<li><span class="caret">Koons (simplified)</span>
<ol class="nested A-list">
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<div class="subtitle">Mereological Axioms</div>
<li>x is a <div class="tooltip"><b>part of</b><span class="tooltiptext"><b>part of</b> The relation of ‘part of’ is reflexive and anti- symmetric</span></div> y IFF anything that <div class="tooltip"><b>overlaps</b><span class="tooltiptext"><b>overlaps</b> x overlaps y IFF x and y have a part in common</span></div> x overlaps y.
<li>If there is a thing of type F, then there is an aggregate of all such types.
<li>x = y IFF x is a part of y and y is a part of x.
<li>If a whole exists, so do all of its parts.
<li>If all of the parts of a whole exist, so does thewhole.
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<ol class="nested D-list">
<li>A wholly contingent thing is something thathas no necessary parts. (Def.)
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<ol class="nested C-list">
<li>A cause and its effect must be distinct (i.e., a cause can’t overlap its effect).
<li>Every wholly contingent thing has a cause.
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<ol class="nested L-list">
<li>All parts of a necessary thing are necessary.(A4, modal system K)ⓘ
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<ol class="nested T-list">
<li>If there are any contingent things, then the universe has a cause that is a necessary thing. (L4, C1, L5, A1)
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<span class="baret"> </span>
<ul class="bested">
<li>Robert Koons, “A New Look at the Cosmological Argument,” <i>American Philosophical Quarterly</i> 34/2 (1997), pp. 193-211. For a similar argument, see John O’Leary Hawthorne and Andrew Cortens, “The Principle of Necessary Reason,” <i>Faith and Philosophy 10/1</i> (1993), pp. 60-67.
</ul>