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This makes sense because propositions of this form are all either tautologies or contradictions and as such do not express information about the state of events in the world. 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<!--replace-end-7--><!--replace-end-4--><!--replace-end-1--></head><body><div class="ui fluid container universe"><!--replace-start-2--><!--replace-start-3--><!--replace-start-6--><div class="ui text container" id="zettel-container" style="position: relative"><div class="zettel-view"><article class="ui raised attached segment zettel-content"><div class="pandoc"><h1 id="title-h1">Logical indeterminacy</h1><p>The vast majority of propositions in natural and formal logical languages are **neither <a href="Logical_truth_and_falsity.md#logical-truth">logically true</a> or <a href="Logical_truth_and_falsity.md#logical-falsity">logically false</a>**. This makes sense because propositions of this form are all either tautologies or contradictions and as such do not express information about the state of events in the world. We call propositions that are neither logically true or logically false, <strong>logically indeterminate</strong> propositions.</p><h2 id="informal-definition">Informal definition</h2><p>A proposition is logically indeterminate if it is neither logically true or logically false. This is to say: it can be both <span class="zettel-link-container errors"><span class="zettel-link" title="Wiki-link does not refer to any existing zettel"><a>Consistency</a></span></span> asserted and consistently denied.</p><p>For example the proposition:</p><pre><code class="language-none">It is raining.</code></pre><p>May be true or false thus it can it both be asserted and denied quite consistently. It is true if it actually is raining and false if it actually is not raining. There is no logical contradiction implied by saying it is raining when it isn’t raining, this assertion is simply false. There is a contradiction in saying that both states obtain. Thus the proposition:</p><pre><code class="language-none">It is raining and it is not raining.</code></pre><p>Cannot be consistently asserted as there is no possibility of the proposition being true. It is either raining or it isn’t raining. Given the law for conjunction, both conjuncts must be true for the proposition as a whole to be true. But in the case of this proposition if one conjunct is true, the other must be false and vice versa, hence it is not possible for the proposition to be true at all. It can <em>only</em> be false.</p><p>Contrariwise the proposition:</p><pre><code class="language-none">It is raining or it is not raining.</code></pre><p>Cannot be consistently denied as there is no possibility of it being false. It is either raining or not raining. Given the law for disjunction, either disjunct can be true to make the proposition as a whole true. Given that it is either raining or not raining in either scenario, the proposition as a whole will be true. Therefore there is no possibility of it being false, it can <em>only</em> be true.</p><h2 id="formal-definition">Formal definition</h2><blockquote><p>A proposition P is truth-functionally indeterminate if and only if it is neither truth-functionally true or truth-functionally false. should be avoided in arguments, they ‘prove’ everything whi</p></blockquote><pre><code class="language-none">P</code></pre><h3 id="truth-table">Truth-table</h3><table class="ui table"><thead><tr><th><span class="math inline">\(P\)</span></th><th><span class="math inline">\(P\)</span></th></tr></thead><tbody><tr><td>T</td><td>T</td></tr><tr><td>F</td><td>F</td></tr></tbody></table></div></article><nav class="ui attached segment deemphasized backlinksPane" id="neuron-backlinks-pane"><h3 class="ui header">Backlinks</h3><ul class="backlinks"><li><span class="zettel-link-container cf"><span class="zettel-link"><a href="Truth_functional_connectives.html">Truth-functional connectives</a></span></span><ul class="context-list" style="zoom: 85%;"><li class="item"><div class="pandoc"><p>We know that <span class="zettel-link-container cf"><span class="zettel-link" title="Zettel: Logical indeterminacy"><a href="Logical_indeterminacy.html">logically determinant</a></span></span> propositions express a truth value. When simple propositions are joined with a connective to make a compound proposition they also have a truth value. This is determined by the nature of the connective and the truth value of the constituent propositions. We therefore call connectives of this nature truth <em>functional</em> connectives since the <strong>truth value of the compound is a function of the truth values of its components</strong>.</p></div></li></ul></li></ul></nav><nav class="ui attached segment deemphasized bottomPane" id="neuron-tags-pane"><div><span class="ui basic label zettel-tag" title="Tag">logic</span><span class="ui basic label zettel-tag" title="Tag">propositional-logic</span></div></nav><nav class="ui bottom attached icon compact inverted menu blue" id="neuron-nav-bar"><!--replace-start-9--><!--replace-end-9--><a class="right item" href="impulse.html" title="Open Impulse"><i class="wave square icon"></i></a></nav></div></div><!--replace-end-6--><!--replace-end-3--><!--replace-end-2--><div class="ui center aligned container footer-version"><div class="ui tiny image"><a href="https://neuron.zettel.page"><img alt="logo" src="https://raw.githubusercontent.com/srid/neuron/master/assets/neuron.svg" title="Generated by Neuron 1.9.35.3" /></a></div></div></div></body></html> |