Logical validity

2020 ◽  
pp. 44-51
Keyword(s):  
2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Francisco Salto ◽  
Carmen Requena ◽  
Paula Álvarez-Merino ◽  
Luís F. Antón-Toro ◽  
Fernando Maestú

AbstractNeuroscience has studied deductive reasoning over the last 20 years under the assumption that deductive inferences are not only de jure but also de facto distinct from other forms of inference. The objective of this research is to verify if logically valid deductions leave any cerebral electrical trait that is distinct from the trait left by non-valid deductions. 23 subjects with an average age of 20.35 years were registered with MEG and placed into a two conditions paradigm (100 trials for each condition) which each presented the exact same relational complexity (same variables and content) but had distinct logical complexity. Both conditions show the same electromagnetic components (P3, N4) in the early temporal window (250–525 ms) and P6 in the late temporal window (500–775 ms). The significant activity in both valid and invalid conditions is found in sensors from medial prefrontal regions, probably corresponding to the ACC or to the medial prefrontal cortex. The amplitude and intensity of valid deductions is significantly lower in both temporal windows (p = 0.0003). The reaction time was 54.37% slower in the valid condition. Validity leaves a minimal but measurable hypoactive electrical trait in brain processing. The minor electrical demand is attributable to the recursive and automatable character of valid deductions, suggesting a physical indicator of computational deductive properties. It is hypothesized that all valid deductions are recursive and hypoactive.


Author(s):  
José Miguel Sagüillo Fernández-Vega

I discuss Putnam’s conception of logical truth as grounded in his picture of mathematical practice and ontology. i begin by comparing Putnam’s 1971 Philosophy of Logic with Quine’s homonymous book. Next, Putnam’s changing views on modality are surveyed, moving from the modal pre-formal to the de-modalized formal characterization of logical validity. Section three suggests a complementary view of Platonism and modalism underlying different stages of a dynamic mathematical practice. The final section argues for the pervasive platonistic conception of the working mathematician.


Author(s):  
A. W. Price

Richard Hare's ambition was to have united elements from Aristotle, Kant and Mill in a logically cogent way that solved the fundamental problems of ethics (though with unfinished business); and he usually believed himself to have achieved this. For much of his career, his ‘prescriptivism’ formed an important part of the curriculum, certainly in Britain. His disappointment was not to have persuaded others (an occasional ‘we prescriptivists’ was always uncertain of reference), and to have left no disciples; he once told John Lucas that this made his life a failure. Yet he leaves behind generations of pupils grateful for the transmission not of a doctrine but of a discipline; and posterity, while unlikely to ratify the logical validity of his theory, will admire it for its uniting of apparent opposites: freedom and reason, tradition and rationalism, eclecticism and rigour.


Author(s):  
Hans Blumenberg

This chapter assesses Hans Blumenberg's essay, “Light as a Metaphor for Truth” (1957). With this essay, Blumenberg formulated the seed of the project for which he is, at least in Germany, best known: his “metaphorology.” While metaphorology initially seemed to be an extension of conceptual history — a research project aimed at investigating the semantic changes to central concepts of philosophy — it at the same time called into question the very centrality of concepts and terminologies as the only and authentic bearers of philosophical thought. Instead, it makes the case for studying the role pre- and nonconceptual speech plays in the language of philosophy. Where traditionally theories of truth would be interpreted in terms of their propositional content or logical validity, Blumenberg's article instead looks at the metaphors with which truth is described and which operate, as he puts it in the subtitle, “At the Preliminary Stage of Concept Formation.”


Mind ◽  
1915 ◽  
Vol XXIV (1) ◽  
pp. 70-74
Author(s):  
ELTON MAYO
Keyword(s):  

Vivarium ◽  
2015 ◽  
Vol 53 (2-4) ◽  
pp. 322-335
Author(s):  
Mikko Yrjönsuuri

The paper considers two kinds of medieval obligational disputations (positio, rei veritas) and the medieval genre of sophismata in relation to the kinds of inferences accepted in them. The main texts discussed are the anonymous Obligationes parisienses from the early 13th century and Richard Kilvington’s Sophismata from the early 14th century. Four different kinds of warranted transition from an antecedent to a consequent become apparent in the medieval discussions: (1) the strong logical validity of basic propositional logic, (2) analytic validity based on conceptual containment, (3) merely semantic impossibility of the antecedent being true without the consequent, and (4) intuitively true counterfactual conditionals. As these different kinds of consequences are spelled out by means of obligational disputations, it appears that the genre of obligations is indeed useful for the “knowledge of consequences,” as the anonymous Obligationes parisienses claims.


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