Author: Rossberg, Marcus

What Problem Did Ladd-Franklin (Think She) Solve(d)?

Sara Uckelman

Christine Ladd-Franklin is often hailed as a guiding star in the history of women in logic—not only did she study under C.S. Peirce and was one of the first women to receive a PhD from Johns Hopkins, she also, according to many modern commentators, solved a logical problem which had plagued the field of syllogisms since Aristotle. In this paper, we revisit this claim, posing and answering two distinct questions: Which
logical problem did Ladd-Franklin solve in her thesis, and which problem did she think she solved? We show that in neither case is the answer “a long-standing problem due to Aristotle”. Instead, what
Ladd-Franklin solved was a problem due to Jevons that was first articulated in the 19th century.

Logic Group videos and new Logic Supergroup channel

There are number of new recordings of UConn Logic Group colloquium talks on our youtube channel. We are also introducing playlists: for example, for last year’s “If” by any other name workshop here, or the recordings of the SEP 2018 conference (which was hosted by the UConn Logic Group) here.

We’re also happy to announce that the Logic Supergroup also has a youtube channel now, where many of the talks that are given in Supergroup online talks series will be available. Four videos are already up!

Logical Nihilism

Éno Agolli

Logical nihilism is the view that there is no logic, or more precisely that no single, universal consequence relation governs natural language reasoning. Here, I present three different arguments for logical nihilism from philosophically palatable premises. The first argument comes from a combination of pluralism with the desideratum that logical consequence should be universal, properly understood. The second argument is a slippery slope argument against monists who support weak logical systems on account of their power to characterize a vast range of true theories. The third argument is a general strategy of generating counterexamples to any inference rule, including purportedly fundamental ones such as disjunction introduction. I close by discussing why a truth-conditional approach to the meaning of the logical connectives not only does not force us to reject such counterexamples but also reveals that right truth-conditions are far more general than the classical ones, at the price of nihilism.

Ordering Anything: Rejiggering Linnebo’s Ordinal Abstraction

Eileen Nutting

Øystein Linnebo develops an abstractionist account of the natural numbers as ordinals. On this account, the natural numbers are abstracted from orderings of concrete numerals. But Linnebo also gestures towards an alternative version of his account, on which the restriction to concrete numerals is lifted. I develop something like this alternative account, show how it avoids the Burali-Forti paradox, and show how it guarantees that every number has a successor. Given these and other good features, I claim that Linnebo should prefer this alternative account to the one he develops.

Contextual analysis, epistemic probabilities, and paradoxes

Ehtibar Dzhafarov

Contextual analysis deals with systems of random variables. Each random variable within a system is labeled in two ways: by its content (that which the variable measures or responds to) and by its context (conditions under which it is recorded). Dependence of random variables on contexts is classified into (1) direct (causal) cross-influences and (2) purely contextual (non-causal) influences. The two can be conceptually separated from each other and measured in a principled way. The theory has numerous applications in quantum mechanics, and also in such areas as decision making and computer databases. A system of deterministic variables (as a special case of random variables) is always void of purely contextual influences. There are, however, situations when we know that a system is one of a set of deterministic systems, but we cannot know which one. In such situations we can assign epistemic (Bayesian) probabilities to possible deterministic systems, create thereby a system of epistemic random variables, and subject it to contextual analysis. In this way one can treat, in particular, such logical antinomies as the Liar paradox. The simplest systems of epistemic random variables describing the latter have no direct cross-influences and the maximal possible degree of purely contextual influences.

References:

Kujala, J.V., Dzhafarov, E.N., & Larsson, J.-A. (2015). Necessary and sufficient conditions for extended noncontextuality in a broad class of quantum mechanical systems. Physical Review Letters 115, 150401 (available as arXiv:1407.2886.).

Dzhafarov, E.N., Cervantes, V.H., Kujla, J.V. (2017). Contextuality in canonical systems of random variables. Philosophical Transactions of the Royal Society A 375: 20160389 (available as arXiv:1703.01252).

Cervantes, V.H., & Dzhafarov, E.N. (2018). Snow Queen is evil and beautiful: Experimental evidence for probabilistic contextuality in human choices. Decision 5, 193-204 (available as arXiv:1711.00418).

Core type theory

David Ripley

The Curry-Howard correspondence between intuitionistic logic and the simply-typed lambda calculus forms an important bridge between logical and computational research. This talk develops a variant typed lambda calculus, called “core type theory”, that stands in a similar correspondence to Neil Tennant’s “core logic” (fka “intuitionistic relevant logic”), and shows some basic (and some surprising!) results about this calculus.