http://wiki.karljones.com/index.php?action=history&feed=atom&title=Formal_system 2026-10-24T00:44:15Z Revision history for this page on the wiki MediaWiki 1.24.2 http://wiki.karljones.com/index.php?title=Formal_system&diff=11875&oldid=prev 2016-04-20T15:34:15Z

<p>‎<span dir="auto"><span class="autocomment">External links</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 15:34, 20 April 2016</td> </tr><tr><td colspan="2" class="diff-lineno">Line 43:</td> <td colspan="2" class="diff-lineno">Line 43:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* [https://en.wikipedia.org/wiki/Formal_system Formal system] @ Wikipedia</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* [https://en.wikipedia.org/wiki/Formal_system Formal system] @ Wikipedia</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Category:Logic]]</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Category:Mathematics]]</ins></div></td></tr> </table>

Karl Jones http://wiki.karljones.com/index.php?title=Formal_system&diff=8736&oldid=prev 2016-02-20T21:17:51Z

<p>Created page with &quot;A &#039;&#039;&#039;formal system&#039;&#039;&#039; is broadly defined as any well-defined system of abstract thought based on the model of <a href="/index.php/Mathematics" title="Mathematics">mathematics</a>. == Description == The entailment of the system...&quot;</p> <p><b>New page</b></p><div>A '''formal system''' is broadly defined as any well-defined system of abstract thought based on the model of [[mathematics]].<br /> <br /> == Description ==<br /> <br /> The entailment of the system by its logical foundation is what distinguishes a formal system from others which may have some basis in an abstract model.<br /> <br /> Often the formal system will be the basis for or even identified with a larger theory or field (e.g. [[Euclidean geometry]]) consistent with the usage in modern mathematics such as model theory.<br /> <br /> A formal system need not be mathematical as such; for example, [[Spinoza's Ethics]] imitates the form of [[Euclid's Elements]].<br /> <br /> Each formal system has a [[formal language]], which is composed by [[primitive symbols]].<br /> <br /> These symbols act on certain rules of formation and are developed by inference from a set of [[Axiom|axioms]].<br /> <br /> The system thus consists of any number of formulas built up through finite combinations of the primitive symbols.<br /> <br /> These combinations that are formed from the axioms in accordance with the stated rules.<br /> <br /> == Mathematics ==<br /> <br /> Formal systems in [[mathematics]] consist of the following elements:<br /> <br /> * A finite set of symbols (i.e. the alphabet), that can be used for constructing formulas (i.e. finite strings of symbols).<br /> * A grammar, which tells how well-formed formulas (abbreviated wff) are constructed out of the symbols in the alphabet. It is usually required that there be a decision procedure for deciding whether a formula is well formed or not.<br /> * A set of axioms or axiom schemata: each axiom must be a wff.<br /> * A set of inference rules.<br /> <br /> == Recursion ==<br /> <br /> A formal system is said to be recursive (i.e. effective) if the set of axioms and the set of inference rules are decidable sets or semidecidable sets, according to context.<br /> <br /> == Formalism ==<br /> <br /> Some theorists use the term formalism as a rough synonym for formal system, but the term is also used to refer to a particular style of notation, for example, Paul Dirac's bra–ket notation.<br /> <br /> == See also ==<br /> <br /> * [[Formal language]]<br /> * [[Logic]]<br /> * [[Mathematics]]<br /> <br /> == External links ==<br /> <br /> * [https://en.wikipedia.org/wiki/Formal_system Formal system] @ Wikipedia</div>

Karl Jones