Logical Consequence
P. Blanchette · Elsevier eBooks · 2006
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About 5,336 papers for “Logical consequence”
Logical Consequence
Christopher J. Martín · Oxford University Press eBooks · 2012
This article presents an outline of the history of logical consequence. The first part considers the material transmitted to the Early Middle Ages from Antiquity in order to show how thinking about consequence and, in particular, about the conditional proposition became the central project of early twelfth-century logic. The section part summarizes the extraordinary development by Peter Abelard of a unified relevantistic theory of the conditional and argument on the basis of Boethius's confused accounts of the hypothetical syllogism and topical inference. The third part examines a period of crisis and its resolution late in the twelfth century in favor of the medieval version of the classical account of logical consequence. It also looks at William of Ockham's rejection of this pair of consequence relations in favor of a contrast between what he calls material and formal consequences in which relevance as a semantical requirement no longer has a place.
Cited by 1
Logical Consequence
Alex Citkin, Alexei Muravitsky · 2022
Abstract This chapter explains the central concept of this book — the concept of consequence relation, as well as its counterpart, that of consequence operator. We prove the main properties of these concepts. In addition, we show several ways in which consequence relations can be defined and modified. We pay special attention to the determination of consequence relations using logical matrices and inference rules. The first way leads to the Lindenbaum method and the Lindenbaum theorem. The second method is very natural, and we consider several of its options. In particular, we discuss in some detail the definition of consequence relations defined by modus rules. We also discuss in this chapter the idea of completeness.
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Logical consequence
Carrara, Massimiliano, J., Murzi · Research Padua Archive (University of Padua) · 2014
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Logical Consequence
Patricia Blanchette · Elsevier eBooks · 2025
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Logical Consequence
Jc Beall · 2005
Abstract This chapter explores the concept of logical consequence and defends logical pluralism. Logic, in the core tradition, involves the study of formal languages. However, the primary aim is to consider such languages as interpreted: languages which may be used either directly to make assertions and denials, or to analyse natural languages. Logic, whatever it is, must be a tool useful for the analysis of the inferential relationships between premises and conclusions expressed in arguments actually employed. If a discipline does not manage this, it cannot claim to be logic in its traditional sense. Many different basic units of evaluation have been taken to be the components of arguments: assertions, judgements, claims, utterances, interpreted sentences, sentences in contexts-of-use and propositions have all been singled out as the right kinds of things for logic to take as its raw material. Three features of logical consequence are necessity, normativity, and formality.
Cited by 3
Logical Consequence
Gila Sher · The Monist · 2002
Logical Consequence: An Epistemic Outlook Author(s): Gila Sher Source: The Monist, Vol. 85, No. 4, Consequences (OCTOBER 2002), pp. 555-579 Published by: Oxford University Press Stable URL: http://www.jstor.org/stable/27903798 Accessed: 10-08-2015 00:28 UTC Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://www.jstor.org/page/ info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Oxford University Press is collaborating with JSTOR to digitize, preserve and extend access to The Monist. http://www.jstor.org This content downloaded from 137.110.34.89 on Mon, 10 Aug 2015 00:28:56 UTC All use subject to JSTOR Terms and Conditions
Cited by 4
Logical Consequence and Logical Expressions
Mario Gómez‐Torrente · THEORIA An International Journal for Theory History and Foundations of Science · 2008
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Cited by 5Open access
Logical Pluralism and Logical Consequence
Erik Stei · Cambridge University Press eBooks · 2023
Logical pluralism is the view that there is more than one correct logic. This is not necessarily a controversial claim but in its most exciting formulations, pluralism extends to logics that have typically been considered rival accounts of logical consequence – to logics, that is, which adopt seemingly contradictory views about basic logical laws or arguments. The logical pluralist challenges the philosophical orthodoxy that an argument is either deductively valid or invalid by claiming that there is more than one way for an argument to be valid. In this book, Erik Stei defends logical monism, provides a detailed analysis of different possible formulations of logical pluralism, and offers an original account of the plurality of correct logics that incorporates the benefits of both pluralist and monist approaches to logical consequence. His book will be valuable for a range of readers in the philosophy of logic.
Cited by 9Open access
Hierarchical logical consequence
Carlos Caleiro, P.A. Gouveia, Jaime Ramos · Logic Journal of IGPL · 2010
The modern view of logical reasoning as modeled by a consequence operator (instead of simply by a set of theorems) has allowed for huge developments in the study of logic as an abstract discipline. Still, it is unable to explain why it is often the case that the same designation is used, in an ambiguous way, to describe several distinct modes of reasoning over the same logical language. A paradigmatic example of such a situation is ‘modal logic’, a terminology which can encompass reasoning over Kripke frames, but also over Kripke models, and in any case either locally (at a fixed world) or globally (at all worlds). Herein, we adopt a novel abstract notion of logic presented as a lattice-structured hierarchy of consequence operators, and explore some common proof-theoretic and model-theoretic ways of presenting such hierarchies through a collection of meaningful examples. In order to illustrate the usefulness of the notion of hierarchical consequence operators we address a few questions in the theory of combined logics, where a suitable abstract presentation of the logics being combined is absolutely essential. We show how to define the operation, in general, and we achieve a number of interesting preservation results for fibring within the context of 2-hierarchies.
Cited by 1
Concept of logical consequence
Štěpán Kubalík · Digital Repository (National Repository of Grey Literature) · 2007
What does i t mean for a gi ven sentence to be a logical consequence of another one? Some basic articulation of this notion is easily available: no matter what is the case, if the premisses are true, then the conclusion is true. Alfred Tarski proposed in 1936 his famous no-counterexample analysis of this notion which was supposed to refine this intuitions and become conceptually adequate formal counterpart of pre-theoretic notion: a sentence X is a logical consequence of K if and only if there is no possible interpretation (model) of the nonlogical terminology of L according to which all the sentences in K are true and X is false. This definition has been considered a conceptually adequate analysis of the pre-formal notion of logical consequence up to present day. I am tryting to find out in this text if this believe can be justified. Various realizations of Tarski's definitional proposal exhibi ts various faul ts, and in the end i t seems like the model-theoretic approach to account of logical notions is not useful for this purpose at all.
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Foundations of Logical Consequence
Colin R. Caret, Ole Thomassen Hjortland · Oxford University Press eBooks · 2015
I INTRODUCTION II CONSEQUENCE: MODELS AND PROOFS III PROPERTIES AND STRUCTURE OF LOGICAL CONSEQUENCE IV APPLICATIONS OF LOGICAL CONSEQUENCE
Cited by 103
Causality & Logical Consequence
Seremonia, Meta · Figshare · 2024
<b>Abstract</b>Why do logical consequences underlie cause and effect? Why are logical consequences behind cause and effect? Isn't cause and effect the foundation of all occurrences? So, genuine philosophizing goes beyond just reasoning cause and effect
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Concepts of logical consequence
Cutler, Darcy · Library and Archives Canada (Government of Canada) · 1997
Cited by 0
Context and Logical Consequence
Ching Su · Journal of Philosophical Research · 2017
Cited by 0
Etchemendy and Logical Consequence
Graham Priest · Canadian Journal of Philosophy · 1995
Logical consequence is a notion that every person who reasons must possess, at least implicitly. To give a precise and accurate characterization of this notion is the fundamental task of logic. In a similar way, the notion of effectivity is a concept that anyone with a basic training in mathematics possesses, and the most fundamental task of a theory of computability is to give a precise characterization of this notion. The problem concerning effectivity was solved (at least to the satisfaction of most people) in the 1930s, almost as soon as it was raised, by the work of Turing, Church, and others. By contrast, the correct and precise characterization of logical consequence has been hotly contested through the two and a half thousand-year history of logic.
Cited by 34
Causality & Logical Consequence
Meta, Seremonia · PhilPapers (PhilPapers Foundation)
Why do logical consequences underlie cause and effect? Why are logical consequences behind cause and effect? Isn't cause and effect the foundation of all occurrences?\n \n So, genuine philosophizing goes beyond just reasoning cause and effect.
Cited by 0
Logical Consequence for Nominalists
Marcus Rossberg, Daniel Cohnitz · THEORIA An International Journal for Theory History and Foundations of Science · 2009
It is often claimed that nominalistic programmes to reconstruct mathematics fail, since they will at some point involve the notion of logical consequence which is unavailable to the nominalist. In this paper we use an idea of Goodman and Quine to develop a nominalistically acceptable explication of logical consequence.
Cited by 4Open access
Causality and Logical Consequence
Meta, Seremonia · Zenodo (CERN European Organization for Nuclear Research) · 2024
&lt;p&gt;&lt;strong&gt;CAUSALITY &amp; LOGICAL CONSEQUENCE&lt;/strong&gt;&lt;/p&gt;\n&lt;p&gt;WHY IS LOGICAL CONSEQUENCE NECESSARY, AND NOT CAUSE-EFFECT❓&lt;strong&gt;❌&lt;/strong&gt;&lt;br&gt;&lt;br&gt;Without cause and effect, we cannot proceed to logical consequences.&lt;br&gt;&lt;br&gt;So, we need to prepare (understand - trace) the cause and effect first to establish a suitable communication network.&lt;br&gt;&lt;br&gt;Cause and effect can help us adapt to circumstances so that the connection network can be established in different situations.&lt;br&gt;&lt;br&gt;After observing (making connections) relevant cause and effect relationships (according to needs), then (logical consequences help) we can create communication or monitor situations far away accurately (through the logical consequences of cause and effect relationships)&lt;br&gt;&lt;br&gt;&lt;strong&gt;PHILOSOPHIZE GENUINELY&lt;/strong&gt;&lt;br&gt;&lt;br&gt;So, genuine philosophizing goes beyond just reasoning cause and effect.&lt;br&gt;&lt;br&gt;It's not limited to empirical or what is said to be "this makes sense, scientific," which is actually just reasoning cause and effect.&lt;br&gt;&lt;br&gt;But philosophize, think, or more broadly, reason beyond the limits of cause and effect.&lt;br&gt;&lt;br&gt;🔰 START A NEW PHILOSOPHICAL PARADIGM - PHILOSOPHY WITH LOGICAL CONSEQUENCES.&lt;/p&gt;\n&lt;p&gt;&lt;strong&gt;FOUNDATION OF CAUSE AND EFFECT&lt;/strong&gt;&lt;br&gt;&lt;br&gt;Why do logical consequences underlie cause and effect? Why are logical consequences behind cause and effect? Isn't cause and effect the foundation of all occurrences?&lt;br&gt;&lt;br&gt;👉 Because logically, cause and effect are stages in the process, so they need a place as the foundation of the process.&lt;br&gt;&lt;br&gt;✅ Cause and effect are sequences of events, but they forget that behind the sequence of events, there is a floor that serves as the venue for the process to take place&lt;br&gt;&lt;br&gt;&lt;strong&gt;LOGICAL CONSEQUENCE AMBIGUITY &lt;/strong&gt;❓ &lt;u&gt;Overlapping Interpretation Issues&lt;/u&gt;&lt;br&gt;&lt;br&gt;Even though the cause implies logical consequences, or the logical consequences depend on the cause, it seems that the logical consequences are inconsistent❓&lt;br&gt;&lt;br&gt;Remember, many things we understand overlap in meaning because two meanings are similar, making them appear as one meaning, even though they are different.&lt;br&gt;&lt;br&gt;Example: if hit, the logical consequence is pain. This is not a logical consequence, even though it is commonly expressed that way.&lt;br&gt;&lt;br&gt;When a stone is hit, it doesn't hurt like a human. There are situations where a blow doesn't cause pain.&lt;br&gt;&lt;br&gt;Or "if you're rude, the consequence is that he can get angry." However, the logical consequence is not just a tendency, or not a probability of getting angry.&lt;br&gt;&lt;br&gt;Because if the logical consequence still falls under the probability category, where is the certainty?&lt;br&gt;&lt;br&gt;Without certainty, all probabilities can surpass impossible limits.&lt;br&gt;&lt;br&gt;For example, when possibilities can go in any direction, this affirms the absence of certainty, meaning the unreasonable becomes reasonable, the reasonable becomes unreasonable, and there is no recognizable pattern.&lt;br&gt;&lt;br&gt;Nothing can be formulated because&lt;br&gt;&lt;br&gt;✅ PROBABILITIES MUST BE BASED ON CERTAINTY. AND FROM CERTAINTY, PROBABILITIES CAN ARISE AS POSSIBILITIES.&lt;br&gt;&lt;br&gt;👉 Like the certainty of numbers that produces (probabilities) combinations of numbers.&lt;br&gt;&lt;br&gt;This means that, no matter how shallow or deep, from classical physics limits to quantum physics limits, or even deeper, there must be a certainty limit that serves as its foundation. THAT IS THE LOGICAL CONSEQUENCE THAT IS NOT CAUSE-EFFECT, NOT PROBABILITY.&lt;br&gt;&lt;br&gt;SIMPLY...&lt;br&gt;&lt;br&gt;✅ ... There is probability and its underlying factor, which is certainty.&lt;br&gt;&lt;br&gt;⭕️ Whether called consequences, risks, logical consequences, or any term, the key is that something underlies probability, and that (once again) is certainty.&lt;br&gt;&lt;br&gt;WE JUST NEED TO SEE THE DISTINCTION WITH CAUSE AND EFFECT.&lt;br&gt;&lt;br&gt;&lt;strong&gt;CAUSE AND EFFECT &amp; LOGICAL CONSEQUENCES&lt;br&gt;&lt;/strong&gt;&lt;br&gt;CAUSE AND EFFECT IS A PROCESS, SO THERE ARE STAGES, AND THERE IS ROOM TO FILL IN A PROCESS.&lt;br&gt;&lt;br&gt;Cause and effect manifest diversity; cause and effect need space to process.&lt;br&gt;&lt;br&gt;Space precedes the process, even encompasses the process.&lt;br&gt;&lt;br&gt;The cause becomes the origin for its effect. If there is no cause, there is no effect.&lt;br&gt;&lt;br&gt;That space is the cause underlying the continuation of the cause-and-effect process.&lt;br&gt;&lt;br&gt;No space, no cause-and-effect process, so the main cause of cause and effect must have existed before its cause and effect, affirming that the main cause as a support goes beyond the process, meaning the main cause of its cause and effect is simultaneous without a process, or its process precedes all cause-and-effect processes.&lt;br&gt;&lt;br&gt;So❓What underlies all cause-and-effect is simultaneity, and that is the logical consequence.&lt;br&gt;&lt;br&gt;CAUSE AND EFFECT &amp; LOGICAL CONSEQUENCES&lt;br&gt;&lt;br&gt;As an example....&lt;br&gt;&lt;br&gt;"If there is a change, then there is a difference," so "change" is not the cause of "difference," and also "different" is not the cause of "change."&lt;br&gt;&lt;br&gt;Because both "change" and "difference" have no cause-and-effect relationship but a logical consequence relationship, not a probabilistic logical consequence, but a logical consequence affirming definite simultaneity.&lt;br&gt;&lt;br&gt;Between "change" and "difference," there is no precedence. We may perceive that if there is "change," there is "difference," but this does not imply a cause-and-effect process. This is our sequential perception, but fundamentally, both "change" and "difference" are inseparable unity.&lt;br&gt;&lt;br&gt;That is one example of a genuine logical consequence, affirming certainty as the cause of the diversity of cause-and-effect processes&lt;/p&gt;
Cited by 0Open access
Causality and Logical Consequence
Meta, Seremonia · Zenodo (CERN European Organization for Nuclear Research) · 2024
&lt;p&gt;&lt;strong&gt;&lt;span&gt;CAUSALITY &amp; LOGICAL CONSEQUENCE&lt;/span&gt;&lt;/strong&gt;&lt;/p&gt;\n&lt;p&gt;&lt;span&gt;WHY IS LOGICAL CONSEQUENCE NECESSARY, AND NOT CAUSE-EFFECT&lt;/span&gt;&lt;span&gt;❓&lt;strong&gt;❌&lt;/strong&gt;&lt;/span&gt;&lt;span&gt;&lt;br&gt;&lt;br&gt;Without cause and effect, we cannot proceed to logical consequences.&lt;br&gt;&lt;br&gt;So, we need to prepare (understand - trace) the cause and effect first to establish a suitable communication network.&lt;br&gt;&lt;br&gt;Cause and effect can help us adapt to circumstances so that the connection network can be established in different situations.&lt;br&gt;&lt;br&gt;After observing (making connections) relevant cause and effect relationships (according to needs), then (logical consequences help) we can create communication or monitor situations far away accurately (through the logical consequences of cause and effect relationships)&lt;br&gt;&lt;br&gt;&lt;strong&gt;PHILOSOPHIZE GENUINELY&lt;/strong&gt;&lt;br&gt;&lt;br&gt;So, genuine philosophizing goes beyond just reasoning cause and effect.&lt;br&gt;&lt;br&gt;It's not limited to empirical or what is said to be "this makes sense, scientific," which is actually just reasoning cause and effect.&lt;br&gt;&lt;br&gt;But philosophize, think, or more broadly, reason beyond the limits of cause and effect.&lt;br&gt;&lt;br&gt;&lt;/span&gt;&lt;span&gt;🔰&lt;/span&gt;&lt;span&gt; START A NEW PHILOSOPHICAL PARADIGM - PHILOSOPHY WITH LOGICAL CONSEQUENCES.&lt;/span&gt;&lt;/p&gt;\n&lt;p&gt;&lt;strong&gt;&lt;span&gt;FOUNDATION OF CAUSE AND EFFECT&lt;/span&gt;&lt;/strong&gt;&lt;span&gt;&lt;br&gt;&lt;br&gt;Why do logical consequences underlie cause and effect? Why are logical consequences behind cause and effect? Isn't cause and effect the foundation of all occurrences?&lt;br&gt;&lt;br&gt;&lt;/span&gt;&lt;span&gt;👉&lt;/span&gt;&lt;span&gt; Because logically, cause and effect are stages in the process, so they need a place as the foundation of the process.&lt;br&gt;&lt;br&gt;&lt;/span&gt;&lt;span&gt;✅&lt;/span&gt;&lt;span&gt; Cause and effect are sequences of events, but they forget that behind the sequence of events, there is a floor that serves as the venue for the process to take place&lt;br&gt;&lt;br&gt;&lt;strong&gt;LOGICAL CONSEQUENCE AMBIGUITY &lt;/strong&gt;&lt;/span&gt;&lt;span&gt;❓&lt;/span&gt;&lt;span&gt; &lt;u&gt;Overlapping Interpretation Issues&lt;/u&gt;&lt;br&gt;&lt;br&gt;Even though the cause implies logical consequences, or the logical consequences depend on the cause, it seems that the logical consequences are inconsistent&lt;/span&gt;&lt;span&gt;❓&lt;/span&gt;&lt;span&gt;&lt;br&gt;&lt;br&gt;Remember, many things we understand overlap in meaning because two meanings are similar, making them appear as one meaning, even though they are different.&lt;br&gt;&lt;br&gt;Example: if hit, the logical consequence is pain. This is not a logical consequence, even though it is commonly expressed that way.&lt;br&gt;&lt;br&gt;When a stone is hit, it doesn't hurt like a human. There are situations where a blow doesn't cause pain.&lt;br&gt;&lt;br&gt;Or "if you're rude, the consequence is that he can get angry." However, the logical consequence is not just a tendency, or not a probability of getting angry.&lt;br&gt;&lt;br&gt;Because if the logical consequence still falls under the probability category, where is the certainty?&lt;br&gt;&lt;br&gt;Without certainty, all probabilities can surpass impossible limits.&lt;br&gt;&lt;br&gt;For example, when possibilities can go in any direction, this affirms the absence of certainty, meaning the unreasonable becomes reasonable, the reasonable becomes unreasonable, and there is no recognizable pattern.&lt;br&gt;&lt;br&gt;Nothing can be formulated because&lt;br&gt;&lt;br&gt;&lt;/span&gt;&lt;span&gt;✅&lt;/span&gt;&lt;span&gt; PROBABILITIES MUST BE BASED ON CERTAINTY. AND FROM CERTAINTY, PROBABILITIES CAN ARISE AS POSSIBILITIES.&lt;br&gt;&lt;br&gt;&lt;/span&gt;&lt;span&gt;👉&lt;/span&gt;&lt;span&gt; Like the certainty of numbers that produces (probabilities) combinations of numbers.&lt;br&gt;&lt;br&gt;This means that, no matter how shallow or deep, from classical physics limits to quantum physics limits, or even deeper, there must be a certainty limit that serves as its foundation. THAT IS THE LOGICAL CONSEQUENCE THAT IS NOT CAUSE-EFFECT, NOT PROBABILITY.&lt;br&gt;&lt;br&gt;SIMPLY...&lt;br&gt;&lt;br&gt;&lt;/span&gt;&lt;span&gt;✅&lt;/span&gt;&lt;span&gt; ... There is probability and its underlying factor, which is certainty.&lt;br&gt;&lt;br&gt;&lt;/span&gt;&lt;span&gt;⭕️&lt;/span&gt;&lt;span&gt; Whether called consequences, risks, logical consequences, or any term, the key is that something underlies probability, and that (once again) is certainty.&lt;br&gt;&lt;br&gt;WE JUST NEED TO SEE THE DISTINCTION WITH CAUSE AND EFFECT.&lt;br&gt;&lt;br&gt;&lt;strong&gt;CAUSE AND EFFECT &amp; LOGICAL CONSEQUENCES&lt;br&gt;&lt;/strong&gt;&lt;br&gt;CAUSE AND EFFECT IS A PROCESS, SO THERE ARE STAGES, AND THERE IS ROOM TO FILL IN A PROCESS.&lt;br&gt;&lt;br&gt;Cause and effect manifest diversity; cause and effect need space to process.&lt;br&gt;&lt;br&gt;Space precedes the process, even encompasses the process.&lt;br&gt;&lt;br&gt;The cause becomes the origin for its effect. If there is no cause, there is no effect.&lt;br&gt;&lt;br&gt;That space is the cause underlying the continuation of the cause-and-effect process.&lt;br&gt;&lt;br&gt;No space, no cause-and-effect process, so the main cause of cause and effect must have existed before its cause and effect, affirming that the main cause as a support goes beyond the process, meaning the main cause of its cause and effect is simultaneous without a process, or its process precedes all cause-and-effect processes.&lt;br&gt;&lt;br&gt;So&lt;/span&gt;&lt;span&gt;❓&lt;/span&gt;&lt;span&gt;What underlies all cause-and-effect is simultaneity, and that is the logical consequence.&lt;br&gt;&lt;br&gt;CAUSE AND EFFECT &amp; LOGICAL CONSEQUENCES&lt;br&gt;&lt;br&gt;As an example....&lt;br&gt;&lt;br&gt;"If there is a change, then there is a difference," so "change" is not the cause of "difference," and also "different" is not the cause of "change."&lt;br&gt;&lt;br&gt;Because both "change" and "difference" have no cause-and-effect relationship but a logical consequence relationship, not a probabilistic logical consequence, but a logical consequence affirming definite simultaneity.&lt;br&gt;&lt;br&gt;Between "change" and "difference," there is no precedence. We may perceive that if there is "change," there is "difference," but this does not imply a cause-and-effect process. This is our sequential perception, but fundamentally, both "change" and "difference" are inseparable unity.&lt;br&gt;&lt;br&gt;That is one example of a genuine logical consequence, affirming certainty as the cause of the diversity of cause-and-effect processes&lt;/span&gt;&lt;/p&gt;
Cited by 0Open access