Summer School in Logic and Formal Epistemology
There is a long tradition of fruitful interaction between philosophy and the sciences. Logic and statistics emerged, historically, from combined philosophical and scientific inquiry into the nature of mathematical and scientific inference; and the modern conceptions of psychology, linguistics, and computer science are the results of sustained reflection on the nature of mind, language, and computation. In today's climate of disciplinary specialization, however, foundational reflection is becoming increasingly rare. As a result, developments in the sciences are often conceptually ill-founded, and philosophical debates often lack scientific substance.
In 2016, the Department of Philosophy at Carnegie Mellon University will hold a three-week summer school in logic and formal epistemology for promising undergraduates in philosophy, mathematics, computer science, linguistics, economics, and other sciences. The goals are to:
- introduce promising students to cross-disciplinary fields of research at an early stage in their career; and
- forge lasting links between the various disciplines.
The summer school will be held from Monday, June 6 to Friday, June 24, 2016. There will be morning and afternoon lectures and daily problem sessions, as well as planned outings and social events.
The summer school is free. That is, we will provide:
- full tuition
- dormitory accommodations on the Carnegie Mellon campus
So students need only pay for round trip travel to Pittsburgh and living expenses while here. We expect to be able to accept about 25 students in 2016. There are no grades, and the courses do not provide formal course credit.
The summer school is open to undergraduates, as well as to students who will have just completed their first year of graduate school. Applicants need not be US citizens. There is a $30 nonrefundable application fee.
Applications for 2016 are now open and available online.
Topic: Meaning in natural language: from truth conditions to queries
This course is intended as an introduction to formal semantics and as preparation for a weekend workshop on the semantics of questions.
Meaning in natural language had proven to be an elusive target until someone had the idea of substituting truth conditions for meaning. It is easier to specify the conditions under which a sentence would be true than to say what it means, and since you can only know truth conditions of a sentence if you know its meaning, this seemed like a legitimate substitution. But one hardly wants a theory in which the meaning of each sentence is individually spelled out. There are too many sentences for that, and this way of specifying meaning wouldn’t correspond to how a person learns or uses language. The other part of the solution, then, is to supply semantic values for parts of sentences – words and phrases – in such a way that they combine to give truth conditions for entire sentences. The semantic values of sentence-parts can be rendered in an interpreted logic, these values representing what a person must learn, or needs to combine, in understanding and producing novel sentences.
We begin the week applying this program to simple declarative sentences. Basic linguistic tests will be used to discover the constituent structure of such sentences, syntactic structure being the guide to the composition of meaning. We develop a logic as we go along, one particularly suited to apply to sub-sentential pieces of language.
Clearly, however, a language is more than a collection of declarative sentences. There are other grammatical moods than just the declarative, but sentences in interrogative, imperative, or exclamative mood cannot be said to be have truth conditions. How is the basic truth-conditional program to be applied to a broader range of sentence types? The lectures at the conclusion of the week will take up the issue of how the meanings of questions can be understood not in terms of truth conditions, but rather in terms of what constitutes an answer to a question. And to the use of truth-conditional data to indirectly investigate question semantics. The treatment of questions serves as a test case for a more general approach to meaning in natural language, going beyond truth-conditional semantics while taking the declarative mood as its point of departure.
Instructor: B. R. George
Topic: COMPUTABILITY: Mechanical procedures & mathematical minds
Computability is perhaps the most significant and distinctive notion modern logic has introduced; in the guise of decidability and effective calculability it has a venerable history within philosophy and mathematics. Now it is also the basic theoretical concept for computer science, artificial intelligence and cognitive science. We will trace the evolution of the notion starting with Leibniz and ending with an axiomatic characterization of mechanical procedures that is rooted in the work of Alan Turing, Emil Post and Robin Gandy.
With this conceptual analysis in the background we will discuss the proofs of the classical incompleteness and undecidability theorems as well as their impact on foundational programs, in particular, Hilbert’s finitist program. Thus, we are led back to the radical transformation of mathematics in the second half of the 19th century that raised methodological, philosophical issues the foundational programs tried to address. We articulate a position that coherently joins mathematical and philosophical structuralism.
Reading and discussing classical papers in the foundational discussion are supplemented by experimenting with automated proof search procedures in logic and elementary parts of set theory. The basic question here is, how far can mechanical procedures (exploiting structural features of proofs and heuristic considerations) model mathematical thinking?
(June 20 -24)
An Introduction to Decisions with Imprecise Probabilities [IP]
How to understand a decision maker’s uncertainty?
One variety of choice problem is with a single decision maker, YOU. Consider what follows from the simple, prudential consideration that YOUshould not expose YOURSELF to sure-losses. A second variety of choice is in decision problems involving multiple decision makers (who may have competing goals with YOUR own), and to consider what follows from the equally simple prudential consideration that YOU should not play the game in a way that allows the opponents to make YOU worse off than you might be by playing differently, particularly when they benefit at YOURexpense by doing so. A third variety of decision problem involves a group of cooperative decision makers who have the ability to coordinate their individual choices and agree they should not act in such a fashion that, under an alternative plan available to them, each would do strictly better.
How does IP theory improve decision making?