ognitions。　The　concept　of　magnitude　may　be　given　a　priori　in　the　intuition　of　space；　e。g。；　of　the　right　line；　etc。；　the　concept　of　cause　in　impenetrability；　in　the　impact　of　bodies；　etc。　Consequently　both　may　be　verified　by　means　of　an　empirical　intuition；　i。e。；　the　thought　of　them　may　be　indicated　（demonstrated；　exhibited）　in　an　example；　and　this　it　must　be　possible　to　do：　for　otherwise　there　would　be　no　certainty　of　the　thought　not　being　empty；　i。e。；　having　no　object。　　　In　logic　the　expressions　demonstrable　or　indemonstrable　are　ordinarily　employed　only　in　respect　of　propositions。　A　better　designation　would　be　to　call　the　former　propositions　only　mediately；　and　the　latter；　propositions　immediately；　certain。　For　pure　philosophy；　too；　has　propositions　of　both　these　kinds…meaning　thereby　true　propositions　which　are　in　the　one　case　capable；　and　in　the　other　incapable；　of　proof。　But；　in　its　character　of　philosophy；　while　it　can；　no　doubt；　prove　on　a　priori　grounds；　it　cannot　demonstrate…unless　we　wish　to　give　the　complete　go…by　to　the　meaning　of　the　word　which　makes　demonstrate　（ostendere；　exhibere）　equivalent　to　giving　an　accompanying　presentation　of　the　concept　in　intuition　（be　it　in　a　proof　or　in　a　definition）。　Where　the　intuition　is　a　priori　this　is　called　its　construction；　but　when　even　the　intuition　is　empirical；　we　have　still　got　the　illustration　of　the　object；　by　which　means　objective　reality　is　assured　to　the　concept。　Thus　an　anatomist　is　said　to　demonstrate　the　human　eye　when　he　renders　the　concept；　of　which　he　has　previously　given　a　discursive　exposition；　intuitable　by　means　of　the　dissection　of　that　organ。　　　It　follows　from　the　above　that　the　rational　concept　of　the　supersensible　substrate　of　all　phenomena　generally；　or　even　of　that　which　must　be　laid　at　the　basis　of　our　elective　will　in　respect　of　moral　laws；　i。e。；　the　rational　concept　of　transcendental　freedom；　is　at　once　specifically　an　indemonstrable…concept；　and　a　rational　idea；　whereas　virtue　is　so　in　a　measure。　For　nothing　can　be　given　which　in　itself　qualitatively　answers　in　experience　to　the　rational　concept　of　the　former；　while　in　the　case　of　virtue　no　empirical　product　of　the　above　causality　attains　the　degree　that　the　rational　idea　prescribes　as　the　rule。　　　Just　as　the　imagination；　in　the　case　of　a　rational　idea；　fails　with　its　intuitions　to　attain　to　the　given　concept；　so　understanding；　in　the　case　of　an　aesthetic　idea；　fails　with　its　concepts　ever　to　attain　to　the　completeness　of　the　internal　intuition　which　imagination　conjoins　with　a　given　representation。　Now　since　the　reduction　of　a　representation　of　the　imagination　to　concepts　is　equivalent　to　giving　its　exponents；　the　aesthetic　idea　may　be　called　on　inexponible　representation　of　the　imagination　（in　its　free　play）。　I　shall　have　an　opportunity　hereafter　of　dealing　more　fully　with　ideas　of　this　kind。　At　present　I　confine　myself　to　the　remark；　that　both　kinds　of　ideas；　aesthetic　ideas　as　well　as　rational；　are　bound　to　have　their　principles；　and　that　the　seat　of　these　principles　must　in　both　cases　be　reason…the　latter　depending　upon　the　objective；　the　former　upon　the　subjective；　principles　of　its　employment。　　　Consonantly　with　this；　GENIUS　may　also　be　defined　as　the　faculty　of　aesthetic　ideas。　This　serves　at　the　same　time　to　point　out　the　reason　why　it　is　nature　（the　nature　of　the　individual）　and　not　a　set　purpose；　that　in　products　of　genius　gives　the　rule　to　art　（as　the　production　of　the　beautiful）。　For　the　beautiful　must　not　be　estimated　according　to　concepts；　but　by　the　final　mode　in　which　the　imagination　is　attuned　so　as　to　accord　with　the　faculty　of　concepts　generally；　and　so　rule　and　precept　are　incapable　of　serving　as　the　requisite　subjective　standard　for　that　aesthetic　and　unconditioned　finality　in　fine　art　which　has　to　make　a　warranted　claim　to　being　bound　to　please　every　one。　Rather　must　such　a　standard　be　sought　in　the　element　of　mere　nature　in　the　subject；　which　cannot　be　comprehended　under　rules　or　concepts；　that　is　to　say；　the　supersensible　substrate　of　all　the　subject's　faculties　（unattainable　by　any　concept　of　understanding）；　and　consequently　in　that　which　forms　the　point　of　reference　for　the　harmonious　accord　of　all　our　faculties　of　cognition…the　production　of　which　accord　is　the　ultimate　end　set　by　the　intelligible　basis　of　our　nature。　Thus　alone　is　it　possible　for　a　subjective　and　yet　universally　valid　principle　a　priori　to　lie　at　the　basis　of　that　finality　for　which　no　objective　principle　can　be　prescribed。
  REMARK　2。
  The　following　important　observation　here　naturally　presents　itself：　There　are　three　kinds　of　antinomies　of　pure　reason；　which；　however；　all　agree　in　forcing　reason　to　abandon　the　otherwise　very　natural　assumption　which　takes　the　objects　of　sense　for　things…in…themselves；　and　to　regard　them；　instead；　merely　as　phenomena；　and　to　lay　at　their　basis　an　intelligible　substrate　（something　supersensible；　the　concept　of　which　is　only　an　idea　and　affords　no　proper　knowledge）。　Apart　from　some　such　antinomy；　reason　could　never　bring　itself　to　take　such　a　step　as…to　adopt　a　principle　so　severely　restricting　the　field　of　its　speculation；　and　to　submit　to　sacrifices　involving　the　complete　dissipation　of　so　many　otherwise　brilliant　hopes。　For　even　now　that　it　is　recompensed　for　this　loss　by　the　prospect　of　a　proportionately　wider　scope　of　action　from　a　practical　point　of　view；　it　is　not　without　a　pang　of　regret　that　it　appears　to　part　company　with　those　hopes；　and　to　break　away　from　the　old　ties。　　　The　reason　for　there　being　three　kinds　of　antinomies　is　to　be　found　in　the　fact　that　there　are　three　faculties　of　cognition；　understanding；　judgement；　and　reason；　each　of　which；　being　a　higher　faculty　of　cognition；　must　have　its　a　priori　principles。　For；　so　far　as　reason　passes　judgement　upon　these　principles　themselves　and　their　employment；　it　inexorably　requires　the　unconditioned　for　the　given　conditioned　in　respect　of　them　all。　This　can　never　be　found　unless　the　sensible；　instead　of　being　regarded　as　inherently　appurtenant　to　things…in…themselves；　is　treated　as　a　mere　phenomenon；　and；　as　such；　being　made　to　rest　upon　something　supersensible　（the　intelligible　substrate　of　external　and　internal　nature）　as　the　thing…in…itself。　There　is　then　（1）　for　the　cognitive　faculty　an　antinomy　of　reason　in　respect　of　the　theoretical　employment　of　understanding　carried　to　the　point　of　the　unconditioned；　（2）　for　the　feeling　of　pleasure　and　displeasure　an　antinomy　of　reason　in　respect　of　the　aesthetic　employment　of　judgement；　（3）　for　the　faculty　Of　desire　an　antinomy　in　respect　of　the　practical　employment　of　self…legislative　reason。　For　all　these　faculties　have　their　fundamental　a　priori　principles；　and；　following　an　imperative　demand　of　reason；　must　be　able　to　judge　and　to　determine　their　object　unconditionally　in　accordance　with　these　principles。　　　As　to　two　of　the　antinomies　of　these　higher　cognitive　faculties；　those；　namely；　of　their　theoretical　and　of　their　practical　employment；　we　have　already　shown　elsewhere　both　that　they　are　inevitable；　if　no　cognisance　is　taken　in　such　judgements　of　a　supersensible　substrate　of　the　given　objects　as　phenomena；　and；　on　the　other　hand；　that　they　can　be　solved　the　moment　this　is　done。　Now；　as　to　the　antinomy　incident　to　the　employment　of　judgement　in　conformity　with　the　demand　of　reason；　and　the　solution　of　it　here　given；　we　may　say　that　to　avoid　facing　it　there　are　but　the　following　alternatives。　It　is　open　to　us　to　deny　that　any　a　priori　principle　lies　at　the　basis　of　the　aesthetic　judgement　of　taste；　with　the　result　that　all　claim　to　the　necessity　of　a　universal　consensus　of　opinion　is　an　idle　and　empty　delusion；　and　that　a　judgement　of　taste　only　deserves　to　be　considered　to　this　extent　correct；　that　it　so　happens　that　a　number　share　the　same　opinion；　and　even　this；　not；　in　truth；　because　an　a　priori　principle　is　presumed　to　lie　at　the　back　of　this　agreement；　but　rather　（as　with　the　taste　of　the　palate）　because　of　the　contingently　resembling　organization　of　the　individuals。　Or　else；　in　the　alternative；　we　should　have　to　suppose　that　the　judgement　of　taste　is　in　fact　a　disguised　judgement　of　reason　on　the　perfection　discovered　in　a　thing　and　the　reference　of　the　manifold　in　it　to　an　end；　and　that　it　is　consequently　only　called　aesthetic　on　account　of　the　confusion　that　here　besets　our　reflection；　although　fundamentally　it　is　teleological。　In　this　latter　case　the　solution　of　the　antinomy　with　the　assistance　of　transcendental　ideas　might　be　declared　otiose　and　nugatory；　and　the　above　laws　of　taste　thus　reconciled　with　the　objects　of　sense；　not　as　mere　phenomena；　but　even　as　things…in…themselves。　How　unsatisfactory　both　of　those　alternatives　alike　are　as　a　means　of　escape　has　been　shown　in　several　places　in　our　exposition　of　judgements　of　taste。　　　If；　however；　our　deduction　is　at　least　credited　with　having　been　worked　out　on　correct　lines；　even　though　it　may　not　have　been　sufficiently　clear　in　all　its　details；　three　ideas　then　stand　out　in　evidence。　Firstly；　there　is　the　supersensible　in　general；　without　further　determination；　as　substrate　of　nature；　secondly；　this　same　supersensible　as　principle　of　the　subjective　finality　of　nature　for　our　cognitive