Nature? Conclusions</A></B>"<BR><BR><B>Source</B>: Armstrong - What is a Law of Nature?<BR><FONT COLOR = "0000FF"><BR><BR><U>Full Text</U><FONT COLOR = "800080"><ol type="1"><li>I will try to sum up the main positive theses argued for in this essay. </li><li>Laws of nature are dyadic relations of necessitation (or probabilification) holding between <A HREF="../../../Notes/Notes_10/Notes_1008.htm">universals</A><SUP>1</SUP>. They are (higher-order) states of affairs, states of affairs which are simultaneously <A HREF="../../../Notes/Notes_10/Notes_1008.htm">universals</A><SUP>2</SUP>. The instantiations of these <A HREF="../../../Notes/Notes_10/Notes_1008.htm">universals</A><SUP>3</SUP> are the positive instances falling under the law. It is an intelligible notion that a particular first-order state of affairs should necessitate a further first-order state of affairs, yet not in virtue of the <A HREF="../../../Notes/Notes_10/Notes_1008.htm">universals</A><SUP>4</SUP> involved in these states of affairs. But in a law of nature this <em>same</em> relation of necessitation links <em>sorts</em> of states of affairs, that is, <A HREF="../../../Notes/Notes_10/Notes_1008.htm">universals</A><SUP>5</SUP>. Such necessitations 'might have been other than they are', that is, they are contingent. Where one sort of state of affairs necessitates another, then it is entailed, in the absence of further interfering factors (which are always at least logically possible), that the first sort of state of affairs is constantly conjoined with the second sort of state of affairs. </li><li>All genuine laws are instantiated laws. Statements of uninstantiated law are to be construed as counterfactuals about what laws would hold if certain conditions were realized. Such statements depend for their truth upon the existence of higher-order laws. Given the higher-order law and the contrary-to-fact condition, then the uninstantiated law may be deduced. </li><li>Functional laws are higher-order laws governing those lower-order laws which can be deduced from a functional law after substituting particular values for independent variables. Higher-order laws are relations between higher-order <A HREF="../../../Notes/Notes_10/Notes_1008.htm">universals</A><SUP>6</SUP>. These higher-order <A HREF="../../../Notes/Notes_10/Notes_1008.htm">universals</A><SUP>7</SUP> are instantiated by the lower-order <A HREF="../../../Notes/Notes_10/Notes_1008.htm">universals</A><SUP>8</SUP> involved in the lower-order laws. (<em>Mass</em> may be a higher-order universal, instantiated by the determinate mass-values such as one kilogram exact.) </li><li>Irreducibly probabilistic laws are also relations between <A HREF="../../../Notes/Notes_10/Notes_1008.htm">universals</A><SUP>9</SUP>. These relations give (are constituted by) a certain objective probability that individual instantiations of the antecedent universal will <em>necessitate</em> instantiation of the consequent universal. They give a probability of a necessitation in the particular case. Like all laws, they must have (positive) instantiations at some time. Deterministic laws are limiting cases of probabilistic laws (probability 1). </li><li>It is always logically possible that the antecedent universal of a law of nature should be instantiated, yet that, because of the presence of interfering factors, the consequent universal not be instantiated. (The absence of interfering factors is not a factor.) If this possibility is no more than a logical possibility, then the law may be said to be iron. (A probabilistic law can be an iron law.) If interference sometimes actually occurs, then the law may be said to be oaken. </li><li>There are strong, if not conclusive, reasons to reject negative and disjunctive <A HREF="../../../Notes/Notes_10/Notes_1008.htm">universals</A><SUP>10</SUP>. As a result, there is reason to reject exclusion laws, and laws with disjunctive consequents. However, such laws may be freely admitted as <em>derived</em> laws. Derived laws are no more than the logical consequences of the underived or genuine laws. They involve no further <A HREF="../../../Notes/Notes_10/Notes_1008.htm">universals</A><SUP>11</SUP> or relations between <A HREF="../../../Notes/Notes_10/Notes_1008.htm">universals</A><SUP>12</SUP>. </li><li>It appears that all laws link a state of affairs where a particular has a property with a state of affairs where <em>that same particular</em> has a further property. However, the properties involved may be <em>relational</em> properties. The relations involved in these relational properties will regularly involve temporal relations. </li><li>The necessitation relation, unlike logical necessitation, is not reflexive, is not transitive, cannot be contraposed, and is not symmetrical. </li></ol></FONT></P> <a name="ColourConventions"></a><hr><br><B><U>Text Colour Conventions</U> (see <A HREF="../../../Notes/Notes_10/Notes_1025.htm">disclaimer</a>)</B><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> </center> <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="2018-08-02T02:51" pubdate>02/08/2018 02:51:19</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>