[HN Gopher] Using Logic in Writing
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Using Logic in Writing
Author : benjacksondev
Score : 58 points
Date : 2025-05-27 08:46 UTC (14 hours ago)
(HTM) web link (owl.purdue.edu)
(TXT) w3m dump (owl.purdue.edu)
| keiferski wrote:
| 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.
|
| https://archive.org/details/understandingsym0000klen
| cubefox wrote:
| 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 wrote:
| 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 wrote:
| 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_ wrote:
| By "natural deduction", I assume both of you refer to the
| system which is related to "sequent calculus" ? [1].
|
| [1] https://en.wikipedia.org/wiki/Natural_deduction
| lo_zamoyski wrote:
| 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].
|
| [0] https://a.co/d/61YNOCC
|
| [1] https://a.co/d/3VNAGst
|
| [2]
| https://archive.org/details/thescienceoflogi01coffuoft/page/...
| keiferski wrote:
| 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 wrote:
| > 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 wrote:
| Chapter 2 is when they start introducing logical symbols
| justin66 wrote:
| 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.
|
| https://ocw.mit.edu/courses/24-241-logic-i-fall-2009/
|
| https://ocw.mit.edu/courses/24-242-logic-ii-spring-2004/
| magical_spell wrote:
| 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.
| riehwvfbk wrote:
| 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.
| ogogmad wrote:
| 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.
| blackbear_ wrote:
| 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.
| add-sub-mul-div wrote:
| 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.
| constantcrying wrote:
| 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 wrote:
| 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.
| czarit wrote:
| 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.
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