The formalization of mathematics

1954 ◽  
Vol 19 (4) ◽  
pp. 241-266 ◽  
Author(s):  
Hao Wang
Keyword(s):  
Large Body ◽  
Axiom System ◽  
Original Sin ◽  
Axiomatic Method ◽  
Formalization Of Mathematics ◽  
Rigid System ◽  
Mathematical Experience ◽  
Mental Operations ◽  
The Mind

Zest for both system and objectivity is the formal logician's original sin. He pays for it by constant frustrations and by living ofttimes the life of an intellectual outcaste. The task of squeezing a large body of stubborn facts into a more or less rigid system can be a painful one, especially since the facts of mathematics are among the most stubborn of all facts. Moreover, the more general and abstract we get, the farther removed we are from the raw mathematical experience. As intuition ceases to operate effectively, we fall into many unexpected traps. The formal logician gets little sympathy for his frustrations. He is regarded as too rigid by his philosophical colleagues and too speculative by his mathematical friends. The life of an intellectual outcaste may be a result partly of temperament and partly of the youthfulness of the logic profession. The unfortunate lack of wide appeal of logic may, however, be prolonged partly on account of the fact that very little of the well-established techniques of mathematics seems applicable to the treatment of serious problems of logic.The axiomatic method is well suited to provide results which are both exact and systematic. How attractive would it be if we could get an axiom system in which all the axioms and deductions were intuitively clear and all theorems of mathematics were provable? Such a system would undoubtedly satisfy Descartes who admits solely intuition and deduction, which are, for him, the only “mental operations by which we are able, wholly without fear of illusion, to arrive at the knowledge of things.” Indeed, according to Descartes, intuition and deduction “are the most certain routes to knowledge, and the mind should admit no others. All the rest should be rejected as suspect of error and dangerous.”

Practical Implementation of Integrative Bilingual Teaching/Learning at a Technical University

2020 ◽  
pp. 98-117
Author(s):  
Eduard Krylov
Keyword(s):  
Dynamic Balance ◽  
Practical Implementation ◽  
Pilot Projects ◽  
Integrative Education ◽  
Bilingual Teaching ◽  
Mental Operations ◽  
Technical University ◽  
Teaching Learning ◽  
The Mind ◽  
Practical Recommendations

The value and importance of the integrative bilingual teaching/learning foreign language and engineering is building bridges between cognition and communication, finding ways for establishing a dynamic balance between them in the mind of an engineering student. This explains the choice of study exercises and activities, related to mental operations and psychological patterns. The chapter discusses the peculiarities of solving problems, other active exercises, and gives some practical recommendations. Here also is the eternal problem of CLIL-like integrative education: How much language? How much content? Concerning language material, it is determined by some basic volume, demand driven by professional duties and interests. All the suggested ideas were tested at a Russian technical university for years. The difficulties, findings, and results of the pilot projects for bachelors and masters are discussed.

Why We Should Reject Transhumanists’ Entire Lens on the Mind and Brain

2021 ◽  
pp. 42-84
Author(s):  
Susan B. Levin
Keyword(s):  
Dual Process ◽  
Appraisal Theory ◽  
Basic Emotion ◽  
Theoretical Approaches ◽  
Mind And Brain ◽  
Mental Operations ◽  
The Mind ◽  
The Brain

“Basic-emotion” and “dual-process” theorists, joined by transhumanists, view the mind as a set of compartments whose functionality is explained by dedicated areas or systems in the brain. The two theoretical approaches reflect core misconceptions and have been supplanted by “appraisal theory.” Beyond capturing well the entwining of reason and emotion in our mental operations, Klaus Scherer’s version of appraisal theory is compatible with mounting evidence of the brain’s complexity. Having developed a scientific line of argument against transhumanists’ lens on the mind and brain, the author turns to Aristotle’s rational essentialism. Wrongly invoked to support transhumanists’ extreme version, Aristotle’s rational essentialism incorporates a necessary role for nonrational faculties and intrapsychic harmony. While transhumanists’ lens on the mind and brain is at odds with contemporary findings, Aristotle’s view of the mind shares important commitments with Scherer’s appraisal theory and is broadly compatible with an emerging picture of the brain’s complexity.

Freedom and Responsibility

2020 ◽  
pp. 137-184
Author(s):  
Thomas H. McCall ◽  
Keith D. Stanglin
Keyword(s):  
Nineteenth Century ◽  
Race And Ethnicity ◽  
Theological Anthropology ◽  
Original Sin ◽  
Trinitarian Theology ◽  
Reformed Theology ◽  
Doctrine Of God ◽  
Knowledge Of God ◽  
The Mind ◽  
Freedom And Responsibility

In Chapter 4, we survey how claims to knowledge of God were defended in the nineteenth-century Methodist context; we look both at the theological methods that were employed and how apologetic impulses functioned within those prolegomena. Turning to the doctrine of God, we trace some of the momentous changes that took place as Wesleyan theology wrestled with modern challenges in relation to its classical inheritance (especially in relation to classical doctrines of perfection, simplicity, aseity, immutability, and omniscience as well as Trinitarian theology). With regard to theological anthropology, we see how the major Methodist theologians wrestled not only with long-standing disputes (for example, the mind–body relation) but also with current debates (for example, race and ethnicity). We trace the Wesleyan debates (both internally, and against traditional Reformed theology as well as revisionism and modernism) over the doctrine of original sin.

‘Ghettos of the Mind’: Realities and Myths in the Construction of the Social Identity of a Dublin Suburb

2014 ◽  
Vol 19 (3) ◽  
pp. 15-29 ◽  
Author(s):  
Martina Byrne ◽  
Brid Ni Chonaill
Keyword(s):  
Social Identity ◽  
Large Body ◽  
Lower Class ◽  
Data Sets ◽  
The North ◽  
The Social ◽  
Irish People ◽  
The Republic ◽  
The Mind ◽  
Short Time

The Republic of Ireland became a country of net immigration for the first time in 1996 and a large body of literature has since examined, at macro and meso levels, migration rates and flows, impacts on the economy, and issues around integration. However, there is a paucity of sociological literature on the effect of unprecedented immigration at local or community level. This article addresses this deficit by demonstrating how the social identity of a place, home to a particularly high proportion of immigrants over the past two decades, is differentially constructed in the perceptions of those situated within, and outside. We combine data sets from two qualitative studies of Irish people living inside and outside the north Dublin suburb of Blanchardstown firstly to underpin our argument that place identities are processes which can change in a relatively short time and that some place identities are more mythical than real. Secondly, we problematise the term ‘ghetto’, as employed by some participants in this study and argue that racial, ethnic and class positionality is implicated in the construction of the relational identities of the place. Our findings contrast residents’ awareness of the heterogeneity of their area with outsiders’ construction of a homogenous raced and classed identity for the place, namely, one where large numbers of lower class and black immigrants live.

Practical Implementation of Integrative Bilingual Teaching/Learning at a Technical University

2022 ◽  
pp. 352-372
Author(s):  
Eduard Krylov
Keyword(s):  
Dynamic Balance ◽  
Practical Implementation ◽  
Pilot Projects ◽  
Integrative Education ◽  
Bilingual Teaching ◽  
Mental Operations ◽  
Technical University ◽  
Teaching Learning ◽  
The Mind ◽  
Practical Recommendations

The value and importance of the integrative bilingual teaching/learning foreign language and engineering is building bridges between cognition and communication, finding ways for establishing a dynamic balance between them in the mind of an engineering student. This explains the choice of study exercises and activities, related to mental operations and psychological patterns. The chapter discusses the peculiarities of solving problems, other active exercises, and gives some practical recommendations. Here also is the eternal problem of CLIL-like integrative education: How much language? How much content? Concerning language material, it is determined by some basic volume, demand driven by professional duties and interests. All the suggested ideas were tested at a Russian technical university for years. The difficulties, findings, and results of the pilot projects for bachelors and masters are discussed.

scholarly journals XXII. On the mechanical performance of logical inference

1870 ◽  
Vol 160 ◽  
pp. 497-518 ◽  
Keyword(s):  
Mechanical Performance ◽  
Human Hand ◽  
Logical Inference ◽  
Decimal System ◽  
Convenient Form ◽  
Mental Operations ◽  
The Mind ◽  
Mechanical Assistance

1. It is an interesting subject for reflection that from the earliest times mechanical assistance has been required in mental operations. The word calculation at once reminds us of the employment of pebbles for marking units, and it is asserted that the word α ' ρiϴμòc is also derived from the like notion of a pebble or material sign. Even in the time of Aristotle the wide extension of the decimal system of numeration had been remarked and referred to the use of the fingers in reckoning; and there can be no doubt that the form of the most available arithmetical instrument, the human hand, has reacted upon the mind and moulded our numerical system into a form which we should not otherwise have selected as the best. 2. From early times, too, distinct mechanical instruments were devised to facilitate computation. The Greeks and Romans habitually employed the abacus or arithmetical board, consisting, in its most convenient form, of an oblong frame with a series of cross wires, each bearing ten sliding beads. The abacus thus supplied, as it were, an unlimited series of fingers, which furnished marks for successive higher units and allowed of the representation of any number. The Russians employ the abacus at the present day under the name of the shtshob , and the Chinese have from time immemorial made use of an almost exactly similar instrument called the schwanpan .

Innateness

2012 ◽  
Author(s):  
Steven Gross ◽  
Georges Rey
Keyword(s):  
Environmental Factors ◽  
John Locke ◽  
External World ◽  
Causal Process ◽  
Common Currency ◽  
Genes And Environment ◽  
Biological Determinants ◽  
Mental Operations ◽  
The Mind ◽  
Relevant Factors

The article describes to what extent the structures and contents of the mind are innate, and to what extent they are learned or otherwise acquired from the environment. Aristotle argued that all ideas are derived from experience by a causal process in which forms (or properties of things) in the external world are transmitted into the mind. John Locke insisted that the simple ideas are derived from sensation, and all other ideas are constructed from the simple ones by the mental operations of compounding, comparing, and abstracting. Sober emphasized that there is no common currency with which to compare the relative contributions of genes and environment and suggested that biological determinants do not in general decompose into amounts of genetic versus nongenetic force. Sober suggested that there might not be a single specification of relevant environments and one might need to fix the range pragmatically as it varies with explanatory interests. Ariew suggested that what matters for innateness is whether a trait's emergence is sensitive to certain specific kinds of environmental factors, where the relevant factors can vary with the trait in question and indeed with one's explanatory interest. Fodor's initial agument for the innateness of concepts was quite simple. He pointed out that standard accounts of learning a trait it as a process of hypothesis confirmation.

scholarly journals Conceptual and Theoretical Issues in Forensic Neuropsychology

2021 ◽  
Author(s):  
◽  
Lucy Jackson
Keyword(s):  
Deception Detection ◽  
Large Body ◽  
Forensic Neuropsychology ◽  
Explicit Consideration ◽  
Experimental Protocols ◽  
Subject Areas ◽  
Offending Behaviour ◽  
The Mind ◽  
Theoretical Issues ◽  
Insight Into

<p>Neuroscience is an increasingly popular area of study in forensic psychology, and there is a large body of empirical research emerging investigating the biological basis of offending behaviour. However, the theoretical and conceptual underpinnings of forensic neuroscience are currently underdeveloped. The aim of this thesis is to provide insight into the potential issues with forensic neuroscience and provide a number of suggestions for researchers to follow. This thesis begins by outlining these theoretical, conceptual, and empirical issues that researchers should be considering, including conceptualisation of the mind, explanation, and the methodological issues in neuroscience. These issues are then examined in more detail using two specific subject areas as exemplars: deception detection and mind-reading by brain-reading. This thesis concludes with suggestions for future researchers, which include making sure that research is based on a strong theoretical framework, clarity around the kind of explanation employed and use of explanatory pluralism, clear and consistent definitions to improve conceptual validity, using consistent and conceptually valid experimental protocols, and explicit consideration of technical limitations and how they impact the validity of the experiment.</p>

Problems of Mind as Action

1998 ◽  
pp. 73-83
Author(s):  
Nikolaj Demjançuk
Keyword(s):  
Theory Of Mind ◽  
Cognitive Science ◽  
Current Literature ◽  
Large Body ◽  
Scientific Understanding ◽  
Philosophical Theory ◽  
Physical Behavior ◽  
Recent Advances ◽  
The Mind

A large body of current literature details significant recent advances in our understanding of the mind. This boom has partly been stimulated by the explosive growth of cognitive science dedicated to advancing scientific understanding. This paper focuses on the nature of philosophical theory of mind, and seeks to find ways of talking about mind. Central to my argument is developing a description of mind as action. Concessive behaviorism depicts the mind as presented in complexes of actions and tendencies to act. If a philosophical theory of the mind emphasizes waving over silent cogitations and brain events, then it is behaviorist. This position defines the eliminative behaviorism. The most powerful and straightforward kind of non-eliminative behaviorism is analytic behaviorism arising from the view that all statements containing mental vocabulary can be analyzed into statements containing just the vocabulary of physical behavior. But perhaps a better way to think of beliefs is to understand only what each of them does, which is at the heart of the view known as functionalism. Therefore, special attention is given to considering behaviorist and functionalist theories.

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