Logic and Cognition in Peter Abelard

 

Logic and Cognition in Peter Abelard

Abelard's Approach to Argument and Words

• Abelard suggests that students should move from studying words to propositions to understand argument.
• He developed a theory of propositional content, a theory of formal validity for syllogisms, and a theory of true conditionals.
• The study of words begins with the imposition of words, where the creator of the language imposes a sound to name an item or its nature or property.
• Abelard assigns two forms of signification to words: the signification of understandings and the signification of things.
• A spoken word signifies an understanding by generating an act of understanding in the mind of a hearer, which should correspond with the speaker's understanding of the same individual, nature, or property.
• Abelard's discussion of words is centered on sentences, where the meaning generated by a sentence is composed of what is signified by the words.
• A declarative sentence signifies what is asserted to be the case, a concept he calls the dictum.
• Abelard discusses different attitudes towards propositional content and develops a theory of propositional logic.
• He treats conditional sentences as assertions of the relation between the propositional content of the antecedent and consequent, not as an assertion of the truth.
• Abelard also developed a theory of propositional negation, which defines the negation of “All As are Bs” as “it is not the case that All As are Bs.”

Abelard's Views on Argument, Inference, and Entailments

Abelard's Distinction Between Perfect and Imperfect Entailment
• Perfect entailment, such as syllogisms or conditionals, is valid due to its form.
• Abelard's criterion for perfect entailment is universal substitution, which is not necessary for a topic or maximal proposition.
• Imperfect entailments require more to warrant the inference, with the criterion being that it is impossible for the premises to be true and the conclusion false.
• Abelard allows non-formal facts about the world to warrant the necessity of the syllogistic inference.

Abelard's Stricter Criteria for Conditionals
• Abelard's stricter criterion for conditionals is that the understanding signified by the antecedent must contain the understanding of the consequent.
• For a conditional to be true, it must also be the case that the understanding signified by the antecedent “contain” the understanding of the consequent.

Cognition and Philosophy of Mind
• Abelard's philosophy of mind was not overly interested in philosophy of mind as such.
• He rejected many core Aristotelian claims, including the theory that cognition involves the formal identity between the mind and the object understood.
• Abelard also denied the view that cognition is the formation of representations, images or likenesses, of the object cognized.

Abelard's Paradigm of Cognition
• In Abelard's paradigm case of cognition, there are three steps: sensation, imagination, and understanding.
• Sensation is a power of the mind, while imagination supplements the present sensation.
• The rational power of the mind can focus on the confused conception and focus its discerning attention on some nature or property of the object sensed or imagined.
• Abelard argues that the act of understanding is just a transient act of thinking about something, not the object of cognition or knowledge.