Truth, function and paradox

Analysis ◽  
2010 ◽  
Vol 71 (1) ◽  
pp. 38-44 ◽  
Author(s):  
S. Shapiro
Keyword(s):  
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Ezgi Türkarslan ◽  
Jun Ye ◽  
Mehmet Ünver ◽  
Murat Olgun

The main purpose of this study is to construct a base for a new fuzzy set concept that is called consistency fuzzy set (CFS) which expresses the multidimensional uncertain data quite successfully. Our motive is to reduce the complexity and difficulty caused by the information contained in the truth sequence in a fuzzy multiset (FMS) and to present the data of the truth sequence in a more understandable and compact manner. Therefore, this paper introduces the concept of CFS that is characterized with a truth function defined on a universal set 0,1 2 . The first component of the truth pair of a CFS is the average value of the truth sequence of a FMS and the second component is the consistency degree, that is, the fuzzy complement of the standard deviation of the truth sequence of the same FMS. The main contribution of a CFS is the reflection of both the level of the average of the data that can be expressed with the different sequence lengths and the degree of the reasonable information in data via consistency degree. To develop this new concept, this paper also presents a correlation coefficient and a cosine similarity measure between CFSs. Furthermore, the proposed correlation coefficient and cosine similarity measure are applied to a multiperiod medical diagnosis problem. Finally, a comparison analysis is given between the obtained results and the existing results in literature to show the efficiency and rationality of the proposed correlation coefficient and cosine similarity measure.


Philosophies ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 25
Author(s):  
Chenguang Lu

Many researchers want to unify probability and logic by defining logical probability or probabilistic logic reasonably. This paper tries to unify statistics and logic so that we can use both statistical probability and logical probability at the same time. For this purpose, this paper proposes the P–T probability framework, which is assembled with Shannon’s statistical probability framework for communication, Kolmogorov’s probability axioms for logical probability, and Zadeh’s membership functions used as truth functions. Two kinds of probabilities are connected by an extended Bayes’ theorem, with which we can convert a likelihood function and a truth function from one to another. Hence, we can train truth functions (in logic) by sampling distributions (in statistics). This probability framework was developed in the author’s long-term studies on semantic information, statistical learning, and color vision. This paper first proposes the P–T probability framework and explains different probabilities in it by its applications to semantic information theory. Then, this framework and the semantic information methods are applied to statistical learning, statistical mechanics, hypothesis evaluation (including falsification), confirmation, and Bayesian reasoning. Theoretical applications illustrate the reasonability and practicability of this framework. This framework is helpful for interpretable AI. To interpret neural networks, we need further study.


2018 ◽  
Vol 4 (1) ◽  
pp. 220
Author(s):  
Leon Farhi Neto

Entre as funções originárias da fotografia está a documental. A foto dá testemunho da verdade. Barthes, em 1980, chegou a encontrar na essência da fotografia o “isso-foi”. Na foto se manifestaria necessariamente a verdade de uma realidade do passado. Ora, o dito popular – uma imagem vale mais que mil palavras! – até há pouco parecia incontestável (hoje desconfiamos mais de uma foto do que há 30 anos atrás). Fotografia documental, medical, policial, foto de identidade, identificação, controle, de tal maneira que aquele dito popular se inscreve em uma série que nos leva a outra frase de nosso cotidiano, de formulação mais recente: sorria, você está sendo filmado! A essa função-verdade da fotografia, ligada ao controle, eu gostaria de opor uma outra: uma pós-função, uma função pós-verdade, no sentido de uma metaverdade, de um para além da verdade fotográfica. – Isso não é verdade! Não é isso o que eu vi! Não pode ser! – essas exclamações podem expressar duas coisas diferentes: seja a denegação da verdade, seja o afloramento na foto de um virtual imagético, de um inconsciente visual. O que me interessa aqui é a segunda alternativa: a de que, numa imagem fotográfica, faça irrupção algo que não tenha sido conscientemente fotografado.   PALAVRAS-CHAVE: Controle; virtual; incosciente.     ABSTRACT Among the originary functions of photography there is the documental function. The photograph testifies to the truth. Barthes, in 1980, came to find the essence of photography in the “that-has-been”. A photograph would necessarily manifest the truth of a past reality. This explains why the popular saying – a picture is worth a thousand words! – until recently seemed incontestable (today we suspect more of a photo than 30 years ago). Documental photography, medical, identity photography, identification, control, in such a way that that popular saying is inscribed in a series that leads us to another sentence of our daily, in a more recent formulation: smile, you are being filmed! To this truth-function of photography, linked to control, I would like to oppose another: a post-function, a post-truth function, in the sense of a meta-truth, one beyond the photographic truth. – This is not true! That's not what I saw! It can not be! – these exclamations can express two different things: either the denial of truth, or the outcropping in the photograph of an imagetic virtual, of a visual unconscious. What interests me here is the second alternative: that in a photographic image something erupts that has not been consciously photographed.   KEYWORDS: Control; virtual; unconcious.     RESUMEN Entre las funciones originarias de la fotografía está la documental. La foto es testigo de la verdad. Barthes, en 1980, llegó a ubicar la esencia de la fotografía en el “esto-ha-sido”. En la foto necesariamente se manifesta la verdad de una realidad del pasado. El dicho popular – una imagen vale más que mil palabras! – hasta hace poco parecía incontestable (hoy día sospechamos más de una foto que hace 30 años). La fotografía documental, medical, policial, foto de identidad, identificación, control, de modo que aquel dicho popular se inscribe en una serie que nos lleva a otra frase de nuestra vida cotidiana, de formulación más reciente: sonría, usted está siendo filmado! A esta función-verdad de la fotografía, conectada al control, me gustaría oponer una otra: una posfunción, una función posverdad , en el sentido de una metaverdad, de un más allá de la verdad fotográfica. – ¡Eso no es verdad! Eso no es lo que vi! ¡No puede ser! – estas exclamaciones pueden expresar dos cosas diferentes: o bien la negación de la verdad, o bien el afloramiento en la foto de una imagen virtual, un inconsciente visual. Lo que me interesa aquí es la segunda alternativa: que en una imagen fotográfica haga irrupción algo que no ha sido conscientemente fotografiado.   PALABRAS CLAVE: Control; virtual; inconsciente.


1970 ◽  
Vol 3 ◽  
pp. 15-26 ◽  
Author(s):  
Takeo Sugihara
Keyword(s):  

1951 ◽  
Vol 16 (1) ◽  
pp. 43-45
Author(s):  
Maurice L'abbé

A general system of axioms has been given by Henkin for a fragment of the propositional calculus having as primitive symbols, in addition to the usual parentheses, variables, and implication sign ⊃, an arbitrarily given truth function symbol ϕ. This system of axioms, which we shall denote by S(⊃, ϕ), contains the following three axiom schemataplus the 2m further axiom schemata involving the symbol ϕwhere ϕ is an m-placed function symbol. We refer to Henkin's paper, p. 43, for the detailed description of the axiom schemata (4).The remark was made in the above mentioned paper that each of the 2m axiom schemata of (4) is trivially independent of the rest of the axioms of S(⊃, ϕ), and it was conjectured that the axiom schemata (1), (2) and (3) are also independent. In this note, we prove the general independence of the axiom schemata (1) and (2). As for (3), we show on the one hand its independence in the systems S(⊃) and S(⊃, f), and, on the other hand, its dependence in the system S(⊃, ∼). The net result is, therefore, that in any of these systems of axioms S(⊃, ϕ) all the axiom schemata are independent, except possibly the axiom schema (3).


1957 ◽  
Vol 4 (2) ◽  
pp. 189-192 ◽  
Author(s):  
William Miehle
Keyword(s):  

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