THE LOGIC OF LEIBNIZ’S<i>GENERALES INQUISITIONES DE ANALYSI NOTIONUM ET VERITATUM</i>

Malink, Marko; Vasudevan, Anubav

doi:10.1017/s1755020316000137

Cited by 5 publications

(3 citation statements)

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“…The assumption where a neuron as active or at rest can be represented by an assignment to binary values, 1 and 0. Boolean algebra defines logical operations with these binary values, and originally named after the 19th century British mathematician George Boole [13], although the German polymath Gottfried Wilhelm von Leibniz had developed an equivalent mathematical system in 1686 [14][15][16]. Leibniz had also developed a mechanical system for computing with binary values, an analog of the modern digital computer [16][17].…”

Section: The Logic Gate Modelmentioning

confidence: 99%

A perspective on information optimality in a neural circuit

Friedman

2021

Preprint

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The nematode worm, Caenorhabditis elegans, is a relatively simple neural system model for measuring the efficiency of information transmission from sensory organ to muscle fiber. With the potential to measure this efficiency, a method is proposed to compare the organization of an idealized neural circuit with a logic gate design. This approach is useful for analysis of a neural circuit that is not tractable to a strictly biological model, and where the assumptions of a logic gate design have applicability. Also, included in the results is an abstract perspective of the electrical-specific synaptic network in the somatic system of the nematode worm.

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Section: The Logic Gate Modelmentioning

confidence: 99%

A perspective on information optimality in a neural circuit

Friedman

2021

Preprint

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“…McCulloch and Pitts introduced the concept of a logic gate model for explaining the processing of information in an animal neuronal system, based on the concept that a neuron is in a resting or active state, and the synaptic connections exhibit specific non-dynamic behaviors [1]. The logic gate design is an efficient model of Boolean algebraic operations, including the basic operators AND, OR, and NOT (Figure 1) [2][3][4][5][6]. However, others consider the biological design of a neuronal network inconsistent with the assumptions of this model [7][8][9][10][11][12][13][14][15][16][17].…”

Section: Introduction 1the Logic Gate Modelmentioning

confidence: 99%

A Perspective on Information Optimality in a Neural Circuit and Other Biological Systems

Friedman

2022

Signals

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The nematode worm Caenorhabditis elegans has a relatively simple neural system for analysis of information transmission from sensory organ to muscle fiber. Consequently, this study includes an example of a neural circuit from the nematode worm, and a procedure is shown for measuring its information optimality by use of a logic gate model. This approach is useful where the assumptions are applicable for a neural circuit, and also for choosing between competing mathematical hypotheses that explain the function of a neural circuit. In this latter case, the logic gate model can estimate computational complexity and distinguish which of the mathematical models require fewer computations. In addition, the concept of information optimality is generalized to other biological systems, along with an extended discussion of its role in genetic-based pathways of organisms.

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“…Some attempts to construct a calculus can be found in 'Ad specimen calculi universalis' (1686a) and 'Ad specimen calculi universalis addenda' (1686b), or in 'Generales Inquisitiones de Analysi Notionum et Veritatum' (1686c). See Rescher (1954), Lenzen (2004b) and Malink & Vasudevan (2016). 13 On Leibniz's influence and, specifically, on the influence of the Leibnizian notions of characteristica universalis and calculus ratiocinator, in Frege's thought, see Patzig (1969), Kluge (1977) and Kluge (1980Kluge ( ).…”

Section: Introductionmentioning

confidence: 99%

LINGUA CHARACTERICAANDCALCULUS RATIOCINATOR: THE LEIBNIZIAN BACKGROUND OF THE FREGE-SCHRÖDER POLEMIC

Millán

2020

The Review of Symbolic Logic

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After the publication of Begriffsschrift, a conflict erupted between Frege and Schröder regarding their respective logical systems which emerged around the Leibnizian notions of lingua characterica and calculus ratiocinator. Both of them claimed their own logic to be a better realisation of Leibniz’s ideal language and considered the rival system a mere calculus ratiocinator. Inspired by this polemic, van Heijenoort (1967b) distinguished two conceptions of logic—logic as language and logic as calculus—and presented them as opposing views, but did not explain Frege’s and Schröder’s conceptions of the fulfilment of Leibniz’s scientific ideal. In this paper I explain the reasons for Frege’s and Schröder’s mutual accusations of having created a mere calculus ratiocinator. On the one hand, Schröder’s construction of the algebra of relatives fits with a project for the reduction of any mathematical concept to the notion of relative. From this stance I argue that he deemed the formal system of Begriffsschrift incapable of such a reduction. On the other hand, first I argue that Frege took Boolean logic to be an abstract logical theory inadequate for the rendering of specific content; then I claim that the language of Begriffsschrift did not constitute a complete lingua characterica by itself, more being seen by Frege as a tool that could be applied to scientific disciplines. Accordingly, I argue that Frege’s project of constructing a lingua characterica was not tied to his later logicist programme.

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THE LOGIC OF LEIBNIZ’SGENERALES INQUISITIONES DE ANALYSI NOTIONUM ET VERITATUM

Cited by 5 publications

References 25 publications

A perspective on information optimality in a neural circuit

A perspective on information optimality in a neural circuit

A Perspective on Information Optimality in a Neural Circuit and Other Biological Systems

LINGUA CHARACTERICAANDCALCULUS RATIOCINATOR: THE LEIBNIZIAN BACKGROUND OF THE FREGE-SCHRÖDER POLEMIC

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