Testing the Validity of Sorites with Venn Diagrams

Fikret Osman

Article Details

Testing the Validity of Sorites with Venn Diagrams

Authors:

Fikret Osman

Publisher:

Kahramanmaras Sutcu Imam University

Main Topics:

Mantık Tarihi

Journal:

Kahramanmaraş Sütçü İmam Üniversitesi Sosyal Bilimler Dergisi Vol.22 Issue 2, pp.1037-1056

Document Type:

Article

Publication Date:

8/2025

Document Language:

Turkish

Document ID (Org No.):

2001357631

pISSN:

1304-8120

Keywords:

Abstract:

 Sorites are polysyllogisms. In these syllogisms, there is a common term in two successive premises. According to the position of this term, sorites are divided into two classes: progressive and regressive sorites. In progressive sorites, the common term comes first as the predicate and then as the subject; however, in regressive sorites, the common term comes first as the subject and then as the predicate. Progressive sorites whose all premises consist of universal positive propositions, regressive sorites whose all premises consist of universal positive propositions, progressive sorites whose last premise is a negative proposition and the other premises are universal positive propositions, regressive sorites whose first premise is a negative proposition and the other premises are universal positive propositions, progressive sorites whose first premise is a particular proposition and the other premises are universal positive propositions, and regressive sorites whose last premise is a particular proposition and the other premises are universal positive propositions are valid. Sorites, other than these are invalid. This study focuses on how the validity of sorites can be demonstrated by the Venn diagrams method. In this context, it is first tried to show how the relationships between the propositions that form the sorites can be revealed with separate binary Venn diagrams; then, it is explained how the relationships between only the premises of the sorites can be accurately reflected in the multiple Venn diagrams created.

 Sorites are polysyllogisms. In these syllogisms, there is a common term in two successive premises. According to the position of this term, sorites are divided into two classes: progressive and regressive sorites. In progressive sorites, the common term comes first as the predicate and then as the subject; however, in regressive sorites, the common term comes first as the subject and then as the predicate. Progressive sorites whose all premises consist of universal positive propositions, regressive sorites whose all premises consist of universal positive propositions, progressive sorites whose last premise is a negative proposition and the other premises are universal positive propositions, regressive sorites whose first premise is a negative proposition and the other premises are universal positive propositions, progressive sorites whose first premise is a particular proposition and the other premises are universal positive propositions, and regressive sorites whose last premise is a particular proposition and the other premises are universal positive propositions are valid. Sorites, other than these are invalid. This study focuses on how the validity of sorites can be demonstrated by the Venn diagrams method. In this context, it is first tried to show how the relationships between the propositions that form the sorites can be revealed with separate binary Venn diagrams; then, it is explained how the relationships between only the premises of the sorites can be accurately reflected in the multiple Venn diagrams created.

 Sorites are polysyllogisms. In these syllogisms, there is a common term in two successive premises. According to the position of this term, sorites are divided into two classes: progressive and regressive sorites. In progressive sorites, the common term comes first as the predicate and then as the subject; however, in regressive sorites, the common term comes first as the subject and then as the predicate. Progressive sorites whose all premises consist of universal positive propositions, regressive sorites whose all premises consist of universal positive propositions, progressive sorites whose last premise is a negative proposition and the other premises are universal positive propositions, regressive sorites whose first premise is a negative proposition and the other premises are universal positive propositions, progressive sorites whose first premise is a particular proposition and the other premises are universal positive propositions, and regressive sorites whose last premise is a particular proposition and the other premises are universal positive propositions are valid. Sorites, other than these are invalid. This study focuses on how the validity of sorites can be demonstrated by the Venn diagrams method. In this context, it is first tried to show how the relationships between the propositions that form the sorites can be revealed with separate binary Venn diagrams; then, it is explained how the relationships between only the premises of the sorites can be accurately reflected in the multiple Venn diagrams created.

 Soritler, çoklu tasımlardır. Bu tasımlarda, artarda gelen iki öncülde ortak bir terim yer alır. Bu terimin konumuna göre, soritler; ileri giden ve geri giden olarak ikiye ayrılır. Ortak terim, ileri giden soritlerde önce yüklem sonra konu; geri giden soritlerde ise önce konu sonra yüklem olarak gelir. Tüm öncülleri tümel olumlu önermelerden oluşan ileri giden, tüm öncülleri tümel olumlu önermelerden oluşan geri giden, son öncülü olumsuz diğer öncülleri tümel olumlu önermelerden oluşan ileri giden, ilk öncülü olumsuz diğer öncülleri tümel olumlu önermelerden oluşan geri giden, ilk öncülü tikel diğer öncülleri tümel olumlu önermelerden oluşan ileri giden ve son öncülü tikel diğer öncülleri tümel olumlu önermelerden oluşan geri giden soritler, geçerlidir. Bunların dışındaki soritler ise geçersizdir. Bu çalışmada, soritlerin geçerliliklerinin Venn diyagramları yöntemiyle nasıl gösterilebileceği üzerinde durulmaktadır. Bu bağlamda, önce soritleri oluşturan önermeler arasındaki ilişkilerin ayrı ayrı ikili Venn diyagramlarıyla nasıl ortaya koyulabileceğine; daha sonra da soritlerin sadece öncül konumundaki önermelerinde yer alan ilişkilerin, oluşturulan çoklu Venn diyagramlarına nasıl doğru bir şekilde yansıtılabileceğine yer verilmektedir.

Article Details

Testing the Validity of Sorites with Venn Diagrams

Authors:

Fikret Osman

Publisher:

Kahramanmaras Sutcu Imam University

Main Topics:

Mantık Tarihi

Journal:

Kahramanmaraş Sütçü İmam Üniversitesi Sosyal Bilimler Dergisi Vol.22 Issue 2, pp.1037-1056

Document Type:

Article

Publication Date:

8/2025

Document Language:

Turkish

Document ID (Org No.):

2001357631

pISSN:

1304-8120

Logic

Sorites

Venn Diagrams

Testing

ValidityMantık

Sorit

Venn Diyagramları

Denetleme

Geçerlilik

Issues

Article Details

Authors: Fikret Osman

Publisher: Kahramanmaras Sutcu Imam University

Main Topics: Mantık Tarihi

Journal: Kahramanmaraş Sütçü İmam Üniversitesi Sosyal Bilimler Dergisi Vol.22 Issue 2, pp.1037-1056

Document Type: Article

Publication Date: 8/2025

Document Language: Turkish

Document ID (Org No.): 2001357631

pISSN: 1304-8120

Issues

Authors:

Fikret Osman

Publisher:

Kahramanmaras Sutcu Imam University

Main Topics:

Mantık Tarihi

Journal:

Kahramanmaraş Sütçü İmam Üniversitesi Sosyal Bilimler Dergisi Vol.22 Issue 2, pp.1037-1056

Document Type:

Article

Publication Date:

8/2025

Document Language:

Turkish

Document ID (Org No.):

2001357631

pISSN:

1304-8120