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Quantum logic and 'logical schizophrenia'


Guido Bacciagaluppi (Descartes Centre for the History and Philosophy of the Sciences and the Humanities, Utrecht)

Hilary Putnam famously claimed that 'quantum logic is the true logic', and that we have empirical reasons for preferring quantum logic to classical logic, so that logic is in fact empirical, because the shift to quantum logic solves the puzzles of quantum mechanics. This talk will not defend these strong claims; indeed, the last of these claims is well-known to be wrong. However, it will defend Putnam against the charge of 'logical schizophrenia', i.e. it will argue that the claim that 'quantum logic is the true logic' is compatible with classical reasoning being admissible in familiar cases (or in Putnam's words, that the classical connectives are the quantum logical connectives 'in disguise'), including the case of reasoning about which logic may be 'true'. Indeed, at least as long as one identifies 'quantum logic' with well-behaved non-distributive logics such as orthologic or orthomodular logic, then the case of quantum logic is perfectly analogous to that of intuitionist logic or paraconsistent logic, where classical logic is recovered when these logics are applied, respectively, to reasoning within finite or consistent domains. Classical reasoning is not logically valid, but admissible because of the special meaning of the propositions to which it is applied.

CFE LECTURE NUMBER 3 (10th of May, 2018)

Paolo Mancosu (UC Berkeley)

Neologicism emerges in the contemporary debate in philosophy of mathematics with Wright’s book Frege’s Conception of Numbers as Objects (1983). Wright’s project was to show the viability of a philosophy of mathematics that could preserve the key tenets of Frege’s approach, namely the idea that arithmetical knowledge is analytic. The key result was the detailed reconstruction of how to derive, within second order logic, the basic axioms of second order arithmetic from Hume’s principle (HP) (and definitions).  This has led to a detailed scrutiny of so-called abstraction principles, of which Basic Law V (BLV) and HP are the two most famous instances. As is well known, Russell proved that BLV is inconsistent. BLV has been the only example of an abstraction principle from (monadic) concepts to objects giving rise to inconsistency, thereby making it appear as a sort of monster in an otherwise regular universe of abstraction principles free from this pathology. We show that BLV is part of a family of inconsistent abstractions. The main result is a theorem to the effect that second-order logic formally refutes the existence of any function F that sends concepts into objects and satisfies a “part-whole” relation. In addition, we study other properties of abstraction principles that lead to formal refutability in second order logic.

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Dear Colleagues, Friends and Supporters of the Institute of Philosophy,
We would like to invite you to the first English edition of the Philosophical Café, dedicated to the international researchers from our Institute. Aside from the language used, however, everything else will stay the same, so you can look forward to an informal meeting of the members of the Institute of Philosophy and their friends and supporters – all as a part of the "Afternoon with the Institute of Philosophy" platform.

In the first international Philosophical Café we will welcome three researchers from the Formal Epistemology Centre directed by Prof. Ladislav Kvasz, namely Joan Bertran-San Millán, Vera Matarese and Aldo Filomeno, and explore some interrelations between logic, the theory of knowledge and the empirical evidence provided by physical science in the following talks:

1) Frege as the Founder of Modern Logic (Joan Bertran-San Millán)
Frege's contributions to logic are traditionally considered as marking the starting point of modern logic. I will evaluate this claim and compare Frege's leading work on logic with that of some of his contemporaries. The focus of this evaluation will be on the relation between mathematics and logic and Frege's critique of a psychological foundation of logic.

2) On the Relation between Ontology and Epistemology in Physical Theorizing (Vera Matarese)
Since modern physical theories are formulated in mathematical language, we must look at mathematics in order to understand what these theories tell us about the physical world. But in what ways does mathematics reveal the nature of the world? Either we let mathematics dictate the structure of our physical world, or we use our intuitions and subjective understanding of the world as guides to interpret mathematical formalism. In my talk, I will discuss these two options and argue for a middle way that appeals to some new epistemological principles.

3) Reasoning under Uncertainty (Aldo Filomeno)
Various arguments in philosophy and science recur to probabilities. For instance, consider the 'anthropic cosmological principle', which is based on recent discoveries in cosmology to support the existence of the multiverse or the existence of God. This argument, however, implicitly assigns unwarranted probabilities. My project consists in the assessment of arguments of this sort found in philosophy and science, in the light of the proper assigning of the probabilities.

Everyone is warmly welcome not only to participate in the audience, but also to take part in the discussion.

About Project

The aim of the project is to develop a formalization of epistemology analogous to Frege’s formalization of logic. The core of the project centres upon five theses setting out the path to a truly formal epistemology. These theses are based on the deeply-held belief that the current trend in the formalization of epistemology is insufficiently radical.

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