# (Pure) logic out of probability.

• Volume: 3, Issue: 1-2, page 137-147
• ISSN: 1134-5632

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## Abstract

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Today, Logic and Probability are mostly seen as independent fields with a separate history and set of foundations. Against this dominating perception, only a very few people (Laplace, Boole, Peirce) have suspected there was some affinity or relation between them. The truth is they have a considerable common ground which underlies the historical foundation of both disciplines and, in this century, has prompted notable thinkers as Reichenbach [14], Carnap [2] [3] or Popper [12] [13] (and Gaifman [5], Scott & Krauss [21], Fenstad [4], Miller [10] [11], David Lewis [9], Stalnaker [22], Hintikka [7] or Suppes [23]) to consider connection-building treatments of Logic and Probability as desirable. Indeed such a line of thinking can be pursued (this author, for one, attempted it in [15-19]). In so doing, one straightforwardly obtains a logic based on -as the simple unifying concept- an additive non-functional truth valuation which, though technically indistinguishable from (axiomatic) Probability, can however be totally decontaminated from parasitical probabilistic interpretations (such as the usual readings of event, probability or conditioning) and be given instead a strictly logical reading and justification (in terms of sentence, truth or relativity). Once some deeply-ingrained reading habits are overcome, the required concepts and formulas flow easily, and the resulting assertion-based sentential calculus becomes a very natural extension of ordinary two-valued reasoning. Furthermore, in the process we get: (a) intuitive geometrical and information-related interpretations of the concepts, (b) a simple theoretical explanation for some poorly justified formulas (intermittently advanced by various authors, some mentioned above),and (c) a semantics -and a proof theory- for general assertions that is unproblematically derived and also fully consistent with empirical or ad hoc approximate-reasoning Bayesian formulas found by Artificial Intelligence researchers.

## How to cite

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Sales, Ton. "(Pure) logic out of probability.." Mathware and Soft Computing 3.1-2 (1996): 137-147. <http://eudml.org/doc/39067>.

@article{Sales1996,
abstract = {Today, Logic and Probability are mostly seen as independent fields with a separate history and set of foundations. Against this dominating perception, only a very few people (Laplace, Boole, Peirce) have suspected there was some affinity or relation between them. The truth is they have a considerable common ground which underlies the historical foundation of both disciplines and, in this century, has prompted notable thinkers as Reichenbach [14], Carnap [2] [3] or Popper [12] [13] (and Gaifman [5], Scott & Krauss [21], Fenstad [4], Miller [10] [11], David Lewis [9], Stalnaker [22], Hintikka [7] or Suppes [23]) to consider connection-building treatments of Logic and Probability as desirable. Indeed such a line of thinking can be pursued (this author, for one, attempted it in [15-19]). In so doing, one straightforwardly obtains a logic based on -as the simple unifying concept- an additive non-functional truth valuation which, though technically indistinguishable from (axiomatic) Probability, can however be totally decontaminated from parasitical probabilistic interpretations (such as the usual readings of event, probability or conditioning) and be given instead a strictly logical reading and justification (in terms of sentence, truth or relativity). Once some deeply-ingrained reading habits are overcome, the required concepts and formulas flow easily, and the resulting assertion-based sentential calculus becomes a very natural extension of ordinary two-valued reasoning. Furthermore, in the process we get: (a) intuitive geometrical and information-related interpretations of the concepts, (b) a simple theoretical explanation for some poorly justified formulas (intermittently advanced by various authors, some mentioned above),and (c) a semantics -and a proof theory- for general assertions that is unproblematically derived and also fully consistent with empirical or ad hoc approximate-reasoning Bayesian formulas found by Artificial Intelligence researchers.},
author = {Sales, Ton},
journal = {Mathware and Soft Computing},
keywords = {Lógica inductiva; Algebras de Boole; Incertidumbre; semantics; laws of probability; generalized truth functions; partial truth},
language = {eng},
number = {1-2},
pages = {137-147},
title = {(Pure) logic out of probability.},
url = {http://eudml.org/doc/39067},
volume = {3},
year = {1996},
}

TY - JOUR
AU - Sales, Ton
TI - (Pure) logic out of probability.
JO - Mathware and Soft Computing
PY - 1996
VL - 3
IS - 1-2
SP - 137
EP - 147
AB - Today, Logic and Probability are mostly seen as independent fields with a separate history and set of foundations. Against this dominating perception, only a very few people (Laplace, Boole, Peirce) have suspected there was some affinity or relation between them. The truth is they have a considerable common ground which underlies the historical foundation of both disciplines and, in this century, has prompted notable thinkers as Reichenbach [14], Carnap [2] [3] or Popper [12] [13] (and Gaifman [5], Scott & Krauss [21], Fenstad [4], Miller [10] [11], David Lewis [9], Stalnaker [22], Hintikka [7] or Suppes [23]) to consider connection-building treatments of Logic and Probability as desirable. Indeed such a line of thinking can be pursued (this author, for one, attempted it in [15-19]). In so doing, one straightforwardly obtains a logic based on -as the simple unifying concept- an additive non-functional truth valuation which, though technically indistinguishable from (axiomatic) Probability, can however be totally decontaminated from parasitical probabilistic interpretations (such as the usual readings of event, probability or conditioning) and be given instead a strictly logical reading and justification (in terms of sentence, truth or relativity). Once some deeply-ingrained reading habits are overcome, the required concepts and formulas flow easily, and the resulting assertion-based sentential calculus becomes a very natural extension of ordinary two-valued reasoning. Furthermore, in the process we get: (a) intuitive geometrical and information-related interpretations of the concepts, (b) a simple theoretical explanation for some poorly justified formulas (intermittently advanced by various authors, some mentioned above),and (c) a semantics -and a proof theory- for general assertions that is unproblematically derived and also fully consistent with empirical or ad hoc approximate-reasoning Bayesian formulas found by Artificial Intelligence researchers.
LA - eng
KW - Lógica inductiva; Algebras de Boole; Incertidumbre; semantics; laws of probability; generalized truth functions; partial truth
UR - http://eudml.org/doc/39067
ER -

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