Jon A and Paola, The amount of research in neuroscience in the past 50 years is immense compared to the studies of the left & right hemispheres in the 1970s. Among other things, the neuroscientists today have much more sympathy with introspective studies than they have with people (in the 1990s) who dismissed introspection as "folk psychology". With fMRI scanners, they can correlate what people say with what areas of the brain light up while they are talking. For the following discussion, please open the slides from Section 6 of eswc: http://jfsowa.com/temp/eswc6.pdf . Slides 2: Today's artificial NNs for machine learning are limited to learning functions. Andrew Ng (slide 3) observed that ANNs automate tasks that take less than one second of time for humans. That's important for perception and classification, but it can't do anything beyond a fish-level or cat-level of cognition (slide 4). Slides 5 to 8: A study of cognitive learning that goes far beyond anything that todays ANNs can do. Slides 9 to 11 relate that kind of learning to the categories by C. S. Peirce. Slide 13 shows a diagram by Robert Rosen (1985) who discussed the way formal reasoning can enable people to anticipate (predict) what will happen. But animals that don't know language or logic can also anticipate the future. Slide 14 shows an extension to Rosen's diagram based on two kinds of reasoning: simulation of mental models and logical inference with symbolic models. Slides 15 to 18 discuss the importance of the cerebellum for mathematics and for a much broader range of mental imagery. It confirms Peirce's claim about the importance of imagery (icons and diagrams). Slide 19 states introspective reports by the mathematician Paul Halmos and the physicist Albert Einstein. Their comments are consistent with the comments by C. S. Peirce about his own methods of reasoning. For more detail, see the slides about Peirce, Polya, and Euclid -- all of whom used imagery as the *foundation* for reasoning in mathematics. As they say, a formal proof is just useful for (a) checking to make sure that no details were omitted, and (b) communicating a precise statement with other mathematicians. But mental imagery is essential for thinking about a problem and discovering a solution. For even more detail, see the 117 slides (with references) about "The virtual reality of the mind", http://jfsowa.com/talks/vrmind.pdf . In particular, see Section 2 "The role of the cerebellum" in slides 33 to 54. Tare are a small number of people who were born without a cerebellum and survived. But their ability to do any kind of complex reasoning is extremely limited. John
Jon A and Paola,
The amount of research in neuroscience in the past 50 years is immense compared to the studies of the left & right hemispheres in the 1970s. Among other things, the neuroscientists today have much more sympathy with introspective studies than they have with people (in the 1990s) who dismissed introspection as "folk psychology".
With fMRI scanners, they can correlate what people say with what areas of the brain light up while they are talking. For the following discussion, please open the slides from Section 6 of eswc: http://jfsowa.com/temp/eswc6.pdf .
Slides 2: Today's artificial NNs for machine learning are limited to learning functions. Andrew Ng (slide 3) observed that ANNs automate tasks that take less than one second of time for humans. That's important for perception and classification, but it can't do anything beyond a fish-level or cat-level of cognition (slide 4).
Slides 5 to 8: A study of cogni tive learning that goes far beyond anything that todays ANNs can do. Slides 9 to 11 relate that kind of learning to the categories by C. S. Peirce.
Slide 13 shows a diagram by Robert Rosen (1985) who discussed the way formal reasoning can enable people to anticipate (predict) what will happen. But animals that don't know language or logic can also anticipate the future. Slide 14 shows an extension to Rosen's diagram based on two kinds of reasoning: simulation of mental models and logical inference with symbolic models.
Slides 15 to 18 discuss the importance of the cerebellum for mathematics and for a much broader range of mental imagery. It confirms Peirce's claim about the importance of imagery (icons and diagrams). Slide 19 states introspective reports by the mathematician Paul Halmos and the physicist Albert Einstein. Their comments are consistent with the comments by C. S. Peirce about his own methods of reasoning.
For more detail, see the slide s about Peirce, Polya, and Euclid -- all of whom used imagery as the *foundation* for reasoning in mathematics. As they say, a formal proof is just useful for (a) checking to make sure that no details were omitted, and (b) communicating a precise statement with other mathematicians. But mental imagery is essential for thinking about a problem and discovering a solution
For even more detail, see the 117 slides (with references) about "The virtual reality of the mind", http://jfsowa.com/talks/vrmind.pdf . In particular, see Section 2 "The role of the cerebellum" in slides 33 to 54. Tare are a small number of people who were born without a cerebellum and survived. But their ability to do any kind of complex reasoning is extremely limited.
John
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