Computational Complexity and the Origin of Universals
ABSTRACT: This paper establishes close relationships between fundamental problems in the philosophical and mathematical theories of mind. It reviews the mathematical concepts of intelligence, including pattern recognition algorithms, neural networks and rule systems. Mathematical difficulties manifest as combinatorial complexity of algorithms are related to the roles of a priori knowledge and adaptive learning, the same issues that have shaped the two-thousand year old debate on the origins of the universal concepts of mind. Combining philosophical and mathematical analyses enables tracing current mathematical difficulties to the contradiction between Aristotelian logic and Aristotelian theory of mind (Forms). Aristotelian logic is shown to be the culprit for the current mathematical difficulties. I will also discuss connections to Gödel’s theorems. The conclusion is that fuzzy logic is a fundamental requirement for combining adaptivity and apriority. Relating the mathematical and philosophical helps clarifying both and helps analyzing future research directions of the mathematics of intelligence.
I. Introduction: Mathematics and Philosophy
The two-thousand year old debate on the origins of universal concepts of mind was about the roles of adaptivity or learning from experience vs. the a priori knowledge (the inborn or God-given). It is closely related to the epistemological problem of the origins of knowledge. The problem of combining adaptivity and a-priority is fundamental to computational intelligence as well as to understanding human intelligence. There is an interrelationship among concepts of mind in mathematics, psychology, and philosophy, which is much closer than currently thought among scientists and philosophers of today. From the contemporary point of view, the questions about mind posed by ancient philosophers are astonishingly scientific. A central question to the work of Plato, Aristotle, Avicenna, Maimonides, Aquinas, Occam, and Kant was the question of the origins of universal concepts. Are we born with a priori knowledge of concepts or do we acquire this knowledge adaptively by learning from experience? This question was central to the work of ancient philosophers, medieval theologists, and it was equally important to theories of Freud, Jung, and Skinner. The different answers they gave to this question are very similar to the answers given by McCulloch, Minsky, Chomsky and Grossberg.
When 2300 years ago Plato faced a need to explain our ability to conceptualize, he concluded that concepts are of a priori origin. The philosophy based on the transcendental, a priori reality of concepts was named realism. During the following 2000 years the concept of a-priority was tremendously strengthened by the development of monotheistic religion in Europe, to the extent that it interfered with empirical studies.
In this paper I will evaluate and present A.M. Turing’s test for machine intelligence and describe how the test works. I will explain how the Turing test is a good way to answer if machines can think. I will also discuss Objection (4) the argument from Consciousness and Objection (6) Lady Lovelace’s Objection and how Turing responded to both of the objections. And lastly, I will give my opinion on about the Turing test and if the test is a good way to answer if a machine can think.
One of the major differences between humans and animals is our ability to reason and differentiate our actions from our instincts (Barrett, 2011, p. 3). Justin Barrett further explains this distinction in the first chapter of his book, Cognitive Science Religion and Theology. He explains that cognitive science recognizes the uniqueness of the human mind and focuses on explaining the thinking processes that take place(Barrett, 2011, p. 5). This may seem similar to what the field of neuroscience aims to do but, cognitive science is not as interested with the biological functions of the brain. Instead of looking at physical structures Barrett writes, that cognitive science focuses on broader processes such as perception, attention, memory, reasoning and learning (Barrett, 2011, p. 7). All of these processes interact with each other to create the big questions asked in cognitive science. Some of these big underlying questions of cognitive science are explored in this first chapter, questions such as “What is innate?” or “How are mind and bodies
There is almost no doubt that there is a relationship between psychology and philosophy. Indeed, many people actually considering that the philosophies related to and concerned with the mind and thought are the precursor to modern psychology. Of course, most of these philosophies were decidedly western, or popular in the west. However, the problem with our western views of consciousness in philosophy and psychology is that often times the way we view the conscious process leads to a so-called "infinite regression." That is to say, if we see consciousness as a set of rules guiding our experiences in life, there must also be another set of rules that defines how we know when to use those rules, and so on and so forth. (Kurak 2001, 18-19). In this paper, I will attempt to show how we can turn to Buddhist principles to help us gain a better understanding of human consciousness.
Rationalism and empiricism were two philosophical schools in the 17th and 18th centuries, that were expressing opposite views on some subjects, including knowledge. While the debate between the rationalist and empiricist schools did not have any relationship to the study of psychology at the time, it has contributed greatly to facilitating the possibility of establishing the discipline of Psychology. This essay will describe the empiricist and rationalist debate, and will relate this debate to the history of psychology.
It could be argued that the most extensive of these theories is Cattell, Horn and Carroll’s (CHC) approach, as it comes from a combination of the three’s work. This essay will explore how the approach came to be, how well it works as an explanation for intelligence and if the theory is well supported.
Research completed on infants, children, and adults across a multitude of cultural environments proposes that no human mind is alike. Spelke found that the four systems on core knowledge are a basis for cognitive systems. This means that some humans learn things easily, while others learn with greater difficulty (Kinzler and Spelke 2007). The core knowledge theory can be seen as both a positive and negative topic. The possible fact that human beings, as well as other species, could potentially be predisposed to cognitive capacities instead of acquiring capacities through experience is an overwhelming and controversial topic. There is not enough research or evidence to deem the core knowledge theory to be an absolute fact, but a strong opinion could be derived. If these cognitive capacities are integrated into us before birth, that would create a strong foundation for building new skills or capacities; it would be difficult to imagine an individual starting their life without this foundation of core symptoms because problems may arise. The core knowledge theory is helpful when studying development because the idea has been apparent in studies since Jean Piaget and could eventually unveil the roots of an evolutionary
One of the hottest topics that modern science has been focusing on for a long time is the field of artificial intelligence, the study of intelligence in machines or, according to Minsky, “the science of making machines do things that would require intelligence if done by men”.(qtd in Copeland 1). Artificial Intelligence has a lot of applications and is used in many areas. “We often don’t notice it but AI is all around us. It is present in computer games, in the cruise control in our cars and the servers that route our email.” (BBC 1). Different goals have been set for the science of Artificial Intelligence, but according to Whitby the most mentioned idea about the goal of AI is provided by the Turing Test. This test is also called the imitation game, since it is basically a game in which a computer imitates a conversating human. In an analysis of the Turing Test I will focus on its features, its historical background and the evaluation of its validity and importance.
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Evolutionary psychology is a specialist field within the spectrum of psychological enquiry, which seeks to examine and understand some of the predominant reasoning behind the concept of why the human species, whilst biologically similar to other species on the planet, is so very distinct in terms of intelligence and mental progression; demonstrated by the multifaceted and complex social structures we have created. Primary to this domain of evolutionary psychological interest is the notion of ‘theory of mind’, which was developed and advocated by Premack and Woodruff (1978), and has been the topic of fierce discussion and analysis since. It has resulted in manifold research studies and commentaries, regarding the topic, from an extensive range of sources within the academic field of psychology. This essay intends to explore the concept of theory of mind, using examples and research studies to fathom its relevance, application and significance within evolutionary psychology as a whole.
Many of the most prominent critics of Evolutionary Psychology (Buller and Kaplan) are deeply skeptical of Evolutionary Psychology’s two defining tenets. The first tenet says the human mind is “massively modular,” composed of a myriad of independent, special purpose (“domain-specific”) modules, each evolved to help our ancestors survive and reproduce during the hunter-gather period of human evolution. The second tenet focuses on the idea that no subsequent cognitive adaptations to novel environments have occurred (Machery 2007; Rellihan 2012). According to prominent critic David Buller (2005), evolutionary psychologists think that humans are a le...
Since antiquity the human mind has been intrigued by artificial intelligence hence, such rapid growth of computer science has raised many issues concerning the isolation of the human mind.
The development of psychology like all other sciences started with great minds debating unknown topics and searching for unknown answers. Early philosophers and psychologists such as Sir Francis Bacon and Charles Darwin took a scientific approach to psychology by introducing the ideas of measurement and biology into the way an indi...
The traditional notion that seeks to compare human minds, with all its intricacies and biochemical functions, to that of artificially programmed digital computers, is self-defeating and it should be discredited in dialogs regarding the theory of artificial intelligence. This traditional notion is akin to comparing, in crude terms, cars and aeroplanes or ice cream and cream cheese. Human mental states are caused by various behaviours of elements in the brain, and these behaviours in are adjudged by the biochemical composition of our brains, which are responsible for our thoughts and functions. When we discuss mental states of systems it is important to distinguish between human brains and that of any natural or artificial organisms which is said to have central processing systems (i.e. brains of chimpanzees, microchips etc.). Although various similarities may exist between those systems in terms of functions and behaviourism, the intrinsic intentionality within those systems differ extensively. Although it may not be possible to prove that whether or not mental states exist at all in systems other than our own, in this paper I will strive to present arguments that a machine that computes and responds to inputs does indeed have a state of mind, but one that does not necessarily result in a form of mentality. This paper will discuss how the states and intentionality of digital computers are different from the states of human brains and yet they are indeed states of a mind resulting from various functions in their central processing systems.
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