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NoahsArk

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### George Boole's Laws of Thought

Hello. I was inspired to try and read George Boole’s Laws of Thought. I'm at a point where I'm stuck and near ready to quit. No you tube videos help. The link to the pdf of the book is: 15114-pdf.pdf (gutenberg.org). I'm so stuck that it's hard for me to even articulate what I'm stuck on. I got up to chapter 5, page 52 which states the following:

f(x) = ax + b(1-x) It's assumed in this expression that x can only have values of 0 and 1. f(1) = a, f(0) = b. Substituting back in we get f(x) = f(1)x +f(0)(1-x). I sort of follow this, but then he gets into very long expressions with f(x,y) which I can't follow at all, and haven't found anything explaining what he means. Also, I'm not sure what is significant about the form f(x) = ax + b(1-x). If you take away the f(x) part, I think the right side, ax + b(1-x) means all x's that have the property a plus all b's which are not x's. What's the reason for making it an equation with f(x)? What does it even mean for an expression like this to be a function of x? When I think of functions, I think of numerical functions like ## f(x) = x^2 ##.

Boole goes haywire then writing expressions involving f(x,y) which go on for three lines or more, then adding zeroes to them, etc. Can someone please help me understand what's on Boole's mind here and what is the general idea of what he is talking about?

Also, what was he thinking when he created a system of math with only 0's and 1's 80 years before computers were invented? What was the possible application of such a system back then? It's supposed to be a book that changed the world, but I can't find any source of information explanation what the light is behind all of it and what Boole's big insight was. At first I just had a feeling that this book was something great, and felt like I had some intuitive understanding of what he might have been getting at. Now I'm just totally lost.

Thanks