scholarly journals Analysis of Penrose’s Second Argument Formalised in DTK System

2021 ◽  
pp. 1-30
Author(s):  
Antonella Corradini ◽  
Sergio Galvan
Keyword(s):  

This article aims to examine Koellner’s reconstruction of Penrose’s second argument – a reconstruction that uses the DTK system to deal with Gödel’s disjunction issues. Koellner states that Penrose’s argument is unsound, because it contains two illegitimate steps. He contends that the formulas to which the T-intro and K-intro rules apply are both indeterminate. However, we intend to show that we can correctly interpret the formulas on the set of arithmetic formulas, and that, as a consequence, the two steps become legitimate. Nevertheless, the argument remains partially inconclusive. More precisely, the argument does not reach a result that shows there is no formalism capable of deriving all the true arithmetic propositions known to man. Instead, it shows that, if such formalism exists, there is at least one true non-arithmetic proposition known to the human mind that we cannot derive from the formalism in question. Finally, we reflect on the idealised character of the DTK system. These reflections highlight the limits of human knowledge, and, at the same time, its irreducibility to computation.

Author(s):  
Barry Stroud

This chapter presents a straightforward structural description of Immanuel Kant’s conception of what the transcendental deduction is supposed to do, and how it is supposed to do it. The ‘deduction’ Kant thinks is needed for understanding the human mind would establish and explain our ‘right’ or ‘entitlement’ to something we seem to possess and employ in ‘the highly complicated web of human knowledge’. This is: experience, concepts, and principles. The chapter explains the point and strategy of the ‘deduction’ as Kant understands it, as well as the demanding conditions of its success, without entering into complexities of interpretation or critical assessment of the degree of success actually achieved. It also analyses Kant’s arguments regarding a priori concepts as well as a posteriori knowledge of the world around us, along with his claim that our position in the world must be understood as ‘empirical realism’.


Author(s):  
Makhmudova Nilufarkhon Ravshanovna

In this article has been illuminated the communicative-pragmatic functions of gradation in English and Uzbek languages. In the scientific literature, cognitive linguistics is also described as “connected semantics” because it deals mainly with semantics. While linguistic units serve to express objects that exist in the world and the actions that take place, semantics connect the interactions between linguistic units in a real or imaginary world. These relations are studied by linguistic semantics as a separate object of study. One of the important features of cognitive linguistics is that it allows us to see the language in relation to a person, that is, his consciousness, knowledge, processes of thinking and understanding, paying particular attention to how language forms and any language phenomena are associated with human knowledge and experience and how they relate to the human mind how to describe. KEY WORDS: English language, Uzbek language, gradation, communicative-pragmatic functions, structural linguistics, cognitive linguistics, semantics, pragmatic influence.


2017 ◽  
Vol 18 (3) ◽  
pp. 37
Author(s):  
Elzbieta Magdalena Wasik

<p>Departing from the biological notion of ecology that pertains to mutual relationships between organisms and their environments, this paper discusses theoretical foundations of research on the nature of human mind in relation to knowledge, cognition and communication conducted in a broader context of social sciences. It exposes the view, explicitly formulated by Gregory Bateson, that the mind is the way in which ideas are created, or just the systemic device for transmitting information in the world of all living species. In consequence, some crucial points of Bateson’s reasoning are accentuated, such as the recognition of the biological unity of organism and environment, the conviction of the necessity to study the ecology in terms of the economics of energy and material and/or the economy of information, the belief that consciousness distorts information coming to the organism from the inside and outside, which is the cause of its functional disadaptation, and the like. The conception of the ecology of an overall mind, as the sets of ideas, notions or thoughts in the whole world, is presented against the background of theoretical and empirical achievements of botany and zoology, anthropology, ethology and psychiatry, sociology and communication studies in connection with the development of cybernetics, systems theory and information theory.</p>


2015 ◽  
Vol 18 (1) ◽  
pp. 66-86
Author(s):  
Pirmin Stekeler-Weithofer

In order to understand Hegel’s form of philosophical reflection in general, we must read his ‘speculative’ sentences about spirit and nature, rationality and reason, the mind and its embodiment as general remarks about conceptual topics in topographical overviews about our ways of talking about ourselves in the world. The resulting attitude to traditional metaphysics gets ambivalent in view of the insight that Aristotle’s prima philosophia is knowledge of human knowledge, developed in meta-scientific reflections on notions like ‘nature’ and ‘essence’, ‘reality’ (or ‘being’) and ‘truth’, about ‘powers’ and ‘faculties’ – and does not lead by itself to an object-level theory about spiritual things like the soul. We therefore cannot just replace critical metaphysics of the human mind by empirical investigation of human behaviour as empiricist approaches to human cognition in naturalized epistemologies do and neuro-physiological explanations propose. Making transcendental forms and material presuppositions of conceptually informed perception and experience explicit needs some understanding of figurative forms of speech in our logical reflections and leads to other forms of knowledge than empirical observation and theory formation.


Author(s):  
Bonnie Kent

Bonaventure (John of Fidanza) developed a synthesis of philosophy and theology in which Neoplatonic doctrines are transformed by a Christian framework. Though often remembered for his denunciations of Aristotle, Bonaventure’s thought includes some Aristotelian elements. His criticisms of Aristotle were motivated chiefly by his concern that various colleagues, more impressed by Aristotle’s work than they had reason to be, were philosophizing with the blindness of pagans instead of the wisdom of Christians. To Bonaventure, the ultimate goal of human life is happiness, and happiness comes from union with God in the afterlife. If one forgets this goal when philosophizing, the higher purpose of the discipline is frustrated. Philosophical studies can indeed help in attaining happiness, but only if pursued with humility and as part of a morally upright life. In the grander scheme of things, the ascent of the heart is more important than the ascent of the mind. Bonaventure’s later works consistently emphasize that all creation emanates from, reflects and returns to its source. Because the meaning of human life can be understood only from this wider perspective, the general aim is to show an integrated whole hierarchically ordered to God. The structure and symbolism favoured by Bonaventure reflect mystical elements as well. The world, no less than a book, reveals its creator: all visible things represent a higher reality. The theologian must use symbols to reveal this deeper meaning. He must teach especially of Christ, through whom God creates everything that exists and who is the sole medium by which we can return to our creator. Bonaventure’s theory of illumination aims to account for the certitude of human knowledge. He argues that there can be no certain knowledge unless the knower is infallible and what is known cannot change. Because the human mind cannot be entirely infallible through its own power, it needs the cooperation of God, even as it needs God as the source of immutable truths. Sense experience does not suffice, for it cannot reveal that what is true could not possibly be otherwise; so, in Bonaventure’s view, the human mind attains certainty about the world only when it understands it in light of the ‘eternal reasons’ or divine ideas. This illumination from God, while necessary for certainty, ordinarily proceeds without a person’s being conscious of it.


1936 ◽  
Vol 29 (3) ◽  
pp. 123-128
Author(s):  
Mary A. Potter

If we scrutinize mathematics carefully looking for its human side, we shall observe that in its teaching we find the human element displayed from several different angles. Teachers are, or at least they should be, human beings; pupils are younger human beings; mathematics is a priceless heritage of knowledge developed by the human mind to meet the requirements of human needs. Hence, the teaching of mathematics is the imparting of this heritage of human knowledge to human beings by human beings.


2019 ◽  
Author(s):  
Jenny Wang ◽  
Lisa Feigenson

The origins of human knowledge are an enduring puzzle: what parts of what we know require learning, and what emerges regardless of experience? Despite nature-nurture defining debate for millennia and inspiring much contemporary research in psychology and neuroscience, it remains unknown whether people share intuitive, pre-scientific theories about the answer. Here in a series of experiments with 1188 participants, we find that people explain fundamental perceptual and cognitive abilities by appeal to learning and instruction, rather than genes or innateness. U.S. adults, adults from a culture with a belief in reincarnation, young children, and professional scientists-- including psychologists and neuroscientists, all believed these basic abilities to emerge significantly later than they actually do, and ascribed them to nurture rather than nature. These findings suggest that, regardless of age, culture, and education, people share an intuitive empiricist theory about the human mind.


1978 ◽  
Vol 4 ◽  
pp. 207-218
Author(s):  
Arthur R. Greenberg

In recent years renewed interest in Thomas Reid's philosophy has led to fruitful discussion of Reid's theories of sensation and perception. Although certain aspects of these topics can be discussed without setting out Reid's version of the primary-secondary quality distinction, the ultimate evaluation of Reid's work on both sensation and perception requires discussion of his views on primary and secondary qualities. Current Reid literature virtually ignores this important topic. This paper is an attempt to remedy this situation. In addition to setting out Reid's position on primary and secondary qualities I will discuss Reid's curious relation to the New Science of his day and will explain how Reid thought he could reintroduce the primary-secondary quality distinction despite Berkeley's attacks on the doctrine.In both of his major works, An Inquiry Into The Human Mind (1764), and Essays On The Intellectual Powers Of Man (1785), Thomas Reid was intent upon examining the philosophical problems of human knowledge. In the Inquiry perception received his exclusive attention. In the Essays other cognitive operations were examined as well. The impetus for these investigations was provided by Reid's negative assessment of the achievements of his philosophical predecessors.


Author(s):  
Charles A. Corr

Christian Wolff was a rationalistic school philosopher in the German Enlightenment. During the period between the death of Leibniz (1714) and the publication of Kant’s critical writings (1780s), Wolff was perhaps the most influential philosopher in Germany. There are many reasons for this, including Wolff’s voluminous writings in both German and Latin in nearly every field of philosophy known to his time, their unvarying employment of a strict rationalistic method to establish their conclusions, the attention directed to Wolff and his views as a result of bitter controversies with some theological colleagues, his banishment from Prussia by King Frederick Wilhelm I in 1723 and triumphant return from Hesse–Cassel in 1740 after Frederick the Great assumed the throne, and his active teaching at the Universities of Halle and Marburg for nearly 50 years. Through his work as a university professor, his prolific writings, and the rigour and comprehensiveness of his philosophy, Wolff influenced a very large group of followers, educators and other writers. Even after his influence had begun to wane, Kant still referred to ‘the celebrated Wolff’ and spoke of ‘the strict method of the celebrated Wolff, the greatest of all dogmatic philosophers’. Wolff thought of philosophy as that discipline which provides reasons to explain why things exist or occur and why they are even possible. Thus, he included within philosophy a much broader range of subjects than might now be recognized as ‘philosophical’. Indeed, for Wolff all human knowledge consists of only three disciplines: history, mathematics and philosophy. The reasons provided by Wolff’s philosophy were to be established through unfailing adherence to a strict demonstrative method. Like Descartes, Wolff first discovered this method in mathematics, but he concluded that both mathematical and philosophical methods had their ultimate origins in a ‘natural logic’ prescribed to the human mind by God. In fact, the heart of Wolff’s philosophical method is a deductive logic making use of syllogistic arguments. For Wolff, the immediate objective of philosophical method is to achieve certitude by establishing an order of truths within each discipline and a system within human knowledge as a whole. The ultimate goal is to establish a reliable foundation for the conduct of human affairs and the enlargement of knowledge. Wolff applied his philosophical method unfailingly in each of the three principal parts of philosophy: metaphysics – knowledge of those things which are possible through being in general, the world in general, human souls, and God; physics – knowledge of those things which are possible through bodies; and practical philosophy – knowledge of those things which are concerned with human actions. Wolff’s philosophical system also includes logic, an art of discovery (to guide the investigation of hidden truth and the production of new insights), some experiential disciplines (for example, empirical psychology) and several bodies of philosophical knowledge that were not well developed in Wolff’s time concerning law, medicine, and both the practical and liberal arts.


Author(s):  
Richard Albert Wilson

But that same Where (Space), with its brother When (Time), are from the first the master-colours of our Dream-Grotto; the Canvas (the warp and woof thereof) whereon all our Dreams and Life-Visions are painted.—CARLYLE, Sartor Resartus, 1830.When Kant in his investigation of the nature and validity of human knowledge in the Critique of Pure Reason (1781) undertook an examination of the nature of Space and Time as the starting point in the discussion, he struck the path which all fruitful philosophical investigation has followed since. Since Space and Time are the two ‘forms’ within which the whole system of life and nature unfolds itself to the human mind, and are at the same time the ‘warp and woof on which man elaborates his mental sense-picture of the world, an examination of these two sense-forms should be the self-evident starting point in any true cosmic philosophy. Yet it seems to have taken something more than a century for the full significance of Kant’s method to sink into the general philosophical consciousness, and it is only in our own time that its fruits have begun to mature. What strikes one in the philosophical writings of the present century, whether starting from mathematics, or science, or pure speculation, is the common assumption in all of them that some exposition of Space and Time must form the foundation of any adequate treatment of the nature of the world, the human mind, and the structure of human knowledge. The title of Professor Alexander’s book, Space, Time, and Deity (1920), is symbolic of the modern point of view.


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