The Logic Forum Discussion Area

Logic
Start a New Topic 
Author
Comment
View Entire Thread
Re: I'm offering a prize to solve one of Lewis Carroll's elementary logic problems using modern me


I looked at the index of Gregg's book. It looks like the same old stuff. Can you be more specific about this new method in his book?


I'll post an example here in the next day or two, using one of Carroll's syllogisms. I don't have time today.


I would suggest looking at Lewis Carroll's Symbolic logic by Bartley (1970s) if you haven't already.


Yes, I have that book. I particularly like the introduction in which he talks about the three main periods of logic:

1. The traditional Aristotelian logic which lasted from Aristotle to Boole.
2. The 'algebraic' phase which was initiated by Boole, and includes De Morgan, Venn, Jevons, Keynes... and Carroll. It came to an end at the close of the 19th century.
3. Modern mathematical logic which started with Frege/Russell, and is now the dominant force.

He notes that while period 2 was revolutionary, it never really got a chance to take off because it was eclipsed by period 3, which was equally revolutionary. But the conception of logic and its purpose was quite different between the periods. Modern mathematical logic was intended to be a tool for analysing the foundations of mathematics, and isn't especially suitable for general philosophy or everyday use. Its main concern is with axiomatisation, proof construction, decision procedures, consistency proofs, metalogic, etc. In modern logic texts, both the premises and conclusion are given, and the aim is to examine the argument for validity.

But the main aim of the algebraic logic, as conceived by Boole and others in this period, was to extract as much information as possible with regard to a term or combination of terms, given a set of premises. Apparently, Bartley sent Carroll's Schoolboy Problem to logicians of "high distinction" over a period of 10 years, and none of them were able to solve it. He also complains that even though contemporary philosophers are given specialised education in mathematical logic, their ordinary work in philosophy is littered with elementary logical mistakes, and argues that these are just the kind of mistakes that 19th century logical algebra works to prevent, whereas modern logic is largely irrelevant to their prevention.


I would also suggest looking a Bernard Lonergan's book "Insight".


Will do, although I admit to having a bit of a love-hate relationship with philosophy and often get impatient with it. Much of what passes for philosophy these days is in my opinion pretentious drivel, or mere word salad. It's not so bad if the writing is clear, but this isn't common in my experience. That said, I don't have any formal education in philosophy (my background is electronics and mathematics), and tire easily reading long tracts, so maybe I'm being a bit harsh.


What's the site's address? You can email if it's not ready for the public.


I want to build up the content before I publish it, and what I have at the moment is little more than notes, but I'll post the link here when it goes live. This is long term project though, so it might be several months away.

Re: I'm offering a prize to solve one of Lewis Carroll's elementary logic problems using modern me

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.

Something about you (optional) I'm issuing logic puzzle challenges