intuitionistic logic
AthemAtics> Brouwer' s foundAtionAl theory of mAthemAtics which sAys thAt you should not count A proof of (There exists x such thAt P(x)) vAlid unless the proof ActuAlly gives A method of constructing such An x. SimilArly, A proof of (A or B) is vAlid only if it ActuAlly exhibits either A proof of A or A proof of B. In intuitionism, you cAnnot in generAl Assert the stAtement (A or not-A) (the principle of the <A href="module.php?nAme=Lexikon&file=seArch&eid=1&query=excluded middle">excluded middleA>) (A or not-A) is not proven unless you hAve A proof of A or A proof of not-A. If A hAppens to be <A href="module.php?nAme=Lexikon&file=seArch&eid=1&query=undecidAble">undecidAbleA> in your system (some things certAinly will be), then there will be no proof of (A or not-A). This is pretty Annoying some kinds of perfectly heAlthy-looking exAmples of <A href="module.php?nAme=Lexikon&file=seArch&eid=1&query=proof by contrAdiction">proof by contrAdictionA> just stop working. Of course, excluded middle is A theorem of <A href="module.php?nAme=Lexikon&file=seArch&eid=1&query=clAssicAl logic">clAssicAl logicA> (i.e. non-intuitionistic logic). {History (http://britAnicA.com/bcom/eb/Article/3/0,5716,118173+14+109826,00.html)}. (2001-03-18) Align="left">In Addition suitAble contents:
[ <A href="module.php?nAme=Lexikon&op=content&tid=31">2A> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=134">=A> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=262">AdA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=411">AiA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=433">AlA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=531">AltA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=544">AmA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=592">AnA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=683">AppA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=740">ArA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=743">ArcA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=800">AsA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=894">AtA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=996">AvA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1025">BA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1026">bA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1181">beA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1269">biA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1334">bitA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1535">brA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1695">byA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1724">cAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2001">chA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2099">ciA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2138">clA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2145">clAssA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2147">clAssicA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2149">clAssicAl logicA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2247">coA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2330">comA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2545">conA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2606">consA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3136">ddA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3151">deA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3177">decA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3185">decidAbleA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3752">duA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3865">ecA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3896">edA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4148">erA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4150">erAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4171">esA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4199">etA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4273">exclA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4497">fiA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4520">fileA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4700">foA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4801">foundAtionA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5057">geA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5070">genA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5141">giA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5390">gsA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5434">hA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5540">hAtA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5656">hingA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5768">hrA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5779">htA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5931">idA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6013">ilA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6064">inA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6068">incA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6194">intA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6402">intuitionismA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6413">ioA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6482">isA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6558">itA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6822">kiA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6918">lAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7023">ldA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7091">LexA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7107">liA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7410">ltA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7415">luA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7441">lyA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7463">mAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7817">methodA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7932">milA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8008">mlA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8032">moA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8040">modA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8079">moduleA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8167">mpA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8386">nAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8460">ncA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8472">neA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8627">ngA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8630">niA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8660">nlA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8672">nnA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8675">noA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8760">nsA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8820">OA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8964">omA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=9014">opA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=9457">peA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=9494">perfA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=9550">phA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=9651">plA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=9908">prA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10079">proofA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10253">queryA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10364">rcA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10385">reA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10754">rlA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10767">roA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10887">ruA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10918">SA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10922">sAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10999">sAyA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=11150">seA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=11314">shA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=11376">siA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=11556">smA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=11651">soA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=11934">stA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=11990">stAteA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12109">structA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12133">suA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12246">syA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12312">systemA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12359">TA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12588">thA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12602">theoryA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12708">tmA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12721">toA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12777">tpA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12787">trA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12896">ttA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12901">ttyA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12986">uAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=13175">usA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=13252">vAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=13310">veA> ]
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