The first book, "Of the Understanding," goes into Hume's idea that all of human knowledge is based off of our senses and experiences. Within this book, he claims that fact is something that does not come about from an instinct, but is instead experienced, that abstract ideas like the soul of God can not be proven via metaphysics because they cannot be experienced, and talks about how experience is used to infer math and space, which consist of a plethora of related ideas. He then goes into his various methods of philosophical exploration, such as the "fork," which divides truth into two categories: the connection of ideas, and the the necessary truths, and the "microscope" and the "razor," in which the microscope is the understanding of a concept by understanding it in its simplest terms, and the razor, which is the principle that is something cannot be broken into a simpler element, it has no meaning.
The second book, "Of the Passions," he discusses passions as an element of "secondary" impressions. Secondary impressions are those that arise from reflection, rather than original impressions which arise from the senses. Hume then distinguishes between direct and indirect passions, in which direct consist of feelings such as desire, joy, hope, and fear, and indirect consist of love, hate, and pride. After these explanations, he states that human actions are driven by passions, rather than reasoning, and therefore our actions cannot be deemed "reasonable" or "unreasonable."
The third book, "Of Morals," goes into Hume's thoughts on vice and virtue in relation to the concepts deliberated on in the first two books. He states that vice and virtue are not solid ideas, but rather impressions. He says that vice can be deduced when pain is felt, and virtue through feeling pleasure. Hume then says that inanimate objects and animals cannot be the cause for our impressions on morality. Lastly, he says that morality is not something that can be inferred through introspection, but rather through the impact our actions have on others.
So, what does this all have to do with cognitive science? Well, this piece was one of the first to describe a coherent argument of the connection between human perception, emotion, and reasoning, which are all cornerstone objects of cognitive science, along with the more modern incorporations of memory and attention. Hume also makes a natural, psychological examination of human's relationship with math and science, which today has evolved into the studies of neuroscience and artificial intelligence. Many of Hume's ideas ultimately serve to stand as part of the philosophical aspect to cognitive science, which now, after being combined with linguistics, neuroscience, anthropology, and artificial intelligence, has become one of the most comprehensive fields concerning human behavior.
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