What is an Artefact Design?

2009 ◽  
Vol 13 (2) ◽  
pp. 137-149
Author(s):  
Pawel Garbacz ◽  
Keyword(s):  
Formal Theory ◽  
States Of Affairs ◽  
Intentional States ◽  
First Order ◽  
Design Specifications ◽  
Criterion Of Identity ◽  
Ontological Framework

The paper contains a first order formal theory pertaining to artefact designs, designs which are construed as the results of designing activities. The theory is based on a minimal ontology of states of affairs and it is inspired by the ideas of the Polish philosopher Roman Ingarden. After differentiating the philosophical notion of design from the engineering notion of design specifications, I then go on to argue that the philosophical category of artefact designs may be compared with Ingarden’s category of intentional states of affairs. At least some artefacts are found to be determined by more than one design. I also show how this ontological framework allows for the distinction between artefact tokens and artefact types. That leads to a proposal on how to define a criterion of identity for artefact types. The proposed theory serves as a basis both for a better understanding of what artefacts are and for the construction of computer-readable models of design specifications.

Are there Non-Propositional Intentional States?

2018 ◽  
Author(s):  
John R. Searle
Keyword(s):  
Intentional State ◽  
States Of Affairs ◽  
Intentional States ◽  
The World ◽  
Essential Idea ◽  
Limited Class ◽  
The Mind

Intentionality is that feature of the mind by which it is directed at or about objects and states of affairs in the world. Intentionality is simply aboutness or directedness. “Proposition” is more difficult, but the essential idea is this: every intentional state has a content. Sometimes it seems that the content just enables a state to refer to an object. So if John loves Sally, then it appears that the content of his love is simply “Sally”. But if John believes that it is raining, then the specification of the content requires an entire “that” clause. “Are there non-propositional intentional states?” amounts to the question, “Are there intentional states whose content does not require specification with a ‘that’ clause?” This chapter explores whether there are any non-propositional states, and suggest that a very limited class, such as boredom, is in fact non-propositional.

A formal theory of objects, space and time

1990 ◽  
Vol 55 (1) ◽  
pp. 74-89 ◽  
Author(s):  
Wayne D. Blizard
Keyword(s):  
Formal Theory ◽  
Order Theory ◽  
First Order ◽  
Space And Time ◽  
First Order Theory ◽  
Logical Nature

The two statements “Two different objects cannot occupy the same place at the same time” and “An object cannot be in two different places at the same time” are axioms of our everyday understanding of objects, space and time. We develop a first-order theory OST (Objects, Space and Time) in which formal equivalents of these two statements are taken as axioms. Using the theory OST, we uncover other fundamental principles of objects, space and time. We attempt to understand the logical nature of these principles, to investigate their formal consequences, and to identify logical alternatives to them. For easy reference, all of the nonlogical axioms of OST are listed together at the end of §2. In §3, we introduce two possible extensions of OST.

scholarly journals Collective intentionality and the state theory of money

2015 ◽  
Vol 8 (2) ◽  
pp. 1 ◽  
Author(s):  
Georgios Papadopoulos
Keyword(s):  
State Theory ◽  
The State ◽  
Collective Intentionality ◽  
Convertible Currency ◽  
Intentional States ◽  
Ontological Analysis ◽  
Ontological Framework

The circulation of non-convertible currency and the source of its value raise important ontological questions that touch upon the conditions of its acceptance. The aim of this paper is to address such questions by illustrating how collective intentionality and constitutive declarations can be employed in order to develop an adequate ontological framework for explaining the emergence and the persistence of the current monetary standard. This analysis of money differs from that of mainstream commodity theory in that it argues against individualism, which traditionally underwrites both economic and philosophical analyses of money. The resulting ontology is based on an account of collective intentionality developed upon the "sharedness" of individual intentional states; this account supports the state theory of money, combining it with an ontological analysis of the state and its authority.

scholarly journals Much Ado About the Many

2021 ◽  
Vol 25 (1) ◽  
Author(s):  
Jonathan Mai
Keyword(s):  
Set Theory ◽  
Formal Theory ◽  
Order Logic ◽  
First Order Logic ◽  
Plural Quantification ◽  
First Order ◽  
Order Language ◽  
The Many ◽  
Second Order Logic ◽  
Alternative Theories

English distinguishes between singular quantifiers like "a donkey" and plural quantifiers like "some donkeys". Pluralists hold that plural quantifiers range in an unusual, irreducibly plural, way over common objects, namely individuals from first-order domains and not over set-like objects. The favoured framework of pluralism is plural first-order logic, PFO, an interpreted first-order language that is capable of expressing plural quantification. Pluralists argue for their position by claiming that the standard formal theory based on PFO is both ontologically neutral and really logic. These properties are supposed to yield many important applications concerning second-order logic and set theory that alternative theories supposedly cannot deliver. I will show that there are serious reasons for rejecting at least the claim of ontological innocence. Doubt about innocence arises on account of the fact that, when properly spelled out, the PFO-semantics for plural quantifiers is committed to set-like objects. The correctness of my worries presupposes the principle that for every plurality there is a coextensive set. Pluralists might reply that this principle leads straight to paradox. However, as I will argue, the true culprit of the paradox is the assumption that every definite condition determines a plurality.

scholarly journals Informal Provability, First-Order BAT Logic and First Steps Towards a Formal Theory of Informal Provability

2021 ◽  
pp. 1-27
Author(s):  
Pawel Pawlowski ◽  
Rafal Urbaniak
Keyword(s):  
Formal Theory ◽  
Order System ◽  
First Order ◽  
Do So

BAT is a logic built to capture the inferential behavior of informal provability. Ultimately, the logic is meant to be used in an arithmetical setting. To reach this stage it has to be extended to a first-order version. In this paper we provide such an extension. We do so by constructing non-deterministic three-valued models that interpret quantifiers as some sorts of infinite disjunctions and conjunctions. We also elaborate on the semantical properties of the first-order system and consider a couple of its strengthenings. It turns out that obtaining a sensible strengthening is not straightforward. We prove that most strategies commonly used for strengthening non-deterministic logics fail in our case. Nevertheless, we identify one method of extending the system which does not.

Undecidability in diagonalizable algebras

1997 ◽  
Vol 62 (1) ◽  
pp. 79-116 ◽  
Author(s):  
V. Yu. Shavrukov
Keyword(s):  
Wide Class ◽  
Formal Theory ◽  
First Order ◽  
Unary Operator ◽  
Diagonalizable Algebra

AbstractIf a formal theory T is able to reason about its own syntax, then the diagonalizable algebra of T is defined as its Lindenbaum sentence algebra endowed with a unary operator □ which sends a sentence φ to the sentence □φ asserting the provability of φ in T. We prove that the first order theories of diagonalizable algebras of a wide class of theories are undecidable and establish some related results.

scholarly journals Computability logic: Giving Caesar what belongs to Caesar

2019 ◽  
Vol 25 (1) ◽  
pp. 100-119
Author(s):  
Giorgi Japaridze
Keyword(s):  
Classical Logic ◽  
Formal Theory ◽  
Order Logic ◽  
Conservative Extension ◽  
Logical Operators ◽  
First Order ◽  
Game Semantics ◽  
Wide Range ◽  
Algorithmic Solvability

The present article is a brief informal survey o$\textit {computability logic}$ (CoL). This relatively young and still evolving nonclassical logic can be characterized as a formal theory of computability in the same sense as classical logic is a formal theory of truth. In a broader sense, being conceived semantically rather than proof-theoretically, CoL is not just a particular theory but an ambitious and challenging long-term project for redeveloping logic. In CoL, logical operators stand for operations on computational problems, formulas represent such problems, and their "truth" is seen as algorithmic solvability. In turn, computational problems – understood in their most general, interactive sense – are defined as games played by a machine against its environment, with "algorithmic solvability" meaning existence of a machine which wins the game against any possible behavior of the environment. With this semantics, CoL provides a systematic answer to the question "What can be computed?", just like classical logic is a systematic tool for telling what is true. Furthermore, as it happens, in positive cases "What can be computed" always allows itself to be replaced by "How can be computed", which makes CoL a problem-solving tool. CoL is a conservative extension of classical first order logic but is otherwise much more expressive than the latter, opening a wide range of new application areas. It relates to intuitionistic and linear logics in a similar fashion, which allows us to say that CoL reconciles and unifies the three traditions of logical thought (and beyond) on the basis of its natural and "universal" game semantics.

Semantics, situation

2018 ◽  
Author(s):  
John R. Perry
Keyword(s):  
Possible Worlds ◽  
Formal Theory ◽  
Relational Theory ◽  
Situation Semantics ◽  
Possible Worlds Semantics ◽  
States Of Affairs ◽  
Situation Theory ◽  
Truth Values ◽  
Theory Of Meaning

Situation semantics attempts to provide systematic and philosophically coherent accounts of the meanings of various constructions that philosophers and linguists find important. It is based on the old idea that sentences stand for facts or something like them. As such, it provides an alternative to extensional semantics, which takes sentences to stand for truth-values, and to possible worlds semantics, which takes them to stand for sets of possible worlds. Situations are limited parts or aspects of reality, while states of affairs (or infons) are complexes of properties and objects of the sort suitable to constitute a fact. Consider the issue of whether Jackie, a dog, broke her leg at a certain time T. There are two states of affairs or possibilities, that she did or she did not. The situation at T, in the place where Jackie was then, determines which of these states of affairs (infons) is factual (or is the case or is supported). Situation theory, the formal theory that underlies situation semantics, focuses on the nature of the supports relation. Situation semantics sees meaning as a relation among types of situations. The meaning of ’I am sitting next to David’, for example, is a relation between types of situations in which someone A utters this sentence referring with the name ’David’ to a certain person B, and those in which A is sitting next to B. This relational theory of meaning makes situation semantics well-suited to treat indexicality, tense and other similar phenomena. It has also inspired relational accounts of information and action.

Nominalism

2018 ◽  
Author(s):  
Michael J. Loux
Keyword(s):  
Middle Ages ◽  
Mental Representations ◽  
States Of Affairs ◽  
General Terms ◽  
Abstract Entities ◽  
Abstract Ideas ◽  
The Mind ◽  
Ontological Framework ◽  
Reductionist Approach ◽  
The Middle Ages

‘Nominalism’ refers to a reductionist approach to problems about the existence and nature of abstract entities; it thus stands opposed to Platonism and realism. Whereas the Platonist defends an ontological framework in which things like properties, kinds, relations, propositions, sets and states of affairs are taken to be primitive and irreducible, the nominalist denies the existence of abstract entities and typically seeks to show that discourse about abstract entities is analysable in terms of discourse about familiar concrete particulars. In different periods, different issues have provided the focus for the debate between nominalists and Platonists. In the Middle Ages, the problem of universals was pivotal. Nominalists like Abelard and Ockham insisted that everything that exists is a particular. They argued that talk of universals is talk about certain linguistic expressions - those with generality of application - and they attempted to provide an account of the semantics of general terms rich enough to accommodate the view that universals are to be identified with them. The classical empiricists followed medieval nominalists in being particularists, and they sought to identify the kinds of mental representations associated with general terms. Locke argued that these representations have a special content. He called them abstract ideas and claimed that they are formed by removing from ideas of particulars those features peculiar to the particulars in question. Berkeley and Hume, however, attacked Locke’s doctrine of abstraction and insisted that the ideas corresponding to general terms are ideas whose content is fully determinate and particular, but which the mind uses as proxies for other particular ideas of the same sort. A wider range of issues has dominated recent ontological discussion, and concern over the existence and status of things like sets, propositions, events and states of affairs has come to be every bit as significant as concern over universals. Furthermore, the nature of the debate has changed. While there are philosophers who endorse a nominalist approach to all abstract entities, a more typical brand of nominalism is that which recognizes the existence of sets and attempts to reduce talk about other kinds of abstract entities to talk about set-theoretical structures whose ultimate constituents are concrete particulars.

Generalizations of the one-dimensional version of the Kruskal-Friedman theorems

1989 ◽  
Vol 54 (1) ◽  
pp. 100-121 ◽  
Author(s):  
L. Gordeev
Keyword(s):  
Monotone Function ◽  
Formal Theory ◽  
Peano Arithmetic ◽  
One Dimensional ◽  
First Order ◽  
Countable Ordinal ◽  
Finite Sequences ◽  
Kruskal’S Theorem ◽  
Dimensional Version ◽  
The One

The paper [Schütte + Simpson] deals with the following one-dimensional case of Friedman's extension (see in [Simpson 1]) of Kruskal's theorem ([Kruskal]). Given a natural number n, let Sn+1 be the set of all finite sequences of natural numbers <n + 1. If s1 = (a0,…,ak) ∈Sn+1 and s2 = (b0,…,bm) ∈Sn + 1, then a strictly monotone function f: {0,…, k} → {0,…, m} is called an embedding of s1 into s2 if the following two assertions are satisfied:1) ai, = bf(i), for all i < k;2) if f(i) < j < f(i + 1) then bj > bf(i+1), for all i < k, j < m.Then for every infinite sequence s1, s2,…,sk,… of elements of Sn + 1 there exist indices i < j and an embedding of si into Sj. That is, Sn+1 forms a well-quasi-ordering (wqo) with respect to embeddability. For each n, this statement W(Sn+1) is provable in the standard second order conservative extension of Peano arithmetic. On the other hand, the proof-theoretic strength of the statements W(Sn+1) grows so fast that this formal theory cannot prove the limit statement ∀nW(Sn+1). The appropriate first order -versions of these combinatory statements preserve their proof-theoretic strength, so that actually one can speak in terms of provability in Peano arithmetic. These are the main conclusions from [Schütte + Simpson].We wish to extend this into the transfinite. That is, we take an arbitrary countable ordinal τ > 0 instead of n + 1 and try to obtain an analogous “strong” combinatory statement about finite sequences of ordinals < τ.

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