I highly recommend a course / book in symbolic logic. Sometimes it is called propositional logic.
Essentially it teaches you how to formalize arguments into their abstract symbolic forms, and then evaluate the argument on that form. This is a lot easier than trying to determine an argument’s validity purely from its English written version.
I used Klenk’s Understanding Symbolic Logic, but I’m sure there are more modern courses or books.
I bet you'd probably see Klenk and Copi, both very old textbooks kept at least reasonably up to date, used in some of today's classes. "The Logic Book" (Bergmann, Moor, Nelson) is used around sometimes. I think there'd probably also be an appetite among some HN people to tackle the MIT OpenCourseware offerings, which at first glance look pretty good and challenging.
I can recommend E.J. Lemmon's Beginning Logic as a first book. It also contains an appendix with a list of important logic books and brief description of them. I'm curious to know whether a more recent, equally well-done, list exists.
lo_zamoyski · 7h ago
I don't think symbolic logic is a great tool for most people and most applications. For that, syllogistic logic is a better fit.
The modern Fregean paradigm was motivated by the need for a formalism to solve mathematical problems. It was advanced from a position of complete indifference to the relationship between logic and language/grammar. However, the Aristotelian tradition that dominated logic for two thousand years before Frege is motivated explicitly by the desire to clarify, draw out, and make conspicuous the logical structures within grammar so that arguments can be better evaluated for soundness.
For a rudimentary introduction to this space, Joseph's "The Trivium: The Liberal Arts of Logic, Grammar, and Rhetoric" is a good resource. For something a bit more thorough and specifically focused on logic, Coffey's two volumes of "The Science of Logic" comes highly recommended[1][2].
The beginning of the book I linked to has a section on converting English phrases into formal logical symbols. That part is relevant to the link and to anyone looking to clarify their arguments when writing.
The rest of the book may not be as directly related, although I did find it useful to clarifying my thoughts and structuring arguments more clearly.
cubefox · 5h ago
> The beginning of the book I linked to has a section on converting English phrases into formal logical symbols.
Where? I don't see it.
keiferski · 5h ago
Chapter 2 is when they start introducing logical symbols
cubefox · 7h ago
Propositional logic is about Boolean inferences like "If A then B, A, therefore B". The link you provided expands this to the more complex predicate logic, of which syllogisms (discussed in the article) are special cases. E.g. "Everything that is X is also Y. This is X. Therefore, this is Y."
Though I would also note that most introductions to symbolic logic do ommit the (in this context) most important part: On how to translate natural language arguments to formal logic, and the other way round. This task is very much non-trivial. A few textbooks aimed at philosophers do this, though most don't.
vouaobrasil · 7h ago
Actually, propositional logic is a lot more than that. The core is really about proof theory, natural deduction, and axiomatic systems that form the precursor of first-order logic and the foundations of model theory.
cubefox · 6h ago
Well, natural deduction is one specific form of proof theory (it's a kind of proof system), but there are others. Moreover, proof theory and model theory are independent (neither relies on the other) and various logicians would say that we don't really need one of them, though they would disagree on which. Proof theorists tend to be skeptical of the necessity of model theory, model theorists tend to be skeptical of the necessity of proof theory. Mathematicians tend to be skeptical of both.
But yes, to the degree that any such theoretical parts are part of predicate logic, they are already part of propositional logic. The former is an extension of the latter. Perhaps similar to how higher-order logic (simple type theory) extends or generalizes both propositional and first-order predicate logic.
astrobe_ · 4h ago
By "natural deduction", I assume both of you refer to the system which is related to "sequent calculus" ? [1].
Slightly OT: Regarding the raising of the minimum wage example, is there a reason why the following linear argument is not universally accepted?
> The more something costs, the less of it people buy;
> THEREFORE the more that hiring people costs, the fewer people get hired;
> SO raising the minimum wage raises unemployment.
I doubt anything in economics is as linear as WHEN PRICES GO UP THEN PURCHASES GO DOWN, especially given demand inelasticity, feedback loops, and other things that complicate such a model.
czarit · 1h ago
It is absolutely accepted in microeconomics, where one can assume that preferences are exogenous to the model (that is: not affected by changing the model's variables).
In macroeconomics it is not so simple, because the effects of a higher price for labor are felt all over the economy, leading to feedbacks that might increase overall employment. The Ford wage increase to increase demand for Ford's products is often cited - because there is a multiplier effect from economic activity even a single firm can theoretically benefit from handing out more money to its employees.
There are also arguments from near term versus long term. In the long term, economies with no access to very cheap labor feel more pressure to robotize production, leading to higher productivity and more production overall, and also might lead to a better educated workforce by simply excluding below-minimum-wage productive labor from getting any jobs, and therefore push some of them to school. Those are short term costs that have proven to lead to long term gains.
But I do also think it's not very common to assume that higher minimum wages will lead to a net increase in employment. It is more common to argue that it will lead to a better outcome (for some definition of good) in the aggregate, _even if_ it might lead to some unemployment.
blackbear_ · 5h ago
It definitely works in the short term, but what matters is the long term effects: how will people and businesses adapt, and will that lead to a better society?
Case in point: At least as far back as the 17th century, many people believed that idle children were a source of crime and poverty. To combat such idleness, apprenticeships were common for children of working-class families. Child labor, rather than being viewed as exploitive, was often considered an act of charity (https://www.bls.gov/opub/mlr/2015/article/labor-law-highligh...).
In the early 1900s, one could have argued in a similar way as yours and argue that enforcing a minimum age for workers would reduce the labor supply, leading to increased labor cost, leading to reduced profits for companies, leading to higher prices for consumers, leading to less demand for products, leading to less innovation, reduced standards of living, and so on and so forth.
Maybe that did indeed happen in the first years, but the long term effects were inarguably positive for everybody.
No comments yet
constantcrying · 4h ago
The argument falls apart at every single step. As a logical deduction it is awful. The premise is just straight up false. And the rest also has obvious holes.
Simple counter example:
If every single person in a population can employed for economic gain by an employer, even if the employer was paying minimum wage, then having a minimum wage would not change anything about employment. An employer would obviously rather make some gain of an employee than not making that gain at all, so no changes to unemployment would happen.
There are obviously ways in which employers can increase the profit they make from employees. E.g. by raising the cost of their products.
ogogmad · 4h ago
I think you're describing inelastic demand for hires. Which I mentioned as a hole in the argument. On that note, I'm not sure why my post has more down than upvotes.
add-sub-mul-div · 5h ago
Hypothetically when minimum wage earners are making more than subsistence wages they'll buy more and business goes up, allowing for growth and hiring.
Don't know if it's true or not, but it should be easy to imagine why a complex issue needs more than a simple take.
No comments yet
riehwvfbk · 7h ago
Or you just fund a celebrity-driven defamation campaign against the supporters of the stadium (or detractors, depending on yours side). Faster and more effective.
Essentially it teaches you how to formalize arguments into their abstract symbolic forms, and then evaluate the argument on that form. This is a lot easier than trying to determine an argument’s validity purely from its English written version.
I used Klenk’s Understanding Symbolic Logic, but I’m sure there are more modern courses or books.
https://archive.org/details/understandingsym0000klen
https://ocw.mit.edu/courses/24-241-logic-i-fall-2009/
https://ocw.mit.edu/courses/24-242-logic-ii-spring-2004/
The modern Fregean paradigm was motivated by the need for a formalism to solve mathematical problems. It was advanced from a position of complete indifference to the relationship between logic and language/grammar. However, the Aristotelian tradition that dominated logic for two thousand years before Frege is motivated explicitly by the desire to clarify, draw out, and make conspicuous the logical structures within grammar so that arguments can be better evaluated for soundness.
For a rudimentary introduction to this space, Joseph's "The Trivium: The Liberal Arts of Logic, Grammar, and Rhetoric" is a good resource. For something a bit more thorough and specifically focused on logic, Coffey's two volumes of "The Science of Logic" comes highly recommended[1][2].
[0] https://a.co/d/61YNOCC
[1] https://a.co/d/3VNAGst
[2] https://archive.org/details/thescienceoflogi01coffuoft/page/...
The rest of the book may not be as directly related, although I did find it useful to clarifying my thoughts and structuring arguments more clearly.
Where? I don't see it.
Though I would also note that most introductions to symbolic logic do ommit the (in this context) most important part: On how to translate natural language arguments to formal logic, and the other way round. This task is very much non-trivial. A few textbooks aimed at philosophers do this, though most don't.
But yes, to the degree that any such theoretical parts are part of predicate logic, they are already part of propositional logic. The former is an extension of the latter. Perhaps similar to how higher-order logic (simple type theory) extends or generalizes both propositional and first-order predicate logic.
[1] https://en.wikipedia.org/wiki/Natural_deduction
In macroeconomics it is not so simple, because the effects of a higher price for labor are felt all over the economy, leading to feedbacks that might increase overall employment. The Ford wage increase to increase demand for Ford's products is often cited - because there is a multiplier effect from economic activity even a single firm can theoretically benefit from handing out more money to its employees.
There are also arguments from near term versus long term. In the long term, economies with no access to very cheap labor feel more pressure to robotize production, leading to higher productivity and more production overall, and also might lead to a better educated workforce by simply excluding below-minimum-wage productive labor from getting any jobs, and therefore push some of them to school. Those are short term costs that have proven to lead to long term gains.
But I do also think it's not very common to assume that higher minimum wages will lead to a net increase in employment. It is more common to argue that it will lead to a better outcome (for some definition of good) in the aggregate, _even if_ it might lead to some unemployment.
Case in point: At least as far back as the 17th century, many people believed that idle children were a source of crime and poverty. To combat such idleness, apprenticeships were common for children of working-class families. Child labor, rather than being viewed as exploitive, was often considered an act of charity (https://www.bls.gov/opub/mlr/2015/article/labor-law-highligh...).
In the early 1900s, one could have argued in a similar way as yours and argue that enforcing a minimum age for workers would reduce the labor supply, leading to increased labor cost, leading to reduced profits for companies, leading to higher prices for consumers, leading to less demand for products, leading to less innovation, reduced standards of living, and so on and so forth.
Maybe that did indeed happen in the first years, but the long term effects were inarguably positive for everybody.
No comments yet
Simple counter example:
If every single person in a population can employed for economic gain by an employer, even if the employer was paying minimum wage, then having a minimum wage would not change anything about employment. An employer would obviously rather make some gain of an employee than not making that gain at all, so no changes to unemployment would happen.
There are obviously ways in which employers can increase the profit they make from employees. E.g. by raising the cost of their products.
Don't know if it's true or not, but it should be easy to imagine why a complex issue needs more than a simple take.
No comments yet