The Distinction Between False Dilemma and False Disjunctive Syllogism

Since a clear account of the fallacy of false disjunctive syllogism is missing in the literature, the fallacy is defined and its three types are differentiated after some preliminaries. Section 4 further elaborates the differentia specifica for each of the three types by analyzing relevant argument criticism of each, as well as the related profiles of dialogue. After defining false disjunctive syllogisms, it becomes possible to distinguish between a false dilemma and a false disjunctive syllogism: section 5 analyzes their similarities (which explains why the fallacies are often confused with one another) and section 6 explains their differences.

Do Monkeys and Young Children Understand Exclusive “Or” Relations? A Commentary on Ferrigno et al. (2021)

Ferrigno et al. (2021) claim to provide evidence that monkeys can reason through the disjunctive syllogism (given A or B, not A, therefore B) and conclude that monkeys therefore understand logical “or” relations. Yet their data fail to provide evidence that the baboons they tested understood the exclusive “or” relations in the experimental task. For two mutually exclusive possibilities—A or B—the monkeys appeared to infer that B was true when A was shown to be false, but they failed to infer that B was false when A was shown to be true. In our own research, we recently found an identical response pattern in 2.5- to 4-year-old children, whereas 5-year-olds demonstrated that they could make both inferences. The monkeys’ and younger children’s responses are instead consistent with an incorrect understanding of A and B as having an inclusive “or” relation. Only the older children provided compelling evidence of representing the exclusive “or” relation between A and B.

Non-Boolean classical relevant logics II: Classicality through truth-constants

This paper gives an account of Anderson and Belnap’s selection criteria for an adequate theory of entailment. The criteria are grouped into three categories: criteria pertaining to modality, those pertaining to relevance, and those related to expressive strength. The leitmotif of both this paper and its prequel is the relevant legitimacy of disjunctive syllogism. Relevant logics are commonly held to be paraconsistent logics. It is shown in this paper, however, that both E and R can be extended to explosive logics which satisfy all of Anderson and Belnap’s selection criteria, provided the truth-constant known as the Ackermann constant is available. One of the selection criteria related to expressive strength is having an “enthymematic” conditional for which a deduction theorem holds. I argue that this allows for a new interpretation of Anderson and Belnap’s take on logical consequence, namely as committing them to pluralism about logical consequence.

Reasoning Through the Disjunctive Syllogism in Monkeys

The capacity for logical inference is a critical aspect of human learning, reasoning, and decision-making. One important logical inference is the disjunctive syllogism: given A or B, if not A, then B. Although the explicit formation of this logic requires symbolic thought, previous work has shown that nonhuman animals are capable of reasoning by exclusion, one aspect of the disjunctive syllogism (e.g., not A = avoid empty). However, it is unknown whether nonhuman animals are capable of the deductive aspects of a disjunctive syllogism (the dependent relation between A and B and the inference that “if not A, then B” must be true). Here, we used a food-choice task to test whether monkeys can reason through an entire disjunctive syllogism. Our results show that monkeys do have this capacity. Therefore, the capacity is not unique to humans and does not require language.

7. Deducing

Detective work is an important tool in philosophy. ‘Deducing’ explains the difference between valid and sound arguments. An argument is valid if its premises are true but is only sound if the conclusion is true. The Greek philosophers identified disjunctive syllogism—the idea that if something is not one thing, it must be another. This relates to another philosophical concept, the ‘law of the excluded middle’. An abduction is a form of logical inference which attempts to find the most likely explanation. Modal logic, an extension of classical logic, is a popular branch of logic for philosophical arguments.

Logical reasoning by a Grey parrot? A case study of the disjunctive syllogism

In Call’s (2004) 2-cups task, widely used to explore logical and causal reasoning across species and early human development, a reward is hidden in one of two cups, one is shown to be empty, and successful subjects search for the reward in the other cup. Infants as young as 17-months and some individuals of almost all species tested succeed. Success may reflect logical, propositional thought and working through a disjunctive syllogism (A or B; not A, therefore B). It may also reflect appreciation of the modal concepts “necessity” and “possibility”, and the epistemic concept “certainty”. Mody & Carey’s (2016) results on 2-year-old children with 3- and 4-cups versions of this task converge with studies on apes in undermining this rich interpretation of success. In the 3-cups version, one reward is hidden in a single cup, another in one of two other cups, and the participant is given one choice, thereby tracking the ability to distinguish a certain from an uncertain outcome. In the 4-cups procedure, a reward is hidden in one cup of each pair (e.g., A, C); one cup (e.g., B) is then shown to be empty. Successful subjects should conclude that the reward is 100% likely in A, only 50% likely in either C or D, and accordingly choose A, thereby demonstrating modal and logical concepts in addition to epistemic ones. Children 2 1/2 years of age fail the 4-cups task, and apes fail related tasks tapping the same constructs. Here we tested a Grey parrot (Psittacus erithacus), Griffin, on the 3- and 4-cups procedures. Griffin succeeded on both tasks, outperforming even 5-year-old children. Controls ruled out that his success on the 4-cups task was due to a learned associative strategy of choosing the cup next to the demonstrated empty one. These data show that both the 3- and 4-cups tasks do not require representational abilities unique to humans. We discuss the competences on which these tasks are likely to draw, and what it is about parrots, or Griffin in particular, that explains his better performance than either great apes or linguistically competent preschool children on these and conceptually related tasks.

Epistemic Gain

Core Logic avoids the Lewis First Paradox, even though it contains ∨-Introduction, and a form of ∨-Elimination that permits core proof of Disjunctive Syllogism. The reason for this is that the method of cut-elimination will unearth the fact that the newly combined premises form an inconsistent set. A new formal-semantical relation of logical consequence, according to which B is not a consequence of A,¬A, is available as an alternative to the conventionally defined relation of logical consequence. Nevertheless we can make do with the conventional definition, and still show that (Classical) Core Logic is adequate unto it. Although Core Logic eschews unrestricted Cut, nevertheless (i) Core Logic is adequate for all intuitionistic mathematical deduction; (ii) Classical Core Logic is adequate for all classical mathematical deduction; and (iii) Core Logic is adequate for all the deduction involved in the empirical testing of scientific theories.

The Relevance Properties of Core Logic

Ironically Anderson and Belnap argue for the rejection of Disjunctive Syllogism by means of an argument that appears to employ it. We aim to establish a ‘variable-sharing’ result for Classical Core Logic that is stronger than any such result for any other system. We define an exigent relevance condition R(X,A) on the premise-set X and the conclusion A of any proof, exploiting positive and negative occurrences of subformulae. This treatment includes first-order proofs. Our main result on relevance is that for every proof of A from X in Classical Core Logic, we have R(X,A). R(X,A) is a best possible explication of the sought notion of relevance. Our result is optimal, and challenges relevantists in the Anderson–Belnap tradition to identify any strengthening of the relation R(X,A) that can be shown to hold for some subsystem of Anderson–Belnap R but that can be shown to fail for Classical Core Logic.