Logic and the Basis of Theology: an Investigation into the Help Logic Can Give to the Understanding of Different Theologies, Following the Contributions to Both Disciplines of Arthur Prior, 1914-1969

<p>My thesis is that modem symbolic mathematical logics have an important contribution to make to theologies. I demonstrate this firstly in a 'theoretical section' (i) by showing what logics are and why they can be trusted; (ii) by showing how all theologies may be correctly treated as axiomatic systems; (iii) by outlining some modern logics which can assist theological thinking, including a logic I construct for this purpose called the Theologic. I demonstrate this, secondly, in an 'applied logic' section, by looking at (iv) the theology of one current branch of Christianity in detail, outlining its logical problems and the consequences of trying to avoid them; (v) 'post-modern' Christian theologies, firstly those that suggest that the word 'God' is a symbol rather than a name, and secondly at three feminist theologies two of which are logically quite radical; (vi) pantheism, in particular at Spinoza's ideas and Lovelock's Gaia; (vii) two religions, Buddhism and Confucianism, which, in their basic religious thinking, can be said to have no gods. I find that all religions I have studied - and they are representative of religions actual, proposed and imagined - have serious logical flaws, some known of old, others brought to light by the modern logics. The consequences of making the religions more logically sound are generally unacceptable to the members of the faiths. The suggestion that the gods use a different sort of logic to us is generally logically unacceptable. This does not leave abandoning religion as the only other possibility: the work of theologians in future, assisted by mathematical logic, may be (a) to bring about changes in basic beliefs, and (b) to assist in the birth of new, logically sound, religions. These investigations are carried out in the spirit of A N Prior, who came to logic through a Christian upbringing which gave him an interest in theology, a desire to make that theology more consistent, and as Professor of Philosophy at Canterbury College (as it then was) taught me. My upbringing was similar. We both, in the end, found conventional Christianity too illogical to believe. Time having past, I have been able to examine the logic of other, and newer, theologies.</p>

Logic and the Basis of Theology: an Investigation into the Help Logic Can Give to the Understanding of Different Theologies, Following the Contributions to Both Disciplines of Arthur Prior, 1914-1969

<p>My thesis is that modem symbolic mathematical logics have an important contribution to make to theologies. I demonstrate this firstly in a 'theoretical section' (i) by showing what logics are and why they can be trusted; (ii) by showing how all theologies may be correctly treated as axiomatic systems; (iii) by outlining some modern logics which can assist theological thinking, including a logic I construct for this purpose called the Theologic. I demonstrate this, secondly, in an 'applied logic' section, by looking at (iv) the theology of one current branch of Christianity in detail, outlining its logical problems and the consequences of trying to avoid them; (v) 'post-modern' Christian theologies, firstly those that suggest that the word 'God' is a symbol rather than a name, and secondly at three feminist theologies two of which are logically quite radical; (vi) pantheism, in particular at Spinoza's ideas and Lovelock's Gaia; (vii) two religions, Buddhism and Confucianism, which, in their basic religious thinking, can be said to have no gods. I find that all religions I have studied - and they are representative of religions actual, proposed and imagined - have serious logical flaws, some known of old, others brought to light by the modern logics. The consequences of making the religions more logically sound are generally unacceptable to the members of the faiths. The suggestion that the gods use a different sort of logic to us is generally logically unacceptable. This does not leave abandoning religion as the only other possibility: the work of theologians in future, assisted by mathematical logic, may be (a) to bring about changes in basic beliefs, and (b) to assist in the birth of new, logically sound, religions. These investigations are carried out in the spirit of A N Prior, who came to logic through a Christian upbringing which gave him an interest in theology, a desire to make that theology more consistent, and as Professor of Philosophy at Canterbury College (as it then was) taught me. My upbringing was similar. We both, in the end, found conventional Christianity too illogical to believe. Time having past, I have been able to examine the logic of other, and newer, theologies.</p>

Investigation of observability property of controlled binary dynamical systems: a logical approach

The property of observability of controlled binary dynamical systems is investigated. A formal definition of the property is given in the language of applied logic of predicates with bounded quantifiers of existence and universality. A Boolean model of the property is built in the form of a quantified Boolean formula accordingly to the Boolean constraints method developed by the authors. This formula satisfies both the logical specification of the property and the equations of the binary system dynamics. Aspects of the proposed approach implementation for the study of the observability property are considered. The technology of checking the feasibility of the property using an applied microservice package is demonstrated in several examples.

The Future of Computational Linguistics: On Beyond Alchemy

Over the decades, fashions in Computational Linguistics have changed again and again, with major shifts in motivations, methods and applications. When digital computers first appeared, linguistic analysis adopted the new methods of information theory, which accorded well with the ideas that dominated psychology and philosophy. Then came formal language theory and the idea of AI as applied logic, in sync with the development of cognitive science. That was followed by a revival of 1950s-style empiricism—AI as applied statistics—which in turn was followed by the age of deep nets. There are signs that the climate is changing again, and we offer some thoughts about paths forward, especially for younger researchers who will soon be the leaders.

Formative digital and online technologies in news and journalism

Online news systems share some affordances of Turing’s universal machine, especially configurability, but the early generation of web standards enabled data sharing, interoperability, and ultimately frameworks to reasoning about digital resources. At the backend of online news, indexing, mark-up languages, and applied logic, provide a base for machine intelligence that ultimately extends to cloud servers and big data. However, XML languages, like RSS, enabled the first phase of sharing stories in the form of newsfeeds. Specific mark-up for online news, such a NewsML, also defined layout and other features of news sites. Tim Berners-Lee established the W3C for online standards in the 1980s, and then on the cusp of the 21st century he proposed semantic and structured approaches for meaningful data sharing online. However, in subsequent years entrepreneurs have appropriated semantic approaches for different ends. The atomisation of data also introduces “personalised” data preferences to pitch news stories.

Logic and the Demands of Kantian “Science”

This chapter examines Kant’s account of logic in the Critique, analyzing his claim that pure general logic is formal, properly scientific, and complete. It distinguishes three aspects of formality, in virtue of which this logic differs from particular logic, applied logic, and transcendental logic and thereby satisfies one necessary condition of a proper science, namely having a unique subject matter. The chapter then explicates the completeness claim as a philosophical claim about logic qua strict science. Drawing on Kant’s account of what it takes to prove a system of pure concepts of the understanding as complete and his caution against the dialectical illusion of using formal logic as an organon, the chapter argues that, to avoid begging questions, he needs a sort of transcendental critique to establish his logic as complete in content and restrict its use to that of a mere canon for the formal assessment of our cognitions.

Kant on the Way to His Own Philosophy of Logic

This chapter considers how Kant, from the mid-1760s through the mid-1770s, navigated between existing accounts of logic before finding his own voice. It highlights two breakthroughs that would contribute most to his mature theory of logic. The first breakthrough concerns Kant’s division of logic into two essentially different though complementary branches: a logic for the learned understanding and one for the common human understanding (to make it healthy), precursors to “pure logic” and “applied logic” respectively. This distinction not only marks a clear departure from the Leibnizian-Wolffian take on the relation between artificial and natural logics, but also pays homage to the humanist and Lockean practices of emphasizing certain ethical dimensions of logic. The second breakthrough is the emergence of “transcendental logic” from Kant’s efforts to secure metaphysics—particularly the first part thereof, ontology—as a proper science.

Common-sense reasoning, theories of

The task of formalizing common-sense reasoning within a logical framework can be viewed as an extension of the programme of formalizing mathematical and scientific reasoning that has occupied philosophers throughout much of the twentieth century. The most significant progress in applying logical techniques to the study of common-sense reasoning has been made, however, not by philosophers, but by researchers in artificial intelligence, and the logical study of common-sense reasoning is now a recognized sub-field of that discipline. The work involved in this area is similar to what one finds in philosophical logic, but it tends to be more detailed, since the ultimate goal is to encode the information that would actually be needed to drive a reasoning agent. Still, the formal study of common-sense reasoning is not just a matter of applied logic, but has led to theoretical advances within logic itself. The most important of these is the development of a new field of ‘non-monotonic’ logic, in which the conclusions supported by a set of premises might have to be withdrawn as the premise set is supplemented with new information.

Formalization as the Immanent Part of Logical Solving

The work is devoted to the logical analysis of the problem solving by logical means. It starts from general characteristic of the applied logic as a tool: 1. to bound logic with its applications in theory and practice; 2. to import methods and methodologies from other domains into logic; 3. to export methods and methodologies from logic into other domains. The precise solving of a precisely stated logical problem occupies only one third of the whole process of solving real problems by logical means. The formalizing precedes it and the deformalizing follows it. The main topic when considering formalization is a choice of a logic. The classical logic is usually the best one for a draft formalization. The given problem and peculiarities of the draft formalization could sometimes advise us to use some other logic. If axioms of the classical formalization have some restricted form this is often the advice to use temporal, modal or multi-valued logic. More precisely, if all binary predicates occur only in premises of implications then it is possible sometimes to replace a predicate classical formalization by a propositional modal or temporal in the appropriate logic. If all predicates are unary and some of them occur only in premises then the classical logic maybe can replaced by a more adequate multi-valued. This idea is inspired by using Rosser–Turkette operator $J_i$in the book [22]. If we are interested not in a bare proof but in construction it gives us it is often to transfer to an appropriate constructive logic. Its choice is directed by our main resource (time, real values, money or any other imaginable resource) and by other restrictions.Logics of different by their nature resources are mutually inconsistent (e.g. nilpotent logics of time and linear logics of money). Also it is shown by example how Arnold’s principle works in logic: too “precise” formalization often becomes less adequate than more “rough”. DOI: 10.21146/2074-1472-2018-24-1-129-145