# The Emergence of First-Order Logic

The SEP entry on “The Emergence of First-Order Logic” by William Ewald is out today.

# Indian Conference on Logic and its Applications 2019

The Association for Logic in India (ALI) announces the eighth edition of its biennial International Conference on Logic and its Applications (ICLA), to be held at the Indian Institute of Technology Delhi from March 3 to 5, 2019.

ICLA is a forum for bringing together researchers from a wide variety of fields in which formal logic plays a significant role, along with mathematicians, computer scientists, philosophers and logicians studying foundations of formal logic in itself. A special feature of this conference is the inclusion of studies in systems of logic in the Indian tradition and historical research on logic.

As in the earlier events in this series, we shall have eminent scholars as invited speakers. Details of the last ICLA 2017 may be found at https://icla.cse.iitk.ac.in. See http://ali.cmi.ac.in for information on past events as well as updates on this conference.

The call for papers is here: https://easychair.org/cfp/icla2019

# forall x is going CC BY

The original forall x by P.D. Magnus, as well as Tim Button’s forall x: Cambridge, and the forallx: Calgary remix are now released under a Creative Commons Attribution (rather than the more restrictive Attribution-ShareALike license). The Fall 2018 version also incorporates some of Tim’s revisions for the latest version of forall x: Cambridge. You can find all three on Github: forall x, forall x: Cambridge, and forall x: YYC.

# Non-analytic tableaux for Chellas’s conditional logic CK and Lewis’s logic of counterfactuals VC

Australasian Journal of Logic 15 (3): 609–28.

Priest has provided a simple tableau calculus for Chellas’s conditional logic Ck. We provide rules which, when added to Priest’s system, result in tableau calculi for Chellas’s CK and Lewis’s VC. Completeness of these tableaux, however, relies on the cut rule.

DOI: 10.26686/ajl.v15i3.4780 (open access)

# PhD, Postdoc with Rosalie Iemhoff

## Postdoc position in Logic at Utrecht University, the Netherlands.

The postdoc is embedded in the research project “Optimal Proofs” funded by the Netherlands Organization for Scientific Research led by Dr. Rosalie Iemhoff, Department of Philosophy and Religious Studies, Utrecht University. The project in mathematical and philosophical logic is concerned with formalization in general and proof systems as a form of formalization in particular. Its mathematical aim is to develop methods to describe the possible proof systems of a given logic and establish, given various criteria of optimality, what the optimal proof systems of the logic are. Its philosophical aim is to develop general criteria for faithful formalization in logic and to thereby distinguish good formalizations from bad ones. The mathematical part of the project focusses on, but is not necessarily restricted to, the (non)classical logics that occur in computer science, mathematics, and philosophy, while the philosophical part of the project also takes into account domains where formalization in logic is less common. The postdoc is expected to contribute primarily to the mathematical part of the project. Whether the research of the postdoc also extends to the philosophical part of the project depends on his or her interests.

# Proof by legerdemain

Peli Grietzer shared a blog post by David Auerbach on Twitter yesterday containing the following lovely quote about Smullyan and Carnap:

I particularly delighted in playing tricks on the philosopher Rudolf Carnap; he was the perfect audience! (Most scientists and mathematicians are; they are so honest themselves ‘that they have great difficulty in seeing through the deceptions of others.) After one particular trick, Carnap said, “Nohhhh! I didn’t think that could happen in any possible world, let alone this one!”

In item # 249 of my book of logic puzzles titled What Is the Name of This Book?, I describe an infallible method of proving anything whatsoever. Only a magician is capable of employing the method, however. I once used it on Rudolf Carnap to prove the existence of God.

“Here you see a red card,” I said to Professor Carnap as I removed a card from the deck. “I place it face down in your palm. Now, you know that a false proposition implies any proposition. Therefore, if this card were black, then God would exist. Do you agree?”

“Oh, certainly,” replied Carnap, “if the card were black, then God would exist.”

“Very good,” I said as I turned over the card. “As you see, the card is black. Therefore, God exists!”

“Ah, yes!” replied Carnap in a philosophical tone. “Proof by legerdemain! Same as the theologians use!”

Raymond Smullyan, 5000 BC and Other Philosophical Fantasies. New York: St. Martin’s Press, 1983, p. 24.

See Auerbach’s post for more Carnap and Smullyan anecdotes.

# Rumfitt on truth-grounds, negation, and vagueness

Philosophical Studies 175 (2018) 2079–2089

In The Boundary Stones of Thought (2015), Rumfitt defends classical logic against challenges from intuitionistic mathematics and vagueness, using a semantics of pre-topologies on possibilities, and a topological semantics on predicates, respectively. These semantics are suggestive but the characterizations of negation face difficulties that may undermine their usefulness in Rumfitt’s project.

Preprint

# Why φ?

Does anyone know why we traditionally use Greek phi and psi for metasyntactic variables representing arbitrary logic formulas? Is it just because ‘formula’ begins with an ‘f’ sound? And chi was being used for other things?

Although Whitehead and Russell already used φ and ψ for propositional functions, the convention of using them specifically as meta-variables for formulas seems to go back to Quine’s 1940 Mathematical Logic. Quine used μ, ν as metavariables for arbitrary expressions, and reserved α, β, γ for variables, ξ, η, σ for terms, and φ, χ, ψ for statement. (ε, ι, λ had special roles.) Why φ for statements? Who knows. Perhaps simply because Whitehead and Russell used it for propositional functions in Principia? Or because “p” for “proposition” was entrenched, and in classic Greek, φ was a p sound, not f?

The most common alternative in use at the time was the use of Fraktur letters, e.g., $$\mathfrak{A}$$ as a metavariable for formulas, and A as a formula variable; x as a bound variable and $$\mathfrak{x}$$ as a metavariable for bound variables. This was the convention in the Hilbert school, also followed by Carnap. Kleene later used script letters for metavariables and upright roman type for the corresponding symbols of the object language. But indicating the difference by different fonts is perhaps not ideal, and Fraktur may not have been the most appealing choice anyway, both because it was the 1940s and because the type was probably not available in American print shops.

# Postdoc in Formalism, Formalization, Intuition and Understanding in Mathematics

Archives Poincaré (Nancy) and IHPST Paris are advertising for a 20-month postdoc fellowship.

# Logic Colloquium, Udine

The European Summer Meeting of the Association of Symbolic Logic will be in Udine, just north of Venice, July 23-28. Abstracts for contributed talks are due on April 27. Student members of the ASL are eligible for travel grants!

lc18.uniud.it