unidade i - capítulo i noçôes de lógica formal - a lógica aristotélica

8/4/2019 UNIDADE I - Captulo I Noes de Lgica Formal - a lgica aristotlica

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FilosofiaFilosofia

11Ano11Ano


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Unidade 1Racionalidadeargumentativa

e Filosofia:Lgica e Filosofia


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Captulo IA Lgica Si logstica

ou Aristotlica


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ndice Captulo I - A Lgica Silogstica ou Aristotlica

Estrutura do Juzo ou Proposio Categrica

Classificao dos Juzos ou Proposies Categricas O Silogismo Categrico O Silogismo Condicional

O Silogismo Disjuntivo
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A Lgica Silogstica OuAristotlica As Trs Formas de Silogismo:

SilogismoCategrico

SilogismoCondicional

Silogismo

Disjuntivo
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A Lgica Silogstica OuAristotlicaSilogismo Categrico:As premissas soproposies que afirmam ou negam algo de forma

absoluta.Exemplo:Todos o s l ee s so mam fe r o sNenhu m l eo he rb vo roLogo , a l guns mam f e ro s no so he rb vo ro s .
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7/73

A Lgica Silogstica OuAristotlicaSilogismo Condicional: A premissa maior

afirma ou nega sob condio.

Se aquecer o metal, ento ele dilatar-se-.

O metal foi aquecido.

Logo, o metal dilatou-se.
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8/73

A Lgica Silogstica OuAristotlicaSilogismo Disjuntivo:A premissamaior estabelece uma alternativa.

O avio ou est no ar ou est no solo.

O avio est no ar.

Logo, o avio no est no solo.
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9/73

A Lgica Silogstica OuAristotlicaEstrutura da proposio categrica:

Alguns filsofos so crentes

Sujeito:aquilo acerca do qual se afirma ou nega algo.

O sujeito deste juzo filsofos

Predicado: a qualidade ou caracterstica que se afirma pertencer ao sujeito.

O predicado deste juzo crentes.

Cpula: o elemento de ligao entre o sujeito e o predicado. Representadopelo verboser.

Quantificador Sujeito Cpula Predicado
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10/73

A Lgica Silogstica OuAristotlicaClassificao da proposio categrica :

Como arelao entre sujeito e predicado uma

relao de incluso ou exclusoimporta esclarecer doisaspectos:

1. Quantidade;

2. Qualidade.

Particular

Universal

Afirmativa

Negativa
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11/73

A Lgica Silogstica OuAristotlicaAs Proposies Categricas Segundo a Quantidade:

Classificar os juzos(proposies)segundo aquantidadeclassific-los segundo aextenso.

Juzos universaisO sujeito tomado em toda a extenso; representa todos os

membros de uma classe.

Juzos particularesO sujeito tomado numa parte da sua extenso; srepresenta uma parte dos membros de uma classe
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12/73

A Lgica Silogstica OuAristotlica1. Juzos Universais:

Exemplo:

Todo o homem mortal.As galinhas no tm dentes.

Os tringulos so trilteros.

No h homem que no seja inteligente.

Qualquer homem inteligente.
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A Lgica Silogstica OuAristotlica1. Juzos Universais:

Na forma padro asproposies universais apresentam

quantificadores universais:Todo;

Nenhum;

Qualquer que seja;

Tudo o que ...

Para os clssicos os juzos singulares so equiparados a

universais

S

S P

P
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A Lgica Silogstica OuAristotlica2. Juzos Particulares:

Umaproposio particular aquela na qual osujeitorepresenta uma parte no determinada dos membros deuma classe, ou seja, tomado em parte da sua extenso.


15/73

A Lgica Silogstica OuAristotlica2. Juzos Particulares:

Exemplo:

Algunsalunos so estudiosos.

Hestudantes preocupados.

Pelo menos esteslpis so azuis.

Nem todosos bolos so de chocolate


16/73

A Lgica Silogstica OuAristotlicaAs Proposies Categricas Segundo a Qualidade: A qualidade de uma proposio a propriedadeque ela tem de ser afirmativa ou negativa. Afirmativa

Negativa

predicado convm ao sujeito

predicado no convm ao sujeito
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17/73

A Lgica Silogstica OuAristotlicaTipos de Proposio Categricas: Tipo Universais Afirmativas Tipo Universais Negativas Tipo Particulares Afirmativas Tipo Particulares Negativas
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18/73

A Lgica Silogstica OuAristotlicaTipo A:

Universais Afirmativas; Opredicado refere-se a todos os membros daclasse representada pelo sujeito. Forma Padro: Todos os homens sointeligentes.

SP
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19/73

A Lgica Silogstica OuAristotlicaOutras formas de formular universais afirmativas TIPO A Os homens so inteligentes No h homem que no seja inteligente Tudo o que homem tambm inteligente S os homens so inteligentes Todos os homens so alguns dos seres dotados de inteligncia Qualquer homem inteligente
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20/73

A Lgica Silogstica OuAristotlicaTipo E:

Universais Negativas; Nega-se um determinado predicadoatodos osmembros da classerepresentada pelo sujeito. Forma Padro: Nenhum homem rptil.

S P


21/73

A Lgica Silogstica OuAristotlicaOutras formas de formular universais negativas - TIPO E

No h ser humano que seja rptil

No existem homens que sejam rpteis

H coisas que so rpteis mas nenhum homem uma delas

Tudo o que humano no rptil

Ser rptil no uma caracterstica do ser humano
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22/73

A Lgica Silogstica OuAristotlicaTipo I:

Particular Afirmativa; O predicado atribui-se somente a uma parteindeterminada dos membros da classerepresentada pelo sujeito. Forma Padro: Alguns homens so inteligentes.

S P


23/73

A Lgica Silogstica OuAristotlicaOutras formas de formular particulares afirmativas - TIPO I

Existem homens inteligentes

H homens que so inteligentes

Pelo menos h um homem que inteligente

Certos seres so homens e tambm so inteligentes
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A Lgica Silogstica OuAristotlicaTipo O:

Particular Negativa; Nega-se um determinado predicado a algunsmembros da classe representada pelo sujeito. Forma Padro: Alguns homens no so belos.

S P


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A Lgica Silogstica OuAristotlicaOutras formas de formular particulares negativas - TIPOO H homens que no so belos Nem todos os homens so belos H seres que so homens mas no so belos H pelo menos um homem que no belo Existem homens que no so belos


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A Lgica Silogstica OuAristotlicaComo descobrir a quantidade do predicado?

A) Uma proposio tipo A: Todos os homens somortais.Oquantificador indica que osujeito esttomado emtoda a sua extenso.O predicado particularporque no se diz que os seres humanos so todosos mortais mas sim que tudo o que humano fazparte da classe dos seres mortais
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B) Uma proposio tipo I: Alguns homens so pessoascultas.Opredicado est quantificado particularmente. No serefere a toda e cada uma das pessoas cultas massomente a algumas.


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C) Uma proposio tipo E: Nenhum homem pssaro. A proposio diz de todo e qualquer pssaro que no

membro da classe "homem": nega-se a todos os pssaros a

incluso na espcie humana (No h pssaro nenhum queseja homem).Predicado universal.


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D) Uma proposio tipo O: Alguns homens no sopessoas belas. A proposio diz de todas as pessoas belas que h alguns

homens que o no so: todos os membros da classe

"pessoas belas" no so alguns dos membros da classe

"homem".Predicado particular.


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A Lgica Silogstica OuAristotlica

Regras parareconhecer aquantidade de umpredicado

Afirmativas

Particular

NegativasUniversal

PredicadoProposies


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A Lgica Silogstica OuAristotlicaO que um silogismo categrico? Umsilogismo categrico um raciocnio dedutivoconstitudo portrs proposies:

1. premissa maior;2. premissa menor;3. concluso.


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A Lgica Silogstica OuAristotlica Consideremos o seguinte silogismo:

Premissa maior: Todos os gatos so mamferosPremissa menor: Os siameses so gatosConcluso: Logo os siamesesso mamferos


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A Lgica Silogstica OuAristotlica Cada silogismo contm trs termos cada um dosquais aparece nas diferentes proposies duas vezes.1. Termo mdio:aquele que aparece em ambaspremissas mas no na concluso.2. Termo maior: o predicado da concluso, aparecendotambm na premissa maior;3. Termo menor: a sujeito da concluso, aparecendotambm na premissa menor.
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A Lgica Silogstica OuAristotlicaRegras da validade dos silogismos categricos .1 O silogismo categrico s pode conter trstermos (maior, mdio e menor) e cada termoter o mesmo significado ao longo doargumento.i logismo invlido Silogismo vlidoTodo o co ladra.Co uma constelao.Logo, uma constelaoladra.

A palavra co usada paradesignar conceitosdiferentes e, por isso,termos diferentes. Estesi logismo tem portantoquatro termos.

Todo o co ladra.Bobby um coLogo, Bobby ladra.O silogismo contemtrs termos.
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A Lgica Silogstica OuAristotlicaRegras da validade dos silogismos categricos .2 O termo mdio s pode aparecer naspremissas.

3 Os termos maior e menor no podem ter naconcluso maior extenso do que nas premissasou um termo deve estar distribudo naspremissas se estiver distribudo na concluso. Exemplo: Todos os mamferos so gatos.Nenhum co gato.Logo, nenhum co mamfero.A concluso fala de todos os mamferos mas aspremissas apenas de alguns.
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A Lgica Silogstica OuAristotlicaSilogismo que comete a falcia da ilcitamaior

Silogismo que comete a falcia da ilcitamenor

Todos os gatos so mamferosNenhum co gatoLogo, nenhum co mamfero O termo maior (mamferos) particular napremissa maior. Predicado de proposioafirmativa particular.

Na concluso, mamfero termo universalporque predicado de proposio negativa.Nenhum co mamfero quer dizer tudo o que mamfero no faz parte da classe dos ces. Otermo mamfero tem mais extenso na conclusodo que na premissa.

Todos os romanos so habitantes de RomaTodos os romanos so italianosLogo, todos os italianos so habitantes de RomaH um problema com o termo menor (italianos).

Na premissa menor diz -se que alguns dositalianos so romanos mas na concluso fala -sede todos os ital ianos.Ora s se pode concluir que alguns ital ianos sohabitantes de Roma porque nem todos ositalianos so romanos. Assim, o termo menortem mais extenso na concluso do que naspremissas.

Regras da validade dos silogismos categricos. Regra 3
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A Lgica Silogstica OuAristotlicaADVERTNCIA IMPORTANTE SOBRE A REGRA 3

S quando os termos maior e menor soparticulares na premissa e universais naconcluso que o silogismo incorrecto.Podem ser universais na premissa e naconcluso e tambm universais napremissa e particulares na concluso.
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A Lgica Silogstica OuAristotlica4 O termo mdio deve ter extenso universal pelo menosem uma premissaou o termo mdio deve estardistribudo pelo menos uma vez.

Todos os homens so seres humanos.Todas as mulheres so seres humanos.Logo, todas as mulheres so homens. Em nenhuma premissa se diz que toda a classe dosseres humanos constituda ou por homens ou pormulheres. Seres humanos predicado particular emambas as premissas e devia ser universal pelo menos

numa delas.

Regras da val idade dos si logismos categricos


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A Lgica Silogstica OuAristotlica5 Premissas afirmativas pedemconcluso afirmativa.Todos os homens so mortais.Todos os mortais so falveis.Logo, alguns seres falveis no so homens. Extrair uma concluso negativa de premissasafirmativas cair em contradio negando umarelao que se afirmou nas premissas. Aconcluso vlida seria: Alguns seres falveis so

homens.

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A Lgica Silogstica OuAristotlica6 De duas premissas negativas nada se podeconcluir.Nenhum co animal de sangue frio.Nenhum animal de sangue frio capaz de ladrar.Logo, nenhum co capaz de ladrar. No se consegue estabelecer uma relaonecessria entre os termos do argumento.

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A Lgica Silogstica OuAristotlica7 De duas premissas particulares nada se podeconcluir.Alguns ces so ruidosos.Alguns ces so animais castanhos.Logo, alguns animais castanhos so ruidosos. A violao desta regra implica sempre aviolao de uma outra regra. Neste caso viola se a regra que exige que o termo mdio sejauniversal em pelo menos uma premissa.

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A Lgica Silogstica OuAristotlica8. A concluso segue sempre a parte mais fraca: sernegativa se houver uma premissa negativa eparticular se houver uma premissa particular.Nenhum amigo do Jos japons.Todos os alunos deste colgio so amigos do Jos.Logo, todos os alunos deste colgio no so japoneses. A segunda premissa afirmativa mas a primeira negativa pelo que a concluso para seguir a partemais fraca deve ser negativa.



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A Lgica Silogstica OuAristotlica8. A concluso segue sempre a parte mais fraca:ser negativa se houver uma premissa negativae particular se houver uma premissa particular.Todos os tigres so mamferos.Alguns animais so tigres.Logo, alguns animais so mamferos.

As premissas so afirmativas a maior universal e a menor particular - pelo queseguir a parte mais fraca significa que aconcluso deve ser particular.

Avaliar a val idade dos si logismos categricos REGRAS


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A Lgica Silogstica OuAristotlicaRegras do silogismo categrico

Regra Violao daRegra

Cumprimento daRegra

1. S pode contertrs termos e cadatermo deve ter omesmo significado.

Todo o touro temchifresTouro um signoLogo, um signo temcornos

Todo o touro animal que temchifresLampeiro touroLogo, Lampeiro animal que temchifres


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2. O termo mdio spode surgir naspremissas.

Regras do silogismo categrico
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Regra Violao daRegra

Cumprimento daRegra

3. Os termos maior emenor no devem termaior extenso naconcluso do que naspremissas.

Todos os mortais sohumanosTodos os humanosso psiclogosTodos os psiclogosso mortais

Todos os humanosso mortaisTodos os psiclogosso humanosTodos os psiclogosso mortais
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4. O termo mdiodeve ter extensouniversal pelomenos uma vez.Todos os ces soanimaisTodos os gatos soanimais.Todos os ces so gatos

Todos os animaisso cesTodos os gatos soanimaisAlguns ces sogatos



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Regra Violao da Regra Cumprimento daRegra5. Premissasafirmativaspedemconcluso

afirmativa.

Todos os brasileiros soamericanosTodos os paulistas so brasileirosAlguns paulistas no soamericanos

Todos os brasileiros soamericanosTodos os paulistas sobrasileirosAlguns paulistas soamericanos


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6. De duaspremissasnegativasnada se podeconcluir.Nenhum portugus argentinoNenhum lisboeta argentinoNenhum lisboeta portugus

Nenhum portugus argentinoAlguns lisboetas soargentinosAlguns lisboetas noso portugueses

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Regra Violao daRegra Cumprimento daRegra7. De duas premissasparticulares nada sepode concluir.Alguns homens soeuropeusAlguns homens soamericanosAlguns americanos soeuropeus

Todos os homens soeuropeusAlguns homens soamericanosAlguns americanos soeuropeus


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8. A conclusosegue a parte maisfraca: ser negativase houver premissasnegativas eparticular se houverpremissasparticulares.

Alguns alunos so malcomportadosAlguns brasileiros no somal comportadosAlguns brasileiros soalunos

Todos os alunos somal comportadosAlguns brasileiros noso mal comportadosAlguns brasileiros noso alunos

Regras do silogismo


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A Lgica Silogstica OuAristotlicaSilogismo Condicional:A premissa maiorafirma ou nega sob condio.

Exemplo:Se Deus existe, ento a vida tem sentido

Deus existe

Logo a vida tem sentido
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A Lgica Silogstica OuAristotlicaSilogismo Condicional pode ser validamenteexpresso de duas maneiras:1. modus ponens;2. modus tollens.
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A Lgica Silogstica OuAristotlica Se Deus existe ento a vida faz sentido A vida faz sentido se Deus existir Caso Deus exista, a vida faz sentido Desde que Deus exista a vida faz sentido Para que a vida faa sentido basta que Deus exista Que Deus exista condio suficiente para que a

vida faa sentido. A vida fazer sentido condio necessria para Deusexistir Deus no existe a menos que a vida faa sentido. A existncia de Deus suficiente para que a vidafaa sentido.

Vrias maneiras de exprimir proposies condicionaisnal inguagem corrente.
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A Lgica Silogstica OuAristotlicaRegras para avaliar um silogismo condicional

1.A afirmao do antecedente implica a afirmao ouconfirmao do consequente.2. A negao do consequente implica a negao doantecedente.3. Da negao do antecedente, nada se pode concluir

necessariamente.4. Da afirmao do consequente, nada se pode concluirnecessariamente.
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A Lgica Silogstica OuAristotlica1. Modus Ponens:

Se apremissa menor afirma o antecedente aconcluso tambm afirmar o consequente.Se Deus existe, ento a vida tem sentido

Deus existe

Logo a vida tem sentido


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A Lgica Silogstica OuAristotlica1. Modus Ponens: Sempre que o antecedente afirmadonapremissa menor, aconcluso tem deafirmar o consequente, mas quando apremissa menorafirma o consequenteno vlido concluir afirmando o antecedente.
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unidade i - capítulo i noçôes de lógica formal - a lógica aristotélica

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