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.
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