Argument

static/images/Maccari-Cicero.jpg

Cicero Denounces Catiline, fresco by Cesare Maccari, 1882-1888.

An argument is an assertion that some proposition is a consequent of some theory.

Arguments differ from expositions in that they show that something is or should be the case, where an explanation shows why or how; an explanation does not attempt to settle whether a claim is true, but instead tries to show why it is true.

Contents

1   Study

The study of arguments is called logic. The study of the forms of arguments is called formal logic (= symolic logic). Formal logic further consists of propositional logic and predicate logic.

Logic instruction at this time was based primarily on a collection of texts by Aristotle known as the Organon and on Porphyry’s third-century text, Isagoge, which served as a preface to the Organon.5 The teaching of these treatises reflected the view that logic should be organized into the three mental operations: apprehension, judgment, and ratiocination (or reasoning by using syllogisms). It is through apprehension, the first operation, that the conception of an object or term is brought to mind: for example, the apprehension of such concepts as “dog” and “mammal”. Through judgment, the second operation, simple concepts are then combined or divided to create propositions ( “Dogs are mammals”). By way of ratiocination, the third operation, the mind organizes these propositions to form syllogisms ( “Dogs are mammals / All mammals are animals / Thus dogs are animals”).

Susanna Berger. The Art of Philosophy: Visualising Aristotle in Early 17th-Century Paris. http://publicdomainreview.org/2017/08/30/the-art-of-philosophy-visualising-aristotle-in-early-17th-century-paris/

2   Function

The purpose of argumentation is to demonstrate the validity of an idea. For example, copywriting, a critical review, an editorial, a job application, a letter of recommendation, a resume, or a sales presentation.

It may be essential that argument aim to cause action of sort some sort (related to praxis_) which differs from explanation.

3   Substance

The material of arguments are propositions.

3.1   Form

The form of an argument is called a schema. Schema may be interpreted to produce a statement. One schema can model many statements, since sentence letters may be interpreted in infinitely many ways.

An interpretation of sentence letters is a correlation of a statement with each of the sentence letters. Given such a correlation, a schemata constructed from the sentence letters is interpreted by replacing each letter with its correlated statements.

Arguments have the form of a tree. They consist of either simpler arguments or:

  1. A theory, called the premises (= hypotheses = givens)
  2. A proposition, called the conclusion (= thesis = main contention)

The conclusion is the most controversial proposition in an argument.

Complex arguments can be constructed in two ways:

  • The simpler arguments can share the same conclusion
  • The conclusions of simpler arguments can be used as premises for other arguments.

In general, in a schemata of n sentence letters, there are 2^n truth-assignments.

3.2   Matter

Argument begin with a lead to draw the reader in.

3.3   Theory of change

Authors appears to have different mental models of how writing changes people's behavior. A rough taxonomy:

  1. "Command" - Tell people to do the right thing, and they'll do the right thing. Perhaps works on the impressionable or desperate.

  2. "Shame" - Shame people for doing the wrong thing, and they'll do the right thing. Frequently backfires.

  3. "Lecture" - Tell people the right facts and they'll do the right thing. This what most people are taught in school, but seems ineffective.

  4. "Theorize" - Explain to people a theory of how something works, and they'll do better things in that domain. This is often useful, even if the theory is simplistic. It also opens itself to discussion of constructing a better model.

  5. "Inspire" - Show people what the right thing looks like and how it's better, and they'll do the right thing. This is often used to explain strategies in games, and is convincing. However, it doesn't always show people how you came to see why it was better, which makes people dependent on you.

  6. "Alter perception" - Show people how to perceive something differently, and they'll do the right thing. Equivalently, articulate things people already know, but don't know how to articulate. This is less of convincing someone of something. This sort of argument attempts to convince the reader that certain things are worth paying attention, and what concepts to use to explain things. Examples of this argument include insight porn, conspiracy theories, and `ludic fallacies`_ (rationalization of events that happened).

    One of the core ideas of `perceptual control theory`_ is that "behavior is the control of perception"; altering perception alters behavior.

    Teaching people to see. Not only teach the model, but build confidence in it.

    Doing the reverse of this is a fast way to learn; reverse engineer the mental models of the people who are smarter than you.

4   Rules of arguing

Philosopher `Daniel Dennett`_ advocates following "Rapoport's Rules" when writing critical commentary. He summarizes the first of Rapoport's Rules this way:

You should attempt to re-express your target's position so clearly, vividly, and that your target says, "Thanks, I wish I’d thought of putting it that way."

One writer who, in my opinion, seems to follow Rapoport's First Rule unusually well is Dennett's "arch-nemesis" on the topic of consciousness, the philosopher David Chalmers. Amazingly, even Dennett seems to think that Chalmers embodies Rapoport's 1st Rule.

Contrast this with what I find to be more typical in the consciousness literature (and in many other literatures), which is for an article’s author(s) to present as many arguments as they can think of for their own view, and downplay or mischaracterize or not-even-mention the arguments against their view.

“In disputes upon moral or scientific points,” Arthur Martine counseled in his magnificent 1866 guide to the art of conversation, “let your aim be to come at truth, not to conquer your opponent. So you never shall be at a loss in losing the argument, and gaining a new discovery.”

5   Properties

An argument is complex if it is built up of simpler ones else it is simple. Complex arguments are necessary when one or more premises are controversial, since these premises must be supported by argument.

An argument is called an enthymeme if it is stated informally and omits a premise. Enthymemes are used when one proposition is obvious. For example, "All metals expand when heated, therefore iron will expand when heated" (omitting the fact that iron is a metal).

Enthymemes can mask their invalidity if the omitted premise is also the weakest. For example, a person might claim that "virtual reality is just a toy" with the implicit premise that there is no way it will ever become more useful. While it may be true that the statement "virtual reality is [presently] a toy" (Benedict Evans calls this "not even wrong"), it's almost not worth saying because it has no predictive power.

6   Classification

Claims typically fall into one of four categories: claims of fact or definition, cause and effect, about value, or about solutions. [2]

6.1   Syllogism

A syllogism (from Greek syn- "together" + logos "reason") is a deductive argument that consists of exactly two premises, a major premise and minor premise, and a conclusion, where each proposition has exactly one term in common with the other.

Syllogisms have the following form, where \(S\) is the subject, \(P\) is the predicate or major term, and \(M\) is the "Middle" or minor term:

  1. Major premise: All M are P.
  2. Minor premise: All S are M.
  3. Conclusion: All S are P.

For example:

All men are mortal (major)

Socrates is a man. (minor)

Socrates is a mortal (conclusion)

An enthymeme (from Greek en- "in" + thymos "spirit", literally "to keep in mind, take to heat") is an informally stated syllogism in which at least one premise is left unsaid. For example:

Socrates is a man.

Therefore, Socrates is mortal.

Or:

All men are mortal.

Therefore, Socrates is mortal.

In Rhetoric 2.22, Aristotle considered enthymemes effective tools for arguing with uneducated audiences. Aristotle also argued that enthymemes should be followed by examples.

6.2   Fallacy

A fallacy (= leap = non-sequitir) (from Latin fallacia "deception", from fallere "deceive") is an invalid argument.

There are many well known fallacies:

  • Appeal to authority: "Barrack Obama says X so " or "Facebook runs on PHP, so PHP must be blazing fast"

  • Divine fallacy: if someone doesn't understand something, then that phenomenon must occur as a result of divine intervention.

  • Monte Carlo fallacy

  • False Dichotomy. "Okay, I'll do it, but my other work will suffer."

  • Appeal to nature: the claim that what is natural is inherently good or right, and that what is unnatural is inherently bad or wrong. For example, "carrots are better for you than candy, because it comes from nature" or "what is pleasant is good". It is a special case of the is-ought problem.

  • The nirvana fallacy is the informal fallacy of comparing actual things with unrealistic, idealized alternatives. It can also refer to the tendency to assume that there is a perfect solution to a particular problem. Under this fallacy, the choice is not between real world solutions; it is, rather, a choice between one realistic achievable possibility and another improbable solution that could in some way be better.

  • Base-rate fallacy.

    "John is a man who wears gothic inspired clothing, has long black hair, and listens to death metal. How likely is it that he is a Christian and how likely is it that he is a Satanist?"

    If people were asked this question, they would likely underestimate the probability of him being a Christian, and overestimate the probability of him being a Satanist. This is because they would ignore that the base rate of being a Christian (there are about 2 billion in the world) is vastly higher than that of being a Satanist (estimated to be in the thousands).[2] Therefore, even if such clothing choices indicated an order of magnitude jump in probability of being a Satanist, the probability of being a Christian is still much larger.

  • Scarcity. People will reason that because something occurs rarely they should see or do it, even if they have no actual interest in the thing, and never expressed a desire for it. For example, seeing a solar eclipse.

An informal fallacy is a fallacy that is logically valid but unpersuasive. A formal fallacy is an argument that is defective because it uses an incorrect deductive step.

6.2.1   Ad hominum

Ad Hominem. For example, "But Glenn Beck is an idiot, you shouldn't listen to anything he says."

Four type of ad hominem:

  1. Attack his character, then equate poor character with argument. But argument may still be valid.

  2. Circumstantial. Reply that your friend works for a vegan food company when she argues killing animals for food is immoral. Attack the circumstance instead of the argument because suspect conflict of interest, and her giving a fault argument in favor of veganism.

  3. Tu quoque ("you also"). For example, suppose your friend argues that animals are sentient beings and killing sentient beings for food is immoral, so therefore killing animals for food is immoral. If you reply "Yeah, but Catherine, you eat meat". In this case, you highlight that she doesn't act in a way that is consistent with her conclusion. You take her hypocrisy to invalidate her argument.

  4. Guilt by association.

    For example, "This is liberal talking points", which invokes tribal tendencies.

6.2.2   Begging the question

In classical logic, begging the question a (mistranslation of the Latin petitio principii) is an `informal fallacy`_ that occurs when a person attempts to support a claim with a premise that itself presupposes the claim. The original phrase used by Aristotle from which the phrase descends is "asking for the initial thing". Begging the question is related to circular reasoning.

For example:

  • Erica: "How do you know that the bible is divinely inspired?" Pedro: "Because is says right in the third chapter of II Timothy that 'all scripture is given by divine inspiration of God.'" [7]
  • Thoughts are not part of the physical world, since thoughts are in their nature non-physical. [7]
  • Happiness is the highest good for a human being, since all other values are inferior to it. [7]
  • This whole abortion debate about when human life begins is ridiculous. We should be thinking about the rights of the baby. [7]

6.2.3   Equivocation (false comparison)

Equivocation is the technique of using a term in a syllogism with different meanings in different statements.

For example, an equivocation is made in the follow argument: "A feather is light. What is light cannot be dark. Therefore, a feather cannot be dark."

Equivocation is the type of ambiguity which occurs when a single word or phrase is ambiguous, and this ambiguity is not grammatical but lexical. So, when a phrase equivocates, it is not due to grammar, but to the phrase as a whole having two distinct meanings.

Equivocation is not always fallacious since it is sometimes necessary to reuse a term to express a different meaning, but it must be wielded carefully to avoid doing so.


Also know as a 'false comparison'.

Ian Bremmer on Twitter wrote:

Lifetime odds of death from...

Heart disease or cancer: 1 in 7
Any injury: 1 in 21
Motor vehicle accident: 1 in 113
Gun assault 1 in 358
Any force of nature 1 in 3,122
Choking on food 1 in 3,409
Foreign-born terrorists (all forms of attack) 1 in 45,808

https://twitter.com/ianbremmer/status/925765918814277632

Bremmer's tweet implies that the reader might be overly-concerned with terrorism.

Nassim Nicholas Taleb pointed out the flaw in response:

  1. Terrorism is fat-tailed
  2. Terrorism is low because we fight it

Terrorism is game-theoretic. Terrorists get the signals to attack if reduce vigilance, unlike health. In other words, what Brenner can't get is that the other car on the high way is not trying to kill you, and therefore is a false comparison.

https://twitter.com/nntaleb/status/925767998182494214

6.2.4   McNamara fallacy

The McNamara fallacy (= "materialist bias") refers to measuring only tangible inputs and outputs (such as firepower), rather than intangible human factors such as strategy, leadership, group cohesion, and the morale of servicement.

6.2.5   Politician's Syllogism

The syllogism goes as follows:

  1. Something must be done.
  2. Something must be done.
  3. Therefore, this must be done. (1, 2)

A more realistic example:

No one criticizing the Green New Deal -- not a single person -- has an alternative plan for transitioning the American energy economy in the timeframe climatologists say we must. Nobody. If you don't think it's realistic, put out something else. What should be done instead?

6.2.6   Slippery slope

Slippery slope refers to a fallacy where a person concludes that if your conclusion is true, then another more extreme conclusion follows. For example, It is a variant of reductio ad absurdem; since the ultimate conclusion they draw is undesirable, then your conclusion must be as well. It works well as an appeal to emotion.

Usually, a person will counter an argument for an exception by point out a need to be consistent. For example:

  • "If I give you free refills, then I'll have to give them to everyone."
  • "If I let you use a computer in class, then I have to let everyone use a computer in class"
  • "If start letting people marry the same sex, then why not let people marry animals?"
  • "I can't join you for a movie tonight because I have to go to the gym. If I skip tonight, then next week you'll make me skip to go shopping or painting"

Arguments for voting:

  • Voting is a duty rather than a right.
  • Your vote affects how other people vote.

Arguments against voting:

  • Your vote only affects the election outcome when it breaks a tie. Voting and not voting has the same outcome because the chances are so low. (According to one article, the chance of any one voter being decisive in the 2004 election was equal to chance of winning the Powerball loterry 128 times consecutively. http://www.slate.com/articles/arts/everyday_economics/2004/09/dont_vote.html)

    Voting is illogical for the same reason that buying a lottery ticket is illogical.

  • Votes are not cumulative; elections are winner-take-all contests. So analogies to "Why don't you litter?" or "Why not buy an SUV and pollute the earth?" don't hold. Further, the examples encourage other people to litter/pollute which is not true of voting.

  • Your vote does not affect how other vote. (Or if it does, you could just lie and say you did.)

  • Even if everyone did vote, voting does not make the world a better place.

6.2.7   Strawman

A straw man is a refutation that misrepresents the opponent's position.

Plato used straw men.

Straw men do not logically follow (non-sequitur), but can give the illusion of disarmament.

For example:

Claim: We should liberalize the laws on beer. Objection: No. Any society with unrestricted access to intoxicants loses its work ethic and goes only for immediate gratification. Rebuttal: The claim did not state anything about unrestricted access to intoxicants.

Straw men are frequently accidental as they happen when someone misunderstand an opponent's argument. It is therefore essential to ensure to that one is representing the opponent's position correctly.

Tucker Carlson is a master of the weak man––as was Jon Stewart.


Scott Alexander. http://slatestarcodex.com/2014/05/12/weak-men-are-superweapons/

One of the cutting-edge advances in fallacy-ology has been the weak man, a terribly-named cousin of the straw man. The straw man is a terrible argument nobody really holds, which was only invented so your side had something easy to defeat. The weak man is a terrible argument that only a few unrepresentative people hold, which was only brought to prominence so your side had something easy to defeat.

For example, “I am a proud atheist and I don’t like religion. Think of the terrible things done by religion, like the actions of the Westboro Baptist Church. They try to disturb the funerals of heroes because they think God hates everybody. But this is horrible. Religious people can’t justify why they do things like this. That’s why I’m proud to be an atheist.”

It’s not a straw man. There really is a Westboro Baptist Church, for some reason. But one still feels like the atheist is making things just a little too easy on himself.


See also Rapaport's Rules.

You should attempt to re-express your target’s position so clearly, vividly, and fairly that your target says, “Thanks, I wish I’d thought of putting it that way.

This is exactly what I was going to post. The iron-man argument. Make your opponents argument better than they can, then dismantle it. A great approach and honestly if you can't defeat the strongest argument you may want to rethink your position.

Also known as steel-manning in contrast to straw-manning.


Daniel Dennett's Rules for Argument

You should attempt to re-express your target’s position so clearly, vividly, and fairly that your target says, “Thanks, I wish I’d thought of putting it that way.

You should list any points of agreement (especially if they are not matters of general or widespread agreement).

You should mention anything you have learned from your target.

Only then are you permitted to say so much as a word of rebuttal or criticism.


Then we would be steelmanning, the art of addressing the best form of the other person’s argument, even if it’s not the one they presented.

Why should we do this? Three reasons: It makes us better rationalists, better arguers, and better people.

If you know of a better counter to your own argument than the one they’re giving, say so.

People are more convinced by arguments which address the real reason they reject your ideas rather than those which address those aspects less important to their beliefs.

6.2.7.1   Not all X are like that

A generalization is a claim that a predicate is true for a majority of the members of some set. For example, "children like candy", "ripe bananas are yellow", "women like tall men", or "humans are killing bees". These statements should not be interpreted as "For all x, p(x)"; the speaker would be willing to admit that there are exceptions to the statement, and pointing this out does not make the claim untrue. To refute a generalization, you must demonstrate instead that the predicate does not apply for the majority of the members of the set.

You can't disprove a generalization with an exception. Therefore, it's invalid to say "Not all X are like that" in response to a claim that "Generally, X are Y".

This often happens when a woman makes a generalization about men to a man, and a man responds "but not all men are like that". Or vice versa.

A person who tries to refute such a claim with a "Not all X" statement are arguing against a position which has not been put forward.

6.2.8   No true Scotsman

Some examples:

  • Islam isn't a bad religion; people who do bad things in the name of Islam do not represent Islam.

    Any ideology that explicitly commands followers to convert, enslave, or kill all non-believers is an evil ideology.

    Islam (which is just a set of ideas) inspires more terrorist attacks than any other modern ideology. Why is this a controversial statement?

  • Communism has never failed because it's never actually been tried. But also flip side: "Capitalist dictator kills his subjects: that particular dictator killed them. Communist dictator kills his subjects: communism killed them."

  • Artificial intelligence no longer is considered intelligent once it is invented

  • Minimalism defining minimalism as having no unnecessary parts

6.2.9   Scapegoating

Often, liberals will cry for a person to resign if they hold unpopular views. Presumably the thinking is that by the person resigning, the issue if being fixed. For instance, Brendan Eich was fired for donating to a anti-gay charity.

Conservatives also do this when a mass shooting occurs, blaming the shooter rather than anything systematic about gun rights in the US.

7   Rhetoric

7.1   Motte and bailey

The motte-and-bailey meme prevents straw-manning, since the "motte" part requires you to accurately characterize someone's fallback position instead of pretending that the bailey is the only position they have.

Perhaps a form of equivocation?

For examples:

7.2   The unborn

"The unborn" are a convenient group to advocate for. They never make demands, they are morally uncomplicated (unlike the incarcerated, addicted, or poor), they don't resent condescension, they don't need money or care, and when they are born you can forget about them.

8   Representation

Informally, arguments necessarily correspond to a sequence of statements, but they do not necessarily correspond to a paragraph (e.g. due to digressions or due to an author's style of writing many short paragraphs). Informal arguments may present the conclusion before or after the premises and may omit premises.

The process of translating sentences in a natural language argument to a formal language to reveal the formal structure of the argument is called logical paraphrase. When translating it is important to provide a symbolization key, a map between the English language sentence and sentence letter.

When reconstructing arguments, we try to make the best argument possible. This is known as the principle of charity, which tells us to assume the author of the enthymeme is a rational person who provides good arguments.

An argument may be represented with an argument map. [3]


"p", "q" and the like are called sentence letters, and the compounds constructed from them and the truth-functional connectives are called truth-functional schemata.

9   Production

The production of arguments is called invention (inventio).

A speaker use invention when he begins the thought process to form and develop an effective argument.

Invention investigates the possible means by which proofs can be discovered. It supplies the speaker and writes with sets of instructions or ideas that help them find and compose argument that are appropriate for a given situation.

Invention is the central part of rhetoric.

9.1   Structure

Invention has two parts:

  1. To derive strategies that will aid students in generating ideas about which they might write.
  2. How writers establish voice in writing and realize individual selves in discourse.

9.2   Topics

Two important concepts within invention were topics (topoi) and stasis.

9.2.1   Topics (Topoi)

Arguments are obtained from various sources of information, or topics.

Topics are categories that help delinate the relationships among ideas.

Aristotle divided these into "common" and "special" groups.

The common group includes categories such as laws, witness, contracts, oaths, comparisons, definitions, divisions, cause and effects, and other items that could be analyzed, researched, or document.

The special group included concepts such as justice, virtue, good, and worthiness.

Four common topics are:

  • Definition: Creation of a thesis by precisely identifying an object's nature
  • Analogy: Discovering resembles or differences
  • Consequence: Investigates cause and effects
  • Testimony: Appeals to authority

9.2.1.1   Stasis

Stasis theory is a procedure for analyzing arguments put forward by Cicero.

Stasis is a procedure by which a speaker poses questions in order to clarify the main issues and persuasive points of a speech or debate.

There are four types of stasis:

  • Conjectural - Question of fact
    Example: Did the person damage the item?
  • Definitional - Question of meaning
    Example: What is minor or major?
  • Qualitative - Question of quality
    Example: Was he justified in damaging the item?
  • Translative - Question of jurisdiction
    Example: Should this be a civil or criminal trial?

9.3   Criticism

One of the oldest criticisms of rhetoric is that as an art it has no proper subject matter; an orator might speak on any topic with his success being measured purely on the brilliance of his rhetorical skills. For example, Plato made this criticism against what he saw as the empty rhetoric of the sophists. Aristotle answered Plato's charged by arguing that reason and rhetoric are intertwined ("rhetoric is the counterpart of dialectic"). According to Aristotle, dialectic reasoning is the mechanism for discovering universal truths; rhetoric is the method for communicating these principles to others.


Example:If a presidential candidate has a long history of philanthropy, he or she will invent an argument that demonstrates personal good character in order to convince the audience that (s)he is the best candidate for office.
Example:If a presidential candidate grew up poor and managed to succeed in life through hard work and education, then the candidate would have to apply that story to the speech-inventing process in order to appeal to the audience’s emotions.

10   Criticism

Criticism (=reflection) is a way of deciding whether a claim is true, partially true, or false.

11   Refutation

To refute an argument, assume the premises of your opponent are true and show that it leads to a contradiction.

12   Debate

A debate is ...


A Gish gallop is a technique used during debating that focuses on overwhelming one's opponent with as many arguments as possible, without regard for accuracy or strength of the arguments. The term was coined by Eugene C. Scott and named after the creationist Duane T. Gish, who used the technique frequently against science-backed opponents on the topic of evolution.

A Gish Galloper is someone who rapidly shifts his or her argument in the middle of a discussion, making a bunch of unrelated points in rapid succession. Usually, all of the points are weak or wrong, but as you try to rebut each one, the Galloper shifts to another.

Example:

Me: "Immigration is helping America!" Galloper: "LEGAL immigration." Me: "Net illegal immigration has been negative since 2006." Galloper: "...Blue-collar jobs!" Me: "Most immigrants are now high-skilled." Galloper: "...Immigrants don't assimilate!"

At first, Gish Galloping might seem like a disingenuous, dishonest debating tactic. Instead, I think it's usually just a sign of loose, disordered thinking. A Gish Galloper is cycling between unrelated arguments because he isn't really considering your points. He's kicking out against your entire worldview.

Hence, it's pointless to argue logically with a Gish Galloper, as you would if you were dealing with a focused thinker. To argue fruitfully with a Gish Galloper, you must focus on gestalt arguments. You must play his game, because he just doesn't know how to play yours.

Ignore the Galloper's points (which aren't really points at all). Focus on a central, memorable message that will allow him to think about the whole issue in a different frame. For example: "The United States is a team, and immigrants are recruits who strengthen that team."

It's important to remember, people have different thinking styles. And people whose thinking styles are different tend to make us angry, because failure to communicate is frustrating.

13   History

Aristotle presented his logic in the six-part book "The Organon", which occupied a central place in the scholarly cannon for more than 2000 years. It was widely believe that Aristotle had written almost all there was to say on the topic. `Immanuel Kant`_ commented that since Aristotle, logic had been "unable to take a single step forward, and therefore seems to all appearance to be finished and complete". [5]

Aristotle's central observation was that argument were valid or not based on their logical structure, independent of the non-logical words involved. He also defined a set of basic axioms from he derived the rest of his logical systems: an object is what it is (law of identity), no statement can be both true and false (law of non-contradiction), and every statement is either true or false (law of excluded middle). [5]

Aristotle's axiomatic approach influenced Euclid's Element's, which became a standard textbook for teaching rigorous deductive reasoning.

13.1   Frege

Logic was expressed in standard language rather than with its own abstract symbolic notation until Gottleib Frege in the 19th century


Boole is often described as a mathematician, but saw himself as a philosopher. He pays tribute to Aristotle, the investor of logic. In his "The Laws of Thoughts", he pays tribute to Aristotle.

Boole's goal was to do for Aristotelian logic what Descartes had done for Euclidian geometry: free it from the limits of human intuition by giving it a precise algebraic notation. The "Laws of Thought" created a new scholarly field - mathematical logic - which in the following years become one of the most active areas of research for mathematicians and philosophers. [1]


Logic was historically one of the core subjects in the trivium.

Modern formal logic was preceded by term logic.

14   See also

15   Further reading

16   References

[1]http://home.southernct.edu/~gillilandr1/Tutorial/Tutorial.htm
[2]https://owl.english.purdue.edu/owl/resource/588/01/
[3]http://en.wikipedia.org/wiki/Argument_map
[4]`Magnus 2005`_
[5](1, 2) Wolf 2008
[6]Jan Corazza. Sep 24, 2016. A short critique of Stallmanism. http://jancorazza.com/2016/09/24/a-short-critique-of-stallmanism/
[7](1, 2, 3, 4) Begging the Question. https://www.txstate.edu/philosophy/resources/fallacy-definitions/Begging-the-Question.html

Aggressive tactics are often met with defensive responses, not open discourse.

Making people feel responsible for animal torture does not incentivize them to listen.

[6]

However, [Stallman's] approach, and the approach of some organizations and individuals drawing inspiration from and collaborating with him, contains a crucial mistake: confounding individual virtue and purity with wider social liberation.

Stallman's rhetoric is filled with this problematic logic on all layers: from trying to correct other people's terminology and purify the language (however sound some of his premises may be), to promoting a type of technological asceticism by using, and encouraging others use, only free software for every conceivable purpose: from applications to firmware... His criticism of these phenomena is desperately needed, but his concrete reactions to it are not: it is not a solution for people to simply stop using e.g. Gmail.

Systematic analysis requires a systematic response: primarily rooted in collective political action to curb business and government intrusions into privacy and collective control, effective alternatives (yes I said it, see the next paragraph), and approachable education: not a puritan, individualistic, "good enough for me" stance. In general, this approach is evocative of, and indeed stems from, the familiar liberal ideological mistake of lifestylism: the belief that changes in one's own personal preferences are the beginning and end of political action.

We don't describe free software as an “alternative” to proprietary, because that word presumes all the “alternatives” are legitimate and each additional one makes users better off. In effect, it assumes that free software ought to coexist with software that does not respect users' freedom.

We believe that distribution as free software is the only ethical way to make software available for others to use. The other methods, nonfree software and Service as a Software Substitute subjugate their users. We do not think it is good to offer users those “alternatives” to free software.

However, how is ignoring your enemies' existence going to change the fact it exists? It is just as effective as not talking about race and racism when trying to combat it.

Telling people to use free software because otherwise they are exploited on an individual level is not a very effective appeal because it essentially puts the weight of the entire oppressive system on their shoulders by presenting it as a simple choice: you choose to be exploited. This is clearly false, in the same way that people rarely have a choice when it comes to participating in other oppressive social relations. The answer is never to sever oneself from society, but to change it.

We ought to look at software not as mere isolated commodities among which we can freely pick, but rather as a social phenomena: defined by its production, usage, and its function in society. It then becomes clear that as the fruits of programmers' labor are essentially closed down and rented to the rest of society, that society is not free.

This type rhetoric breeds elitism (perceived or actual): we give off the message, implicitly, that using free software makes us more virtuous than those who don't. To the outsider, our demands can then seem as mere expressions of personal preference, in the best case, or, attacks on their own preferences, in the worst.

Among regular people, there is hardly any support for free software, or even awareness of its existence as an idea. There are political issues relevant to many computer users regarding software such as iTunes or Steam, centered around the fact that things which were once regular commodities -- music and art -- have entered an even more problematic mode of exchange: what was once our personal property, is being locked away from us and rented.

Imagine if all those who were outraged by, for example, Windows 10 spying on them, were given an integrated political platform to properly understand the root cause of these issues and the proper way to resist them!

Free software activists should accept that software freedom is not an isolated issue, with its own, completely independent value set, but is just one aspect of a wider struggle for justice. Once freed from this isolated logic, the next obvious step is integrating it into our advocacy, critiques, and educational material. We should turn the implication "Free Software => Free Society" on its head: Free Society => Free Software.


A claim may be undecidable given a theory. For example, consider the following statements:

  1. Alice is a Secret Service Agent
  2. Bob has never been to Georgia
  3. All Secret Service Agents have been to Georgia
  4. Fred works with Susan

We can deduce that Susan is not a Secret Service Agent, but we can not determine the truth of whether Fred is or is not a Secret Service Agent.


Before the writing process begins, it is essential to understand what the question assigned is asking you. There are numerous ways to tackle the same questions.

The central words are "egoism" and "interesting". Specifying what you mean by both will be important for a good answer to this question, and you should at the least give a brief definition near the start of your essay. In this case, there are several different theories of egoism, and you may want to argue, for instance, that one version can be both coherent and interesting, while another version cannot. If you decide to make this argument, you will need to define or describe each version that you discuss as well as give a general definition of egoism that makes it clear that all theories you discuss fall under the umbrella term.


Deduction is the only way to prove new things from old in mathematics. But where where do you start? Classical Greek scholars such as Eudoxus, Euclid, and Archimedes provided the answer: the study of every branch of mathematics must begin by accepting some statements without proof ("the axiomatic method"). In the great works of Euclid and his contemporaries, some of the assumed statements were called "axioms" and others were called "postulates". (Axioms were more universal, whereas postulates pertained more to the particular subject.)

How are the axioms for any branch of mathematics determine? Here is where emprical methods come in. The only way to verify that they are true is by intuition and common sense, expereince and lots of examples.

The theory of the axiomatic method has been liberalized somewhat in the last two centuries. The classical Greek idea was that the axioms must be true. Modern mathematics realizes that the idea of truth is often dependent on one's interpretation and that any axiom systems that at least fits some consistent interpretation or "model" should be an allowable area of study. The most famous examples of the liberalization pertains to the parallel postulate of Euclid's geometry, which implies the existence of straight lines in a plane that don't meet. This seems obviously true, but early in the nineteenth century it was noted that this postulate is false on the surface of a sphere (with straight lines interpreted as great circles, since arcs of a great circle are the shortest paths between points on the surface of a sphere). The subject of non-Euclidean geometry may have seemed like a strange curiosity when it was first introduced, but it took on added significance in the twentieth century when Albert Einstein's general theory of relatively showed that our physical universe is actually non-Euclidean.

One twentieth-century school of thought, called "formalism", holds that mathematicians should not worry at all about whether the axioms are "true" or whether the thing they study have any relationship at all to the "real world".


Usually, arguments are made in parallel. That is, I'll list off five reasons why I don't believe X. And as long as one of them stands, I won't believe X. To change my mind you have to refute all five.


Thought this remark on having to be skeptical of people who only try something and don't actually use it was interesting:

Sweet. Hopefully not sweet as in the Pepsi versus Coke trick (i.e. ask me again when I've drunk the whole can) but even if it is regarded as mere sugar for Amazon compute, Domino data labs seems to me to represent good, very reasonably priced sugar that doesn't get in the way of itself or you.

I like this as a way to launch a counterargument:

I see your point, but don't necessarily agree 100%.

Alain de Botton. Hegel Knew There Would Be Days Like These. http://www.thebookoflife.org/hegel-knew-there-would-be-days-like-these/

A dialectic is a philosophical term for an argument made up of three parts: a thesis, an antithesis, and a synthesis. Both the thesis and the antithesis contain parts of the truth, but they are also exaggerations and distortions of the whole, and so need to clash and interact, until their best elements find resolution in a synthesis.

Hegel thought this pattern a constant in history. The world makes progress by lurching from one extreme to another, as it seeks to overcompensate for previous mistakes and generally requires three moves before the right balance on any issue can be found.

For example, the Ancient Athenians discovered the idea of individual liberty, but their regime was blind to the need for collective discipline and organisation. The Ancient Persians knew all about that and were thereby able to conquer the Athenians on the battlefield, yet they were also despotic enemies of free thought, which with time became its own liability. It took many centuries for the correct synthesis between liberty and discipline to be worked out in the form of the Roman Empire.

In Hegel’s own era, the stifling, unfair 18th-century system of inherited monarchy had been abolished by the French Revolution – but what should have been the peaceful birth of representative government ended up in the anarchy and chaos of the Terror. This in turn led to the emergence of Napoleon, who restored order but became a military brute, trampling on the liberty he had professed to love. Only after forty years and much bloodshed did the modern ‘balanced constitution’ emerge, an arrangement which more sensibly balanced up popular representation with the rights of minorities.

Or to take another example, the European Enlightenment had stressed the importance of Reason, but it had in many parts been sterile and reductive. The movement known as Romanticism had then swept in to assert the importance of Emotion but this had carried excesses of its own. Only eventually had a correct reconciliation been worked out between the legitimate, competing needs of Reason and Emotion.



Turing was working in a tradition stretching back to Gottfried Leibniz, the philosophical giant who developed calculus independently of Newton. Among Leibniz’s many contributions to modern thought, one of the most intriguing was the idea of a new language he called the “universal characteristic” that, he imagined, could represent all possible mathematical and scientific knowledge. Inspired in part by the 13th-century religious philosopher Ramon Llull, Leibniz postulated that the language would be ideographic like Egyptian hieroglyphics, except characters would correspond to “atomic” concepts of math and science. He argued this language would give humankind an “instrument” that could enhance human reason “to a far greater extent than optical instruments” like the microscope and telescope.

He also imagined a machine that could process the language, which he called the calculus ratiocinator.

"If controversies were to arise, there would be no more need of disputation between two philosophers than between two accountants. For it would suffice to take their pencils in their hands, and say to each other: Calculemus—Let us calculate."

Leibniz didn’t get the opportunity to develop his universal language or the corresponding machine (although he did invent a relatively simple calculating machine, the stepped reckoner). The first credible attempt to realize Leibniz’s dream came in 1879, when the German philosopher Gottlob Frege published his landmark logic treatise Begriffsschrift. Inspired by Boole’s attempt to improve Aristotle’s logic, Frege developed a much more advanced logical system. The logic taught in philosophy and computer-science classes today—first-order or predicate logic—is only a slight modification of Frege’s system.


Sometimes the same argument can be used both for and against a position. For example, the Sorites paradox can be used to argue people both should and shouldn't vote.

In the same vein:

It's interesting how a modern system that lines up with evolutionary theories can either be framed as "the natural, healthy way we were meant to to do x" (if you're pushing a paleo diet) or "the pre-civilized, caveman way of doing y" (if you don't like Tinder.)

Terrible title. Tinder isn't the cause, it's just a medium, and we're all acting like cave people in every aspect of life if you follow the logic "evolutionary instincts=cave people"

Similarly, sometimes a claim made for one thing cannot be said for another similar situation. For example the headline "New York Attack Underlines Central Asia as Growing Source of Terrorism" appeared in the Wall Street Journal in October 2017. On first reading it sounds okay, butt the claim "Las Vegas Attack Underlines Iowa as Growing Source of Terrorism" is absurd, which suggests something is wrong.


Why is this reasoning wrong?

  1. Correlation is not causation
  2. Islam as a set of idea does not inspire terror. If it did, given size of Muslim population, we'd all be dead.

The terrorist themselves explicitly say they're carrying out jihad based on faith.


Saying that only certain people's opinions matter on X is a tacit admission that X is subjective.


When white people move in, it's gentrification. When they move out, it's white flight.


Usually "I can't understand why ppl think..." is just intellectual laziness, motivated by a desire to portray ppl as unreasonable.

But some views I can't understand even after making a good faith effort. Example: Why is there so much hate for ppl posting food photos online?


Eliezer_Yudkowsky. Oct 5, 2007. Avoiding Your Belief's Real Weak Points. http://lesswrong.com/lw/jy/avoiding_your_beliefs_real_weak_points/

In Modern Orthodox Judaism I have not heard much emphasis of the virtues of blind faith. You're allowed to doubt. You're just not allowed to successfully doubt.

The reason that educated religious people stay religious, I suspect, is that when they doubt, they are subconsciously very careful to attack their own beliefs only at the strongest points—places where they know they can defend.

My point is that, when it comes to spontaneous self-questioning, one is much more likely to spontaneously self-attack strong points with comforting replies to rehearse, then to spontaneously self-attack the weakest, most vulnerable points. Similarly, one is likely to stop at the first reply and be comforted, rather than further criticizing the reply.

More than anything, the grip of religion is sustained by people just-not-thinking-about the real weak points of their religion. I don't think this is a matter of training, but a matter of instinct. People don't think about the real weak points of their beliefs for the same reason they don't touch an oven's red-hot burners; it's painful.


A degenerate case is a limiting case in which a class of object changes its nature so as to belong to another simpler class. For example, the point is a degenerate case of the circle as the radius approaches 0. And the circle is a degenerate form of an ellipse as the eccentricity approaches 0.


"But Stalin was bad" isn't any more of an argument against communism than "but Oliver Cromwell was bad" is an argument against capitalism.


Teaching men not to rape is just as hateful as teaching Muslims not to blow things up or blacks not to steal.


"Black Americans comprise 13% of the population, but they make up 40% of the prison population. Need more evidence that systemic racism is real?"

"Men comprise 49.2% of the population, but they make up 93.2% of the prison population. Need even more evidence that systemic sexism is real?"


Marijuana is sometimes claimed to be a gateway drug, probably because professionals in treatment facilities see that it was for the people there. This is classic selection effect.


If you care about persuading people who disagree with you (especially if you think they've come to their conclusions through motivated reasoning & don't want to agree with you), maybe it's best to set higher standards of evidence for the things you already believe are true.


Arguably, critical reasoning degrades with "promiscuous" reading, which would suggest to choose carefully and read little.


On the terms "involuntarily" implied to incels:

No one says they're involuntarily poor or involuntarily unsuccessful. That would imply that someone else did those things to you.

Argument against a gender wage gap:

Similar with race.


Why do statements imply causation?

Headline: "Women who own horses live longer"

Implied: horses make you live longer

Reality: if you own a horse, you can probably afford health insurance


There are different standards of evidence:

  1. "Innocent until proven guilty" is a legal standard
  2. Job interview standard (which might take mere suspicion into account; "Caesar's wife must be above suspicion")
  3. Reasonable suspicion to investigate. Warrants don't require proof beyond reasonable doubt.

Simply put, describing the call for climate action in economically or politically revolutionary terms is always going to be counterproductive, because the vast majority of ordinary people in most countries don’t want a revolution.


Stephen Trusheim response to a company claiming their AI can detect with 95% accuracy if a person will leave:

95% accuracy? This is a key way to lie with statistics.

Depending on the timeframe, I’d guess ~5% of employees are going to leave. So you make an AI that says “nobody is going to leave!” And voila, it’s 95% accurate.

Sure, it’s missing 100% of the employees that do leave, but that’s called sensitivity - not accuracy!

This is not just a funny note, it’s a key question in AI systems. It’s why we have to look at things like F scores, ROC curves, etc. It’s also a key question, eg for poachability and alerts. We can maximize coverage at the expense of over-inclusion, or we can have a much smaller set of high quality that miss a bunch of important ones. Which do we do?


Inference differs from modus ponus. Illustrated by "What the Tortoise Said to Achille". http://www.ditext.com/carroll/tortoise.html


A wedge issue is a political or social issue which splits apart a demographic or population group.