[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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