DBS Think Tank IX was held on August 25–27, 2021 in Orlando FL with US based participants largely in person and overseas participants joining by video conferencing technology. The DBS Think Tank was founded in 2012 and provides an open platform where clinicians, engineers and researchers can freely discuss current and emerging deep brain stimulation technologies as well as the logistical and ethical issues facing the field. The consensus among the DBS Think Tank IX speakers was that DBS expanded in (...) its scope and has been applied to multiple brain disorders in an effort to modulate neural circuitry. After collectively sharing our experiences, it was estimated that globally more than 230,000 DBS devices have been implanted for neurological and neuropsychiatric disorders. As such, this year’s meeting was focused on advances in the following areas: neuromodulation in Europe, Asia and Australia; cutting-edge technologies, neuroethics, interventional psychiatry, adaptive DBS, neuromodulation for pain, network neuromodulation for epilepsy and neuromodulation for traumatic brain injury. (shrink)

Two more or less standard methods exist for the systematic, logical construction of classical mathematics, the so-called theory of types, due in the main to Russell, and the Zermelo axiomatic set theory. In systems based upon either of these, the connective of membership, “ε”, plays a fundamental role. Usually although not always it figures as a primitive or undefined symbol.Following the familiar simplification of Russell's theory, let us mean by alogical typein the strict sense any one of the following: (i) (...) the totality consisting exclusively of individuals, (ii) the totality consisting exclusively of classes whose members are exclusively individuals, (iii) the totality consisting exclusively of classes whose members are exclusively classes whose members in turn are exclusively individuals, and so on. Any entity from (ii) is said to beone type higherthan any entity from (i), any entity from (iii), one type higher than any entity from (ii), and so on. In systems based upon this simplified theory of types, the only significant atomic formulae involving “ε” are those asserting the membership of an entity in an entity one type higher. Thus any expression of the form “(x∈y)” is meaningless except where “y” denotes an entity of just one type higher than the type of the entity denoted by “x” It is by means of general type restrictions of this kind that the Russell and other paradoxes are avoided. (shrink)

The method of Ramsey sentences has been proposed for handling theoretical constructs within a scientific system. Essentially it consists of constructing a certain "monolithic" sentence for an entire theory. In this present paper several improvements are suggested which help to overcome some of the awkward features of the method. In particular we have here many Ramsey sentences rather than just one, each erstwhile primitive theoretical term giving rise to a Ramsey sentence. Such a sentence in effect defines what we call (...) a Ramsey constant. Using Ramsey constants, we attempt to improve the method in important logical and semantical respects. It is suggested also that such constants are of interest for the philosophy of mathematics. (shrink)

Professor Stevenson's valuable paper [5] calls attention to a number of discrepancies between ‘if’ in English and its usual translation into the horseshoe of material implication. “This is not a reason for distrusting the horseshoe,” he notes, “which is useful so long as it is taken to mean just what it is defined to mean; and it is not a reason for distrusting our English if's, which in spite of their ambiguities are indispensable to our daily discourse”. Accordingly, Stevenson proposes (...) to develop a “richer logic” than the ordinary one, by adding as primitives certain sentential connectives. He speaks throughout in the old terminology of “propositions” rather than in that of the sentences or statements used to express them. Thus he speaks of atomic and molecular propositions, somehow no doubt as real entities in the world, where talk of atomic and molecular sentences would save him from implicit involvement in the notorious difficulties connected with atomic facts. Finally, the inner structure of atomic sentences, and therewith of molecular ones, is never considered. Many molecular sentences contain quantifiers in interesting ways, the clarification of which would seem essential in getting at their structure. Stevenson, however, has no concern with quantifiers, and does not exhibit the quantificational structure of the English sentences considered. (shrink)

Woodger first gives a rough account of the "Boole-Frege" movement in modern logic and persuasively argues as to the importance of formalized language-systems for the methodology of science. Some of these arguments are as follows: A natural language such as English, he notes, "is not only used for purposes of communication in the scientific sense. It is also used for the writing of poetry, for religious devotion, for political controversy, and for persuading people to buy some of the products of (...) industrial activity which they would not otherwise want. But these pursuits make demands upon language which are very different from those made by science. The requirements of science prove on investigation to be quite surprisingly meagre and the excessive riches of a natural language like English are a source of embarrassment. They tempt us to employ linguistic devices borrowed from extra-scientific usages which can have unfortunate consequences. Metaphors, for example, with which some branches of biology abound, are often suggestive and may be harmless enough if they are recognized for what they are. But at best they are makeshifts and substitutes for genuine biological statements, and the fact that recourse is had to them is surely a sign of immaturity. Science demands great linguistic austerity and discipline, and the canons of good style in scientific writing are different from those of good writing in other kinds of literature." Another argument is that "sooner or later the linguistic habits of everyday life will cease to do justice to... the... increasing complexity and novelty of observation and hypothesis." A third argument is that scientific language is used not only for the purpose of communication, for recording observations, or for formulating general laws or hypotheses. It is also used for calculation and the unearthing of the consequences of our assumptions. The logic underlying a formalized language is explicitly designed to enable us to calculate easily and efficiently. The important, and now thoroughly established, methodological distinction between object-language and meta-language is blurred for natural language and is best maintained in terms of formalized language-systems. And, finally, in natural language the important distinction between syntax and semantics also tends to be blurred. "From both the syntactical and the semantical points of view natural languages are incredibly complicated and unruly. The rules of ordinary gram mar are quite insufficient from the standpoint of the requirements of science, and the problems connected with meaning and truth in relation to natural languages are enormously complicated and perhaps insoluble.". (shrink)