CT2.0 » Categorical Logic http://inquiry.mcdaniel.edu Archive of examples of reasoning for use in Critical Thinking classrooms Tue, 17 Jan 2012 21:19:53 +0000 en hourly 1 http://wordpress.org/?v=3.1.1 Venn – Deduction http://inquiry.mcdaniel.edu/blog/2011/06/14/venn-deduction/ http://inquiry.mcdaniel.edu/blog/2011/06/14/venn-deduction/#comments Tue, 14 Jun 2011 14:52:07 +0000 admin http://inquiry.mcdaniel.edu/?p=3999

An extension of the Venn diagram app to demonstrate the non-ampliative* properties of deduction.

*see, e.g. section 3 of Stanford Encyclopedia of Philosophy entry on ‘Arguments and Inference’

 

]]> http://inquiry.mcdaniel.edu/blog/2011/06/14/venn-deduction/feed/ 0 Venn – Induction http://inquiry.mcdaniel.edu/blog/2011/06/14/venn-induction/ http://inquiry.mcdaniel.edu/blog/2011/06/14/venn-induction/#comments Tue, 14 Jun 2011 14:08:37 +0000 admin http://inquiry.mcdaniel.edu/?p=3995

An extension of the Venn diagram app to demonstrate the ampliative* properties of induction.

*see, e.g. section 3 of Stanford Encyclopedia of Philosophy entry on ‘Arguments and Inference’

]]> http://inquiry.mcdaniel.edu/blog/2011/06/14/venn-induction/feed/ 0 Contraposition O http://inquiry.mcdaniel.edu/blog/2011/06/08/contraposition-o/ http://inquiry.mcdaniel.edu/blog/2011/06/08/contraposition-o/#comments Wed, 08 Jun 2011 11:55:52 +0000 admin http://inquiry.mcdaniel.edu/?p=3950

Flash-based interactive example of Venn diagram-enhanced categorical reasoning. This one is of O-type (Particular Negative) contraposition. Does ‘Some cats are not felines’ imply ‘Some non-felines are  not non-cats’?

 

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Flash-based interactive example of Venn diagram-enhanced categorical reasoning. This one is of O-type (Particular Negative) contraposition. Does ‘Some cats are not felines’ imply ‘Some non-felines are  not non-cats’?

 

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]]> http://inquiry.mcdaniel.edu/blog/2011/06/08/contraposition-o/feed/ 0 Obversion http://inquiry.mcdaniel.edu/blog/2011/06/08/obversion-2/ http://inquiry.mcdaniel.edu/blog/2011/06/08/obversion-2/#comments Wed, 08 Jun 2011 11:53:12 +0000 admin http://inquiry.mcdaniel.edu/?p=3955

Obversion is a transition in categorical (Aristotlean) logic.  It involves two steps:

  1. Change the quality.
  2. take the complement of the predicate term.

In…

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Obversion is a transition in categorical (Aristotlean) logic.  It involves two steps:

  1. Change the quality.
  2. take the complement of the predicate term.

In the sentence ‘No 4-chan users are trolls’, the predicate term is ‘troll’ and the quality is negative. So to transform it via obversion, we

  1. Change ‘no’ to ‘all’
  2. Change ‘troll’ to ‘non-troll’

This produces: ‘All 4-change users are non-trolls’.

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]]> http://inquiry.mcdaniel.edu/blog/2011/06/08/obversion-2/feed/ 2 Conversion http://inquiry.mcdaniel.edu/blog/2011/06/08/conversion/ http://inquiry.mcdaniel.edu/blog/2011/06/08/conversion/#comments Wed, 08 Jun 2011 11:50:29 +0000 admin http://inquiry.mcdaniel.edu/?p=3953

Conversion is a transition in categorical (Aristotlean) logic.  It involves only one step:

  1. Switch the subject and predicate terms.

If, for example, one…

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Conversion is a transition in categorical (Aristotlean) logic.  It involves only one step:

  1. Switch the subject and predicate terms.

If, for example, one asserts the I-Type sentence ‘Some 4-chan users are trolls’, a conversion would:

  1. switch ’4-chan users’ and ‘trolls’ in the sentence, producing: ‘Some trolls are 4-chan users’.

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]]> http://inquiry.mcdaniel.edu/blog/2011/06/08/conversion/feed/ 1 Contraposition http://inquiry.mcdaniel.edu/blog/2011/06/08/contraposition/ http://inquiry.mcdaniel.edu/blog/2011/06/08/contraposition/#comments Wed, 08 Jun 2011 11:47:46 +0000 admin http://inquiry.mcdaniel.edu/?p=3951

Contraposition is a transformation in categorical (Aristotlean) logic. It involves two steps:

  1. Switch the subject and predicate terms.
  2. take the complement of both terms.

…

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Contraposition is a transformation in categorical (Aristotlean) logic. It involves two steps:

  1. Switch the subject and predicate terms.
  2. take the complement of both terms.

For example, assume the A-Type sentence ‘All 4-chan users are trolls.’ (in common language, ‘everyone on 4-chan is a troll!’) If we transform this with contraposition we turn it into:

  1. switch the subject and predicate terms: ‘All trolls are 4-chan users’
  2. take the complement of both terms: ‘All non-trolls are non-4-chan users.’

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]]> http://inquiry.mcdaniel.edu/blog/2011/06/08/contraposition/feed/ 1 Contraposition E http://inquiry.mcdaniel.edu/blog/2011/06/08/contraposition-e/ http://inquiry.mcdaniel.edu/blog/2011/06/08/contraposition-e/#comments Wed, 08 Jun 2011 11:41:16 +0000 admin http://inquiry.mcdaniel.edu/?p=3947

Flash-based interactive example of Venn diagram-enhanced categorical reasoning. This one is of E-type (Universal Negative) contraposition. Does ‘No cats are felines’ imply ‘No non-cats are non-felines’?

 

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Flash-based interactive example of Venn diagram-enhanced categorical reasoning. This one is of E-type (Universal Negative) contraposition. Does ‘No cats are felines’ imply ‘No non-cats are non-felines’?

 

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]]> http://inquiry.mcdaniel.edu/blog/2011/06/08/contraposition-e/feed/ 0 Contraposition I http://inquiry.mcdaniel.edu/blog/2011/06/08/contraposition-i/ http://inquiry.mcdaniel.edu/blog/2011/06/08/contraposition-i/#comments Wed, 08 Jun 2011 11:39:44 +0000 admin http://inquiry.mcdaniel.edu/?p=3945

Flash-based interactive example of Venn diagram-enhanced categorical reasoning. This one is of I-type (Particular Affirmative) contraposition. Does ‘Some cats are felines’ imply ‘Some non-cats are non-felines’?

 

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Flash-based interactive example of Venn diagram-enhanced categorical reasoning. This one is of I-type (Particular Affirmative) contraposition. Does ‘Some cats are felines’ imply ‘Some non-cats are non-felines’?

 

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]]> http://inquiry.mcdaniel.edu/blog/2011/06/08/contraposition-i/feed/ 0 Contraposition A http://inquiry.mcdaniel.edu/blog/2011/06/08/contraposition-a/ http://inquiry.mcdaniel.edu/blog/2011/06/08/contraposition-a/#comments Wed, 08 Jun 2011 11:37:26 +0000 admin http://inquiry.mcdaniel.edu/?p=3943

Flash-based interactive example of Venn diagram-enhanced categorical reasoning. This one is of A-type (Universal Positive) contraposition. Does ‘A cats are felines’ imply ‘All non-cats are non-felines’?

 

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Flash-based interactive example of Venn diagram-enhanced categorical reasoning. This one is of A-type (Universal Positive) contraposition. Does ‘A cats are felines’ imply ‘All non-cats are non-felines’?

 

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]]> http://inquiry.mcdaniel.edu/blog/2011/06/08/contraposition-a/feed/ 0 Obversion O http://inquiry.mcdaniel.edu/blog/2011/06/08/obversion-o/ http://inquiry.mcdaniel.edu/blog/2011/06/08/obversion-o/#comments Wed, 08 Jun 2011 11:33:35 +0000 admin http://inquiry.mcdaniel.edu/?p=3938

Flash-based interactive example of Venn diagram-enhanced categorical reasoning. This one is of O-type (Particular Negative) obversion. Does ‘Some cats are not felines’ imply ‘Some cats are non-felines’?

 

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Flash-based interactive example of Venn diagram-enhanced categorical reasoning. This one is of O-type (Particular Negative) obversion. Does ‘Some cats are not felines’ imply ‘Some cats are non-felines’?

 

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