THE SUBSTITUTIONAL QUANTIFICATION IN BASIC LOGIC AND ONTOLOGICAL COMMITMENTS IN FORMAL MATHEMATICAL THEORIES

2016 ◽  
Keyword(s):  
Basic Logic ◽  
Substitutional Quantification ◽  
Ontological Commitments

Quantifiers, substitutional and objectual

2018 ◽  
Author(s):  
Mark Richard
Keyword(s):  
Natural Language ◽  
Truth Conditions ◽  
Substitutional Quantification ◽  
Ontological Commitments ◽  
Substitution Instance

Understood substitutionally, ‘Something is F’ is true provided one of its substitution instances (a sentence of the form ‘a is F’) is true. This contrasts with the objectual understanding, on which it is true provided ‘is F’ is true of some object in the domain of the quantifier. Substitutional quantifications have quite different truth-conditions from objectual ones. For instance, ‘Something is a mythological animal’ is true if understood substitutionally, since the substitution instance ‘Pegasus is a mythological animal’ is true. But understood objectually, the sentence is not true, since there are no mythological creatures to make up a domain for the quantifier. Since substitutional quantifiers do not need domains over which they range, it is easy to introduce substitutional quantifiers which bind predicate or sentential variables, even variables within quotation marks. One reason for interest in substitutional quantification is the hope that it may provide a way to understand discourse which appears to be about numbers, properties, propositions and other ‘troublesome’ sorts of entities as being free of exceptional ontological commitments. Whether natural language quantification is sometimes plausibly construed as substitutional is not, however, clear.

If Not Here, Then Where? On the Location and Individuation of Events in Badiou and Deleuze

2009 ◽  
Vol 3 (1) ◽  
pp. 97-123 ◽  
Author(s):  
James Williams
Keyword(s):  
Short Story ◽  
Space Time ◽  
Alain Badiou ◽  
Ontological Commitments

This paper sets out a series of critical contrasts between Alain Badiou and Gilles Deleuze's philosophies of the event. It does so in the context of some likely objections to their positions from a broadly analytic position. These objections concern problems of individuation and location in space-time. The paper also explains Deleuze and Badiou's views on the event through a literary application on a short story by John Cheever. In conclusion it is argued that both thinkers have good answers to the objections, but that they diverge on the ontological commitments of their definitions of the event.

True Imaginings Integrating Panentheism and A Personal View of God

2019 ◽  
Vol 11 (1) ◽  
pp. 61
Author(s):  
Klaus Müller
Keyword(s):  
Challenging Problem ◽  
Personal View ◽  
Ontological Commitments ◽  
As If

The perhaps most challenging problem for a panentheistic paradigm in Christian god-talk consists in integrating the trait of personhood in the monistic horizon of this approach. A very helpful way to this goal seems to be the concept of imagination. Its logic of an “as if” represents a modified variation of Kant`s idea of the postulates of reason. Reflections of Jürgen Werbick, Douglas Headley, and Volker Gerhardt substantiate the philosophical and theological capabilities of this solution which also include a sensibility for the ontological commitments included in the panentheistic approach.

Proof Theory of the Cut Rule

2018 ◽  
Author(s):  
J. R. B. Cockett ◽  
R. A. G. Seely
Keyword(s):  
Proof Theory ◽  
Graphical Representation ◽  
Basic Component ◽  
Graphical Representations ◽  
Mathematical Language ◽  
Basic Logic ◽  
Cut Rule ◽  
Structural Rules ◽  
The One ◽  
Categorical Semantics

This chapter describes the categorical proof theory of the cut rule, a very basic component of any sequent-style presentation of a logic, assuming a minimum of structural rules and connectives, in fact, starting with none. It is shown how logical features can be added to this basic logic in a modular fashion, at each stage showing the appropriate corresponding categorical semantics of the proof theory, starting with multicategories, and moving to linearly distributive categories and *-autonomous categories. A key tool is the use of graphical representations of proofs (“proof circuits”) to represent formal derivations in these logics. This is a powerful symbolism, which on the one hand is a formal mathematical language, but crucially, at the same time, has an intuitive graphical representation.

Probability and Random Processes

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Random Processes ◽  
Distribution Functions ◽  
Basic Logic ◽  
Heavy Tailed Distributions ◽  
Random Components ◽  
Classical Distribution ◽  
Heavy Tailed ◽  
Basic Facts ◽  
Stochastic Events ◽  
Stochastic Event

Phenomena, systems, and processes are rarely purely deterministic, but contain stochastic,probabilistic, or random components. For that reason, a probabilistic descriptionof most phenomena is necessary. Probability theory provides us with the tools for thistask. Here, we provide a crash course on the most important notions of probabilityand random processes, such as odds, probability, expectation, variance, and so on. Wedescribe the most elementary stochastic event—the trial—and develop the notion of urnmodels. We discuss basic facts about random variables and the elementary operationsthat can be performed on them. We learn how to compose simple stochastic processesfrom elementary stochastic events, and discuss random processes as temporal sequencesof trials, such as Bernoulli and Markov processes. We touch upon the basic logic ofBayesian reasoning. We discuss a number of classical distribution functions, includingpower laws and other fat- or heavy-tailed distributions.

The Structure of Truth

2020 ◽  
Author(s):  
Donald Davidson
Keyword(s):  
Philosophy Of Language ◽  
Logical Form ◽  
Historical Document ◽  
Truth Theory ◽  
Ontological Commitments ◽  
Theory Of Meaning ◽  
First Time

Donald Davidson’s 1970 Locke Lectures appear in print for the first time in this volume, accompanied by an introduction highlighting their significance as a snapshot of his evolving views in the philosophy of language and describing their relationship to the work he published during his lifetime. The lectures comprise an invaluable historical document that illuminates how Davidson was thinking about the theory of meaning, the role of a truth theory therein, the ontological commitments of a truth theory, the notion of logical form, and so on, at a pivotal moment in the development of his thought. Unlike Davidson’s previously published work, they are written so as to be presented to an audience as a fully organized and coherent exposition of his program in the philosophy of language. Had these lectures been widely available in the years following 1970, the reception of Davidson’s work, especially in the philosophy of language, might have been very different. Given the systematic nature of the presentation of Davidson’s semantic program in these lectures, it is hoped that they will be of use to those encountering his thought for the first time.

Social Ontology and Model-Building: A Response to Epstein

2021 ◽  
Vol 51 (2) ◽  
pp. 176-192
Author(s):  
Nadia Ruiz
Keyword(s):  
Social Sciences ◽  
Social Science ◽  
Model Building ◽  
Social Ontology ◽  
Model Construction ◽  
Ontological Commitments ◽  
Starting Point ◽  
The Social

Brian Epstein has recently argued that a thoroughly microfoundationalist approach towards economics is unconvincing for metaphysical reasons. Generally, Epstein argues that for an improvement in the methodology of social science we must adopt social ontology as the foundation of social sciences; that is, the standing microfoundationalist debate could be solved by fixing economics’ ontology. However, as I show in this paper, fixing the social ontology prior to the process of model construction is optional instead of necessary and that metaphysical-ontological commitments are often the outcome of model construction, not its starting point. By focusing on the practice of modeling in economics the paper provides a useful inroad into the debate about the role of metaphysics in the natural and social sciences more generally.

Correction to a definition of negation

1984 ◽  
Vol 49 (1) ◽  
pp. 47-50 ◽  
Author(s):  
Frederic B. Fitch
Keyword(s):  
Fixed Point ◽  
Personal Communication ◽  
The Other ◽  
Transfinite Induction ◽  
Original Form ◽  
Basic Logic ◽  
Double Negation ◽  
Original Letter ◽  
The Law ◽  
Definition Of

In [3] a definition of negation was presented for the system K′ of extended basic logic [1], but it has since been shown by Peter Päppinghaus (personal communication) that this definition fails to give rise to the law of double negation as I claimed it did. The purpose of this note is to revise this defective definition in such a way that it clearly does give rise to the law of double negation, as well as to the other negation rules of K′.Although Päppinghaus's original letter to me was dated September 19, 1972, the matter has remained unresolved all this time. Only recently have I seen that there is a simple way to correct the definition. I am of course very grateful to Päppinghaus for pointing out my error in claiming to be able to derive the rule of double negation from the original form of the definition.The corrected definition will, as before, use fixed-point operators to give the effect of the required kind of transfinite induction, but this time a double transfinite induction will be used, somewhat like the double transfinite induction used in [5] to define simultaneously the theorems and antitheorems of system CΓ.

scholarly journals A Qualitative Theory of Cognitive Attitudes and their Change

2021 ◽  
pp. 1-31
Author(s):  
EMILIANO LORINI
Keyword(s):  
Belief Change ◽  
Qualitative Theory ◽  
The Other ◽  
Logical Framework ◽  
Basic Logic ◽  
Conditional Belief ◽  
Concepts Of Knowledge ◽  
Cognitive Attitudes ◽  
Qualitative Decision Theory ◽  
Qualitative Decision

Abstarct We present a general logical framework for reasoning about agents’ cognitive attitudes of both epistemic type and motivational type. We show that it allows us to express a variety of relevant concepts for qualitative decision theory including the concepts of knowledge, belief, strong belief, conditional belief, desire, conditional desire, strong desire, and preference. We also present two extensions of the logic, one by the notion of choice and the other by dynamic operators for belief change and desire change, and we apply the former to the analysis of single-stage games under incomplete information. We provide sound and complete axiomatizations for the basic logic and for its two extensions.

Kant's Contribution to Moral Epistemology

PARADIGMI ◽  
2012 ◽  
pp. 69-77
Author(s):  
Carla Bagnoli
Keyword(s):  
Ethical Theory ◽  
Moral Epistemology ◽  
Normative Ethics ◽  
Moral Cognition ◽  
Ontological Commitments ◽  
First Order

This paper argues that the most innovative aspect of Kant's ethical theory is not afirst-order normative ethics, even though the importance and long-lasting mark ofKant's ethics of autonomy cannot be questioned. Rather, it consists in a constructivistaccount of moral cognition. This claim may be perplexing in more than one way, sinceconstructivism is often characterized both as a first-order account of moral judgmentsand as a retreat from epistemological and ontological commitments. This characterizationis misleading in general, and mistaken for Kant's constructivism in particular.Kant's constructivism is a methodological claim about the authority and productivefunction of reason and an epistemological claim about the nature of moral cognitions.

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