Leibniz's interpretation of his logical calculi

1954 ◽  
Vol 19 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Nicholas Rescher
Keyword(s):  
Formal Logic ◽  
Point Of View ◽  
Symbolic Logic ◽  
Logical Calculus ◽  
Formal Systems ◽  
Logical Calculi

The historical researches of Louis Couturat saved the logical work of Leibniz from the oblivion of neglect and forgetfulness. They revealed that Leibniz developed in succession several versions of a “logical calculus” (calculus ratiocinator or calculus universalis). In consequence of Couturat's investigations it has become well known that Leibniz's development of these logical calculi adumbrated the notion of a logistic system; and for these foreshadowings of the logistic treatment of formal logic Leibniz is rightly regarded as the father of symbolic logic.It is clear from what has been said that it is scarcely possible to overestimate the debt which the contemporary student of Leibniz's logic owes to Couturat. This gratitude must, however, be accompanied by the realization that Couturat's own theory of logic is gravely defective. Couturat was persuaded that the extensional point of view in logic is the only one which is correct, an opinion now quite antiquated, and shared by no one. This prejudice of Couturat's marred his exposition of Leibniz's logic. It led him to battle with windmills: he viewed the logic of Leibniz as rife with shortcomings stemming from an intensional approach.The task of this paper is a re-examination of Leibniz's logic. It will consider without prejudgment how Leibniz conceived of the major formal systems he developed as logical calculi – that is, these systems will be studied with a view to the interpretation or interpretations which Leibniz himself intends for them. The aim is to undo some of the damage which Couturat's preconception has done to the just understanding of Leibniz's logic and to the proper evaluation of his contribution.

Semiotic analysis of symbolic logic using tagmemic theory: with implications for analytic philosophy

Semiotica ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Vern S. Poythress
Keyword(s):  
Complex System ◽  
Analytic Philosophy ◽  
Formal Languages ◽  
Point Of View ◽  
Symbolic Logic ◽  
Semiotic Analysis ◽  
The World

Abstract This article uses tagmemic theory as a semiotic framework to analyze symbolic logic. It attends particularly to the issue of context for meaning and the role of personal observer/participants. It focuses on formal languages, which employ no ordinary words and from one point of view have “no meaning.” Attention to the context and the theorists who deploy these languages shows that formal languages have meanings at a higher level, colored by the purposes of the analysts. In fact, there is an indefinitely ascending hierarchy of theories of theories, each of which analyzes and evaluates the theories at a lower level. By analogy with Kurt Gödel’s incompleteness theory, no level of the hierarchy can capture within formalism everything in a sufficiently complex system. The personal analysts always have to make judgments about how a formalized system is analogous to the world outside the system. Arguments in analytic philosophy can be useful in clarification, but neither clarification of terms nor clarification of the structure of arguments can eliminate the need for personal judgment.

Disarming Stove’s Paradox: In Defence of Formal Logic

1998 ◽  
pp. 127-134
Author(s):  
R. Rodrigo Soberano
Keyword(s):  
Main Part ◽  
Formal Logic ◽  
Symbolic Logic ◽  
Logical Contradiction ◽  
False Conclusion

The argument (d) ("All arguments with true premises and false conclusions are invalid.") is an argument with true premises and false conclusion. Therefore "(d) is invalid" seems to be formally valid. Thus presumably formal logic has to admit it as valid. But then formal logic finds itself in a bind. For the above argument is problematic and even paradoxical since it involves an internal logical contradiction. The paradox, aptly termed "Stove's paradox," is fully realized by demonstrating with the help of symbolic logic the contradiction within the argument. Then as the main part of this essays shows, the paradox is attacked by exposing the paradox's genesis. It is shown that by appeal to some not so obvious logical considerations regarding sound linguistic construction and usage, the above argument could not have been legitimately construction. For its construction must have involved either equivocation or hiatus of meaningfulness in the use of the symbol (d).

A minimum calculus for logic

1944 ◽  
Vol 9 (4) ◽  
pp. 89-94 ◽  
Author(s):  
Frederic B. Fitch
Keyword(s):  
Truth Table ◽  
Additional Property ◽  
Basic Logic ◽  
Double Negation ◽  
Logical Calculus ◽  
Logical Calculi

A logical calculus will be presented which not only is a formulation of a “basic logic” in the sense of the writer's previous papers, but which has the additional property that no weaker calculus can be a formulation of a basic logic. A sort of minimum logical calculus is thus attained, which has nothing superfluous about it for achieving the purpose for which it is designed.In the case of some logical calculi the question can arise as to whether certain of the postulates are really logically valid and necessary. Sometimes a test is available, such as the truth-table test, enabling us to distinguish between logically valid sentences and others, but often no such test is available, especially where quantifiers are involved. Is or is not the axiom of infinity, for example, to be regarded as logically valid? Or is the principle of double negation really acceptable, even though it satisfies the truth-table test?

scholarly journals Lógicas normativas, moral y derecho

1991 ◽  
Vol 23 (69) ◽  
pp. 27-59
Author(s):  
Leila Z. Puga ◽  
Newton C. A. Da Costa ◽  
Roberto J. Vernengo
Keyword(s):  
Point Of View ◽  
Legal Obligation ◽  
Rational Analysis ◽  
Formal Systems ◽  
Ethical Discourse ◽  
Traditional Problem ◽  
Different Types ◽  
Ethical Thinking ◽  
Politics And Law ◽  
Formal Point

The relationships between moral and legal codes, that is, between specific normative sets, is a traditional problem of ethics, politics and law philosophy. Deontic logics have provided some instruments for a deeper analysis of those relations. The authors try to analyze the logical consequences of the adoption of different axiomaticallogical systems, where deontic modalities are introduced as expressing different senses of moral or legal obligation, prohibition, permission, etc. It tums out, as a result of the analysis , that sorne very traditional thesis about the relationships between law and moral presuppose different logical requirements, some of which are not only interesting from a pure formal point of view, but also as an essay in a rational analysis of normative discourse. Different types of logics, specially sorne called bidimensional deontic systems, are investigated, as sorne mixed alethic-deontic and paraconsistent systems are sketched, Contraintuitive consequences and paradoxes deriving Crom those logical presuppositions are described and their consequences in ethical thinking are underlined. The paper' s purpose is to attain a better understanding of sorne informal ethical notions through the construction of formal systems expressing with sorne precision the very vague notions that sometimes are behind accepted legal or moral conceptions. Thus, the authors think, it would be possible a progressive aproximation to a better analysis of sorne important presuppositions of ethical discourse, a discourse where morals and law have an essential part to play. [Roberto Vemengo]

Beauvoir, Irigaray, and Philosophy

2017 ◽  
Author(s):  
Dorothea E. Olkowski
Keyword(s):  
Formal Logic ◽  
Point Of View ◽  
Binary Logic ◽  
Ethical Implications ◽  
Psychoanalytic Perspective ◽  
Law Of Excluded Middle ◽  
The Law ◽  
And Linguistics ◽  
Excluded Middle ◽  
Epistemological Point

Luce Irigaray’s view of her relationship to Beauvoir’s work is that “there are important differences between our positions.” This should not be surprising given that these two philosophers belong to different even if overlapping philosophical eras. Beauvoir is identified primarily with phenomenological–existentialism and Irigaray with psychoanalysis and linguistics. This essay takes up those differences from an ontological and epistemological point of view suggested by a number of feminist philosophers but not fully examined in the work of Beauvoir and Irigaray. This includes Beauvoir’s rejection of dualist thinking produced by the binary logic of the Law of Excluded Middle, and Irigaray’s critique of formal logic based on her psychoanalytic perspective. Beginning with Beauvoir and moving from there to Irigaray, the essay takes up the question of the ontological and epistemological structures utilized by each of these two feminist philosophers with an eye to their subsequent ethical implications.

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