Another excellent book — notably better, I'd say — on the same topic is William Stanley Jevons' Elementary Lessons in Logic, Deductive and Inductive[1]. It's written with simplicity and clarity, without any showing off of terminology for its own sake.
If we're talking about inductive reasoning then it may pay greater dividends to go to a primary source that really set the stage for everything that came after him. This is David Hume in the form of his Treatise on Human Nature [0]
I agree, this document is really only useful for historical development.
However, it is useful for tracking down some history. I've been trying to track down this expression: "All men are mortal; Socrates is a man; therefore Socrates is mortal". It's often quoted, but no one gave me a source. Using this old book I managed to track it back to at least A System of logic... by John Stuart Mill, 1843, Book II Chapter 3 page 245. https://archive.org/details/systemoflogicrat01millrich/page/...
The quote may be even older, but that was still a help.
If anyone knows an older source, I'd love to know. But that at least helped.
Anyway: while this document is only useful for its historical connection, as a way to investigate the history of logic it's interesting.
I disagree. I think this sort of traditional, verbal logic becomes ingrained in the mind in a way that more modern logical systems don't. While we have a more rigorous, strictly correct understanding of logic now, its separation from the expression of ideas in a subset of natural language makes it harder to apply to one's day-to-day thought. I greatly value my early exposure to syllogistic logic and early Greek philosophy; I think it improved my reasoning and thereby my life.
>Mathematics treats of the relations of all sorts of things considered as quantities, namely, as equal to, or greater or less than, one another.
This was not actually true when this book was written: Euler's formula was discovered in 1748, which I would consider evidence that complex numbers were broadly "around" at least a century before 1898. Complex numbers are not ordered, (for example, is 1 less than or greater than i?), so this claim about math isn't right.
>But, as we have seen, Logic does not investigate the truth, trustworthiness, or validity of its own principles; nor does Mathematics
It does now!
>As a Regulative Science, pointing out the conditions of true inference (within its own sphere), Logic is co-ordinate with [...] (ii) Æsthetics, considered as determining the principles of criticism and good taste.
It is funny now that people would study up on logic so they could prove to their colleagues whether or not the latest production at the local theater was any good.
Your comment seems determined to take the least charitable possible interpretation of the material from the first few pages of the book. I'm sad that you chose not to engage with the value it could provide.
Least charitable? There's no way that the author could have been expected to anticipate how logic would develop over the next century, I'm just looking at it from a modern perspective.
Another excellent book — notably better, I'd say — on the same topic is William Stanley Jevons' Elementary Lessons in Logic, Deductive and Inductive[1]. It's written with simplicity and clarity, without any showing off of terminology for its own sake.
[1]: https://archive.org/details/elementarylesson00jevo/page/n4
If we're talking about inductive reasoning then it may pay greater dividends to go to a primary source that really set the stage for everything that came after him. This is David Hume in the form of his Treatise on Human Nature [0]
[0] http://www.gutenberg.org/files/4705/4705-h/4705-h.htm
This book predates many important developments of the 20th century. I'd say its value is nearly zero nowadays, except from a historical standpoint.
I agree, this document is really only useful for historical development.
However, it is useful for tracking down some history. I've been trying to track down this expression: "All men are mortal; Socrates is a man; therefore Socrates is mortal". It's often quoted, but no one gave me a source. Using this old book I managed to track it back to at least A System of logic... by John Stuart Mill, 1843, Book II Chapter 3 page 245. https://archive.org/details/systemoflogicrat01millrich/page/... The quote may be even older, but that was still a help.
If anyone knows an older source, I'd love to know. But that at least helped.
Anyway: while this document is only useful for its historical connection, as a way to investigate the history of logic it's interesting.
What a great snippet of info to know, thanks for posting this. I often use that syllogism as an example for some visual logic software I'm writing.
I disagree. I think this sort of traditional, verbal logic becomes ingrained in the mind in a way that more modern logical systems don't. While we have a more rigorous, strictly correct understanding of logic now, its separation from the expression of ideas in a subset of natural language makes it harder to apply to one's day-to-day thought. I greatly value my early exposure to syllogistic logic and early Greek philosophy; I think it improved my reasoning and thereby my life.
What would be the modern equivalent? If I want to study the bottom most foundations of mathematics, is logic the right choice?
>Mathematics treats of the relations of all sorts of things considered as quantities, namely, as equal to, or greater or less than, one another.
This was not actually true when this book was written: Euler's formula was discovered in 1748, which I would consider evidence that complex numbers were broadly "around" at least a century before 1898. Complex numbers are not ordered, (for example, is 1 less than or greater than i?), so this claim about math isn't right.
>But, as we have seen, Logic does not investigate the truth, trustworthiness, or validity of its own principles; nor does Mathematics
It does now!
>As a Regulative Science, pointing out the conditions of true inference (within its own sphere), Logic is co-ordinate with [...] (ii) Æsthetics, considered as determining the principles of criticism and good taste.
It is funny now that people would study up on logic so they could prove to their colleagues whether or not the latest production at the local theater was any good.
Your comment seems determined to take the least charitable possible interpretation of the material from the first few pages of the book. I'm sad that you chose not to engage with the value it could provide.
Least charitable? There's no way that the author could have been expected to anticipate how logic would develop over the next century, I'm just looking at it from a modern perspective.