In recent work, Adlam (2022b), Chen & Goldstein (2022), and Meacham (2023) have defended accounts of laws that take laws to be primitive global constraints. A major advantage of these accounts is that they’re able to accommodate the many different kinds of laws that appear in physical theories. In this paper I’ll present these three accounts, highlight their distinguishing features, and note some key differences that might lead one to favor one of these accounts over the others. I’ll conclude by (...) briefly discussing a version of a “constraint” account that I think is especially attractive. (shrink)

It is proved that the relevance logic \ has no structurally complete consistent axiomatic extension, except for classical propositional logic. In fact, no other such extension is even passively structurally complete.

Descartes nimmt in Anspruch, daß sein Argument des Deus malignus über die Einwände der Skeptiker hinausgehe. Was fügt es dem Traumargument hinzu? Die verbreitete Ansicht, der Dämon stelle die Erkenntnis mathematischer und logischer Wahrheiten in Frage, wird im folgenden diskutiert und zurückgewiesen. Die richtige Interpretation lautet: Die Annahme des Dämons unterstützt den Skeptizismus und verstärkt die Zweifel an der Existenz äußerer Objekte. Es werden drei Einwände gegen diese Interpretation erörtert und zurückgewiesen. Eine andere Auffassung vertritt Frankfurt: Die Rolle des Traumarguments (...) sei wesentlich begrenzt; die durch den Dämon aufgeworfenen Zweifel seien umfassender. Eine genaue Analyse der Entwicklung des Traumarguments in der Ersten Meditation führt zur Widerlegung dieser Interpretation. (shrink)

This essay is written on the following premises and argues for them. “Enlightenment” is a word or signifier, and not a single or unifiable phenomenon which it consistently signifies. There is no single or unifiable phenomenon describable as “the Enlightenment,” but it is the definite article rather than the noun which is to be avoided. In studying the intellectual history of the late seventeenth century and the eighteenth, we encounter a variety of statements made, and assumptions proposed, to which the (...) term “Enlightenment” may usefully be applied, but the meanings of the term shift as we apply it. The things are connected, but not continuous; they cannot be reduced to a single narrative; and we find ourselves using the word “Enlightenment” in a family of ways and talking about a family of phenomena, resembling and related to one another in a variety of ways that permit of various generalizations about them. We are not, however, committed to a single root meaning of the word “Enlightenment,” and we do not need to reduce the phenomena of which we treat to a single process or entity to be termed “the” Enlightenment. It is a reification that we wish to avoid, but the structure of our language is such that this is difficult, and we will find ourselves talking of “the French” or “the Scottish,” “the Newtonian” or the “the Arminian” Enlightenments, and hoping that by employing qualifying adjectives we may constantly remind ourselves that the keyword “Enlightenment” is ours to use and should not master us. (shrink)

Logics that do not have a deduction-detachment theorem (briefly, a DDT) may still possess a contextual DDT —a syntactic notion introduced here for arbitrary deductive systems, along with a local variant. Substructural logics without sentential constants are natural witnesses to these phenomena. In the presence of a contextual DDT, we can still upgrade many weak completeness results to strong ones, e.g., the finite model property implies the strong finite model property. It turns out that a finitary system has a contextual (...) DDT iff it is protoalgebraic and gives rise to a dually Brouwerian semilattice of compact deductive filters in every finitely generated algebra of the corresponding type. Any such system is filter distributive, although it may lack the filter extension property. More generally, filter distributivity and modularity are characterized for all finitary systems with a local contextual DDT, and several examples are discussed. For algebraizable logics, the well-known correspondence between the DDT and the equational definability of principal congruences is adapted to the contextual case. (shrink)

Originally published in 1913. Author: Henri Lichtenberger Language: English Keywords: History Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce and increasingly expensive. Obscure Press are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.Keywords: English Keywords 1900s Language English Artwork.

The first English translation of Fichte’s second set of 1804 lectures on the Wissenschaftslehre.

Most Gentzen systems arising in logic contain few axiom schemata and many rule schemata. Hilbert systems, on the other hand, usually contain few proper inference rules and possibly many axioms. Because of this, the two notions tend to serve different purposes. It is common for a logic to be specified in the first instance by means of a Gentzen calculus, whereupon a Hilbert-style presentation ‘for’ the logic may be sought—or vice versa. Where this has occurred, the word ‘for’ has taken (...) on several different meanings, partly because the Gentzen separator ⇒ can be interpreted intuitively in a number of ways. Here ⇒ will be denoted less evocatively by ⊲.In this paper we aim to discuss some of the useful ways in which Gentzen and Hilbert systems may correspond to each other. Actually, we shall be concerned with thededucibility relationsof the formal systems, as it is these that are susceptible to transformation in useful ways. To avoid potential confusion, we shall speak of Hilbert and Gentzenrelations. By aHilbert relationwe mean any substitution-invariant consequence relation onformulas—this comes to the same thing as the deducibility relation of a set of Hilbert-style axioms and rules. By aGentzen relationwe mean the fully fledged generalization of this notion in whichsequentstake the place of single formulas. In the literature, Hilbert relations are often referred to assentential logics. Gentzen relations as defined here are their exactsequentialcounterparts. (shrink)

”Quantum entanglement”, a phrase first coined by Erwin Schr¨ odinger1, describes a condition of the separated parts of the same quantum system in which each of the parts can only be described by referencing the state of other part. This is one of the most counterintuitive aspects of quantum mechanics, because classically one would expect system parts out of speed-of-light contact to be completely independent. Thus, entanglement represents a kind of quantum connectedness in which measurements on one isolated part of (...) an entangled quantum system have non-classical consequences for the outcome of measurements performed on the other (possibly very distant) part of the same system. This quantum connectedness that enforces the measurement correlation and state-matching in entangled quantum systems has come to be called quantum nonlocality. (shrink)

The most time consuming effort has been toward building a precision, servo-controlled rotary drive to turn the attractor. After discovering our Nanomotion HR1 Ultra-High-Vacuum motor was incapable of continuous operation in a vacuum environment (due to heat management issues), we were forced to redesign the system such that the motor remained in atmosphere. We are pleased with the final performance. Fig. 2.1-1A..

The question we have been investigating is whether the nonlocality of standard quantum mechanics is the private domain of Nature, as is generally assumed by the physics community, or whether in special circumstances the nonlocal connection between subsystems can be used to send signals from one observer to another. With the aid of generous private contributions and some use of CENPA resources, we have continued the work on this test of nonlocal quantum communication, which has been reported in the past (...) three years1�2�3. The initial configuration of the experiment, as described in the first two references, employed a high power argon-ion laser operating at about 1 W in the ultraviolet at 351 nm that pumped nonlinear crystals (BBO or LiIO3) to produce pairs of momentum-entangled 702 nm photons, on which measurements were subsequently performed. It was concluded that signal-to-noise limitations from fluoresence photons competing with the down-converted photons prevented the planned measurements using the initial configuration. (shrink)