Sophismata
Encyclopedia
Sophismata in medieval philosophy
are difficult or puzzling sentences presenting difficulties of logical analysis that must be solved. Sophismata-literature grew in importance during the thirteenth and fourteenth centuries, and many important developments in philosophy (particularly in logic
and natural philosophy
) occurred as a result of investigation into their logical and semantic properties.
Sophismata are "ambiguous, puzzling or simply difficult sentences" that were used by Medieval logic
ians for educational purposes and for disputation about logic. Sophismata were written in Latin, and for many of them the meaning is lost, when they get translated to other languages. They can be divided into sentences that:
When in the second half of the 19th century scholastic logic
began to decline and be replaced by formal logic
, discussions about sophismata and syncategoremata
gradually became extinct as the problem posed by them disappeared with the formalisation of the language. Thus, except the Liar paradox
sophismata in general are trivially solved by modern analytical philosophy.
. Albert of Saxony was a German philosopher known for his contributions to logic
and physics
, and his solution may have been influenced by the works of his fellow logician Jean Buridan
.
"All men are donkeys or men and donkeys are donkeys" is an example of the second class of sophismata; an ambiguous sentence that is open to more than one interpretation and could be either true or false depending on what interpretation is chosen.
In accordance with step 1, in order to prove that the sophisma "All men are donkeys or men and donkeys are donkeys" is true then it should be viewed as a logical conjunction's
sentence that is a two-place logical operator "and". It results "true" if both of its operands are true, otherwise it represents "false". So in this case the sophisma could be interpreted as
This presents "All men are donkeys or men" as the first logical operand and "donkeys are donkeys" as the second one. Both of the logical operands connected by "and" are true, and therefore the whole sentence is true. The first logical operand is a logical sentence on its own. It is a logical disjunction's
sentence that is a two-place logical operator or. It results in a true sentence whenever one or more of its operands are true. "All men are donkeys or men" is true because while the first logical operand "All men are donkeys" is false, the second logical operand or "men" is true. Therefore the whole logical disjunction indicates that the sentence is true. The second logical operand "donkeys are donkeys" is true because donkeys are donkeys.
In accordance with step 1, in order to prove that the sophisma "All men are donkeys or men and donkeys are donkeys" is false then it should be looked at as a logical disjunctions sentence. In this case the sophisma could be interpreted as
This presents "All men are donkeys" as the first logical operand and "men and donkeys are donkeys" as the second one. Both of the logical operands connected by "or" are false, and therefore the whole sentence is also false. The first logical operand is false because all men are not donkeys. The second logical operand "men and donkeys are donkeys" is a logical conjunction on its own and is also false. This is because although donkeys are donkeys men are not donkeys. Because it is connected by "and" this logical conjunction with one true logical operand and one false indicates that the sentence is false.
In accordance with step 2, Albert of Saxony proposed his own solution of the sophisma that proved it could result in both being truth and being false depending on the interpretation of the ambiguous sentence.
In accordance with step 3, Albert of Saxony did not have to prove this proposed solution because it covered both possible scenarios (being true and being false).
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Medieval philosophy
Medieval philosophy is the philosophy in the era now known as medieval or the Middle Ages, the period roughly extending from the fall of the Western Roman Empire in the fifth century AD to the Renaissance in the sixteenth century...
are difficult or puzzling sentences presenting difficulties of logical analysis that must be solved. Sophismata-literature grew in importance during the thirteenth and fourteenth centuries, and many important developments in philosophy (particularly in logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
and natural philosophy
Natural philosophy
Natural philosophy or the philosophy of nature , is a term applied to the study of nature and the physical universe that was dominant before the development of modern science...
) occurred as a result of investigation into their logical and semantic properties.
Sophismata are "ambiguous, puzzling or simply difficult sentences" that were used by Medieval logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
ians for educational purposes and for disputation about logic. Sophismata were written in Latin, and for many of them the meaning is lost, when they get translated to other languages. They can be divided into sentences that:
- are odd or have odd consequences
- are ambiguous, and can be true or false according to the interpretation we give it, or
- have nothing special about them in itself, but become puzzling when they occur in definite contexts (or “cases”, casi).
When in the second half of the 19th century scholastic logic
Term logic
In philosophy, term logic, also known as traditional logic or aristotelian logic, is a loose name for the way of doing logic that began with Aristotle and that was dominant until the advent of modern predicate logic in the late nineteenth century...
began to decline and be replaced by formal logic
Formal logic
Classical or traditional system of determining the validity or invalidity of a conclusion deduced from two or more statements...
, discussions about sophismata and syncategoremata
Syncategorematic term
In scholastic logic, a syncategorematic term is a word that cannot serve as the subject or the predicate of a proposition, and thus cannot stand for any of Aristotle's categories, but can be used with other terms to form a proposition...
gradually became extinct as the problem posed by them disappeared with the formalisation of the language. Thus, except the Liar paradox
Liar paradox
In philosophy and logic, the liar paradox or liar's paradox , is the statement "this sentence is false"...
sophismata in general are trivially solved by modern analytical philosophy.
Example: All men are donkeys or men and donkeys are donkeys
All men are donkeys or men and donkeys are donkeys is a sophisma that was first proposed and solved by the 14th century philosopher Albert of SaxonyAlbert of Saxony (philosopher)
Albert of Saxony was a German philosopher known for his contributions to logic and physics...
. Albert of Saxony was a German philosopher known for his contributions to logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
and physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, and his solution may have been influenced by the works of his fellow logician Jean Buridan
Jean Buridan
Jean Buridan was a French priest who sowed the seeds of the Copernican revolution in Europe. Although he was one of the most famous and influential philosophers of the late Middle Ages, he is today among the least well known...
.
"All men are donkeys or men and donkeys are donkeys" is an example of the second class of sophismata; an ambiguous sentence that is open to more than one interpretation and could be either true or false depending on what interpretation is chosen.
Solving the example
Solving the sophisma requires understanding the meaning of the sophisma sentence. In order to accomplish this three steps should be taken:- Pro and contra arguments should be analyzed.
- A person, who proposed a sophisma, should present his own solution.
- A person, who proposed a sophisma, should prove his solution after he presented with a different answer.
In accordance with step 1, in order to prove that the sophisma "All men are donkeys or men and donkeys are donkeys" is true then it should be viewed as a logical conjunction's
Logical conjunction
In logic and mathematics, a two-place logical operator and, also known as logical conjunction, results in true if both of its operands are true, otherwise the value of false....
sentence that is a two-place logical operator "and". It results "true" if both of its operands are true, otherwise it represents "false". So in this case the sophisma could be interpreted as
This presents "All men are donkeys or men" as the first logical operand and "donkeys are donkeys" as the second one. Both of the logical operands connected by "and" are true, and therefore the whole sentence is true. The first logical operand is a logical sentence on its own. It is a logical disjunction's
Logical disjunction
In logic and mathematics, a two-place logical connective or, is a logical disjunction, also known as inclusive disjunction or alternation, that results in true whenever one or more of its operands are true. E.g. in this context, "A or B" is true if A is true, or if B is true, or if both A and B are...
sentence that is a two-place logical operator or. It results in a true sentence whenever one or more of its operands are true. "All men are donkeys or men" is true because while the first logical operand "All men are donkeys" is false, the second logical operand or "men" is true. Therefore the whole logical disjunction indicates that the sentence is true. The second logical operand "donkeys are donkeys" is true because donkeys are donkeys.
In accordance with step 1, in order to prove that the sophisma "All men are donkeys or men and donkeys are donkeys" is false then it should be looked at as a logical disjunctions sentence. In this case the sophisma could be interpreted as
This presents "All men are donkeys" as the first logical operand and "men and donkeys are donkeys" as the second one. Both of the logical operands connected by "or" are false, and therefore the whole sentence is also false. The first logical operand is false because all men are not donkeys. The second logical operand "men and donkeys are donkeys" is a logical conjunction on its own and is also false. This is because although donkeys are donkeys men are not donkeys. Because it is connected by "and" this logical conjunction with one true logical operand and one false indicates that the sentence is false.
In accordance with step 2, Albert of Saxony proposed his own solution of the sophisma that proved it could result in both being truth and being false depending on the interpretation of the ambiguous sentence.
In accordance with step 3, Albert of Saxony did not have to prove this proposed solution because it covered both possible scenarios (being true and being false).
External links
- Sophismata project run by Alain de Libera at the University of GenevaUniversity of GenevaThe University of Geneva is a public research university located in Geneva, Switzerland.It was founded in 1559 by John Calvin, as a theological seminary and law school. It remained focused on theology until the 17th century, when it became a center for Enlightenment scholarship. In 1873, it...
- Catalogue of sophismata
- Sophismata in Stanford Encyclopedia of Philosophy
- Medieval and Renaissance Conceptions of Analysis
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