Now that you remind me, I have heard of Avi Sion before, but I think I was turned off by something. Maybe his book was just too long to read at the time. I'll give him a second look.
Most people can't solve 3 part syllogism, and you can forget about compound deduction. Practical logic is either A) Not taught, or B) Taught extremely badly to the point where you are better off inventing your own methods. I agree that pure deduction is the least used form of logic, simply because the conditions don't often occur where it is profitable. However, it shouldn't be so badly done as it is.
I've never seen a method invented in the 20th century that would be useful for solving a practical problem. People say these new methods are useful, but I never see them used in earnest. Of course, maybe I'm wrong about that. That's the market research.... seeing whether modern logicians/mathematicians think these problems are trivial and how they go about solving them. I've previously sent them out to selected individuals who are philosophy/logic professors and got crickets in return.
I really wanted to post to stackexchange or other sites like that with a wider audience, but they don't seem to allow paying people. You can only earn whatever points they use. Ever since the Drexel math forums got turned into a porno site, it's been tough to find a reasonable forum. So, I'm grateful this forum exists.
The first challenge problem was selected because I thought Dodgson's answer was wrong. I misunderstood what 19th century personal checks were like. So, Dodgson's answer stands.
The second challenge problem is the Brothers problem (I believe problem #7 in the back of Dogdson's 1897 book.) It should legitimately take a while to work. Dodgson didn't give an answer, and in fact it can have many answers. The goal is to find the longest answer that uses the most rules. A secondary goal is to understand why certain rules can't be used at different times. And I think this was even beyond what Dodgson could do. In all his writings I've seen, he really focused on getting an answer rather than understanding a problem. It's a 19th century thing, I suspect. His method of trees (and the various derivatives) will work, but I am going to rule them out. I don't think anyone even knows these methods any more. I need to phrase the problem so that people can't just dig up a method they don't know and don't use for the purpose of winning.
By the way, you may not want to post solutions of advanced problems to the internet. New people come along all the time, and these problems are like sphinxes. If young people find the answers too readily, they won't put in the time to work the problems. And I think solving these puzzle problems is an accomplishment. There should be an age requirement of 30+ years old to view these XXXX answers. :grinning:
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How did you come across this forum? It belongs to Avi, and as far as I'm aware there is only one link to it - at his site. The link isn't particularly visible either, it's near the foot of this page (discussion area). There is very little traffic here either; I'm the only one (apart from Avi) who has posted in the last few months. There are a number of philosophy forums online, but hardly any have a section dedicated exclusively to logic, sadly. Not many people are interested in the subject, but I find it fascinating.
I can understand that many would be put off by Avi's books, because they are not exactly light bedtime reading - even for logic books - and there aren't many examples and applications in them. However, they are worthy of study because they contain many new insights and systems of logic, although very little of what you would call 'modern' logic (if you take 'modern' as being 'mathematical'). The style is very much that of the traditional syllogism, but the content is not just a rehash of traditional methods.
@Avi: Thanks for the email. Nice site, but Captcha is not working. Just deleted my last reply because I tried to preview before submitting and then had no captcha, so it kicked me. Also, the quote option doesn't actually insert code that I can edit. It just quotes the whole thing and won't let me edit the quoted text. Using Chrome on Linux.
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I look forward to hearing about Gregg's work. I couldn't see anything.
I have a love/hate opinion of Bartley. I loved the fact that he made Dodgson's work available. However, I felt he disparaged Dodgson unfairly. I don't remember him being critical of the Logicist school. But, I wasn't really reading the book for Bartley's opinion on logic. I was reading to get a better look at what Dodgson was doing. I view 20th century logic as a retreat into mysticism. This sort of thing happens when progress stalls. I think Bartley entertained thoughts that modern logic represented an advance in human knowledge. I don't remember him bucking any trends.
Where did you see that Bartley sent the schoolboys problem out? I didn't know that. I know that Dodgson was annoying people all over the world with these problems. The schoolboys problem currently has a solution posted on the internet, although not a complete one. I think Froggy's problem is also solved, but I haven't checked it.
Lonergan's Insight is written in the exact style that Thomas Aquinas used. However, Lonergan doesn't mince words, and he intends to be very flexible. Every sentence is loaded with meaning and appreciation for the complexities of human thought and the physical world. The book isn't long in the sense of the number of words, but it's going to be slow reading to comprehend what he's saying. If you like it, you will probably need a tutor, or at least someone to talk with who knows classical philosophy. I had a tutor. The early chapters are a good read, but he's a Jesuit priest, so the end of the book becomes very Roman Catholic at some point. The goal of the book is to justify revealed religion using only philosophy, which is quite a stretch. For example, chapter XIX.10 is "Affirmation of God". Don't feel obligated to read the whole thing.
The real gem is his treatment of epistemology in general.
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