Ko Kant me te Ākiaki Kātegori
Kī tonu te ao o te rapunga whakaaro matatika i ngā ariā uaua me ngā kaitātari hohonu, engari he iti noa iho te hunga e tiaho ana pērā i a Immanuel Kant. Ko tana huarahi pakari ki ngā matatika, i roto i tana ariā o te Whakahau Whakakategoria, kua waiho he tohu pumau ki te whenua o te rapunga whakaaro matatika. He huarahi kē atu i ngā matatika whai hua me ngā matatika pai, e tohe ana ki tētahi momo whakaaro matatika e ahu mai ana i ngā mātāpono whānui, kaua ki ngā putanga ā-tau, ngā āhuatanga rānei o te tangata.
Ngā Tikanga Matatika a Kantian: He Tirohanga Poto
He tohunga whakaaro Tiamana a Immanuel Kant (1724-1804) i whai wāhi nui ki ngā momo mara, tae atu ki te epistemology, te metaphysics, me ngā tikanga matatika. Ko tana ariā matatika e whakatakotoria ana i roto i ana mahi e rua, "Groundwork for the Metaphysics of Morals" me "Critique of Practical Reason." He rerekē te huarahi a Kant ki ngā tikanga matatika nā tōna āhua deontological, arā, e tohe ana ki te tika, te hē rānei o ngā mahi, ahakoa ō rātou hua.
Ko te tikanga matatika Kantian e hangai ana ki te whakaaro ko te whakaaro nui te tūāpapa o te matatika. Hei kaiwhakahaere whakaaro nui, ka taea e te tangata te mārama ki ngā ture matatika me te mahi i runga i aua ture. He rerekē ki ngā ariā whai take, e whakatau ana i te matatika o ngā mahi i runga i ō rātou putanga, e kī ana ngā tikanga matatika Kantian he mea whakahau, he mea rāhui, he mea whakaaetia rānei ētahi mahi i runga i te piripono ki ngā ture matatika i ahu mai i te whakaaro nui.
Te Ākiaki Kāwai: Ngā Pou o te Matatika Kantian
Kei te ngako o te rapunga whakaaro matatika a Kant ko te Whakahau Kātegori. Ko tēnei mātāpono te whakamātautau mō te whakatau i te uara matatika o ngā mahi. He rerekē ki ngā whakahau whakapae—he mea here, ā, e whakawhirinaki ana ki ngā hiahia, ki ngā whāinga rānei (hei tauira, "Ki te hiahia koe kia hauora, me whakakorikori koe")—ka whakahau kore here ngā whakahau kātegori. Ka whakatakotohia e rātou ngā mahi me whai ahakoa ngā hiahia whaiaro, ngā āhuatanga rānei.
He maha ngā whakatakotoranga o te Whakahau Whakakategoria a Kant, e whakamārama ana i ngā āhuatanga rerekē o te kawenga matatika me te whakaaro nui:
1. Te Tātai o te Ture Ao Whānui: "Me mahi noa i runga i taua whakataukī e taea ai e koe te noho hei ture ao whānui i taua wā anō." E whakanui ana tēnei whakataukī me ārahi ngā mahi a te tangata e ngā mātāpono ka taea te whakamahi whānui me te kore e whakahē. Ki te kore e tutuki i tēnei whakamātautau tētahi whakataukī, kāore e taea te whakamana i te taha matatika. Hei tauira, ki te teka te katoa, ka hinga te whakawhirinaki, ā, ka hinga te mahi teka ina whānuitia.
2. Te Tātai o te Tangata: "Me mahi kia rite ai tō whakaaro ki te tangata, ahakoa ko koe anō, ko te tangata rānei o tētahi atu, hei whāinga tonu, kaua rawa hei huarahi noa iho." E whakaatu ana tēnei tātai i te uara tūturu o te tangata, kaua rawa e whakamahia, e rāwekeweketia rānei mō ngā kaupapa matua. E kī ana tēnei mātāpono kia whakautehia te mana whakaaro nui me te mana o ētahi atu.
3. Te Tātai o te Mana Motuhake: "Me mahi kia taea ai e koe te whakaaro ko ia anō te kaihanga ture whānui mā roto i ōna tikanga." E whakaatu ana tēnei i te hiranga o te whakaaro o te tangata ki a ia anō hei mema ture i roto i te rangatiratanga o ngā whāinga. Mā te hiahia whakaaro nui, ka whai wāhi te tangata ki te whakatū ture matatika. E whakaatu ana tēnei i te herekoretanga me te whakahaere whaiaro matatika.
4. Te Rangatiratanga o ngā Mutunga: "Whakahaerehia kia rite ki ngā tikanga a te mema ture ā-ao o tētahi rangatiratanga whainga noa iho." Ko tēnei whakaaro nui e whakaatu ana i tētahi hononga pūnaha o ngā mea whai whakaaro, e manaakitia ana, e whai whakaaro ana tetahi ki tetahi, e hanga ana i tētahi hapori taurite e mau tonu ana ngā ture matatika.
Te Whakamahinga me ngā Pānga
Mā te Ākiaki Whakakategoria ka whakaratohia he anga pakari mō te aromatawai i ngā mahi matatika. Mā te tono kia tutuki i ngā mahi ngā paearu o te āheinga ki te ao whānui, te whakaute i te tangata, me te whakatau whakaaro motuhake, ka tukuna e ngā tikanga matatika a Kant he aratohu tino pakari, he mātāpono mō te whanonga.
He mea nui, ko te tohe a Kant ki te mahi me te whakaaro nui e wero ana i te tangata kia titiro ki tua atu i ngā hiahia whaiaro, i ngā tikanga ahurea, i ngā ture whakapono rānei. E hiahia ana kia tirotirohia e te tangata ngā pūtake whakaaro nui o ā rātou mahi. Ko tēnei ao whānui me te hiahiatanga e whakatairanga ana i te kore whakaaro matatika, e hono ana pea i ngā horopaki ahurea rerekē mā roto i ngā mātāpono whakaaro nui.
Ahakoa he māramatanga me te hanganga matatika ngā tikanga matatika Kantian, he nui ngā wero me ngā whakahē e pā ana ki tēnei. E kī ana ngā kairīti ko te tino pumau o te Whakahau Whakakategoria ka arahi pea ki te pakari o te matatika, me te kore e aro ki ngā āhuatanga rerekē me ngā raruraru e pā ana ki te horopaki. Hei tauira, ko te tohe tonu o te mātāpono ki te kōrero pono ka whakahē i te teka ahakoa hei tiaki i te ora harakore, he tūranga e kitea ana e te tini he kore e taea te pupuri i runga i te matatika.
Hei tāpiritanga, ko te whakarāpopototanga me te uauatanga o ngā whakaaro matatika Kantian te āhua nei he rerekē rawa atu i ngā whakataunga matatika o ia rā. E kī ana ngā kairīti kāore i roto i te tikanga ā-ture a Kant ngā āhuatanga kare ā-roto me te whanaungatanga e whakaatuhia ana e ētahi atu pūnaha matatika, pērā i ngā tikanga matatika o te pai, ngā tikanga matatika manaaki rānei. Ko te whakautu ki ēnei whakahē me mārama ki ngā whāinga a Kant me ngā urutaunga pea o tana ariā ki ngā take matatika o nāianei.
Te Taonga Tuku Iho a Kant i roto i ngā Tikanga Matatika o ēnei Rā
Ahakoa ngā whakahē, he nui tonu te awe o te rapunga whakaaro matatika a Kant. Ko ngā mātāpono o roto i te Categorical Imperative e pā ana ki ngā ariā o nāianei mō ngā tika tangata, te ōritetanga, me te tika. Ko te whakaaro o Kant kia kaua te tangata takitahi e whakaarohia hei huarahi anake e hangai ana ki ngā kōrero mō ngā tika tangata o nāianei, e whakanui ana i te mana tangata me te mana motuhake.
I tua atu, i whakaoho a Kant i ngā tautohetohe me ngā whanaketanga matatika i muri mai. Nāna i whakatakoto te ara mō ngā tohunga whakaaro kore-ontology o muri mai, ā, i waiho he taonga tuku iho e tūhuratia tonutia ana, e whakawhānuihia ana hoki e ngā kaiwhakaaro matatika. Ahakoa ngā tautohetohe whakahē i a Kant, he maha ngā wā ka whakaurua ngā wāhanga nui o tana whakaaro, e whakaatu ana i te hiranga pumau o tana anga matatika.
Opaniraa
Ko te Whakahau Whakakategoriti a Kant he pou tokomanawa i roto i te hanganga o te rapunga whakaaro matatika. E wero ana i ngā tāngata takitahi kia whakatakoto i ā rātou mahi ki runga i ngā mātāpono whaitake e tika ana mō te ao whānui, kia whakaute i te mana o ētahi atu, kia kite hoki i a rātou anō hei kaihanga ture motuhake i roto i te hapori matatika. Mā te arotahi i te matatika ki te mahi me te whakaaro whaitake, ka tukuna e Kant he tirohanga whakahihiri mō te whanonga matatika e whakaoho tonu ana i te whakaaro, te tautohetohe, me te whakamoemiti. Ahakoa kāore i te kore he wero, ka mau tonu te Whakahau Whakakategoriti hei taputapu kaha mō te whakatere i te whenua uaua o te whakatau matatika.
