<!DOCTYPE html><HTML lang="en"> <head><meta charset="utf-8"> <title>Armstrong (David) - What is a Law of Nature? Conclusions (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_11264.htm">What is a Law of Nature? Conclusions</A></th></tr> <tr><th><A HREF = "../../Authors/A/Author_Armstrong (David).htm">Armstrong (David)</a></th></tr> <tr><th>Source: Armstrong - What is a Law of Nature?</th></tr> <tr><th>Paper - Abstract</th></tr> </TABLE> </CENTER> <P><CENTER><TABLE class = "Bridge" WIDTH=600><tr><td><A HREF = "../../PaperSummaries/PaperSummary_11/PaperSummary_11264.htm">Paper Summary</A></td><td><A HREF = "../../PaperSummaries/PaperSummary_11/PapersToNotes_11264.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>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 name="1"></a><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 name="2"></a><A HREF="../../Notes/Notes_10/Notes_1008.htm">universals</A><SUP>2</SUP>. The instantiations of these <a name="3"></a><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 name="4"></a><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 name="5"></a><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 name="6"></a><A HREF="../../Notes/Notes_10/Notes_1008.htm">universals</A><SUP>6</SUP>. These higher-order <a name="7"></a><A HREF="../../Notes/Notes_10/Notes_1008.htm">universals</A><SUP>7</SUP> are instantiated by the lower-order <a name="8"></a><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 name="9"></a><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 name="10"></a><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 name="11"></a><A HREF="../../Notes/Notes_10/Notes_1008.htm">universals</A><SUP>11</SUP> or relations between <a name="12"></a><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><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="2018-08-02T07:32" pubdate>02/08/2018 07:32:36</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>