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Project Logicality: Arguing by Assumption — The Enthymeme

Life restoration of Tiktaalik roseae, a transi...

Life restoration of Tiktaalik roseae, a transitional fossil (“missing link”) between sarcopterygian fishes and tetrapods from the late Devonian period of North America. Original description: “Fossil fish bridges evolutionary gap between animals of land and sea.” (Photo credit: Wikipedia)

Many arguments we make in daily life are incompletely stated, and often less than completely certain in both structured debates and in informal discussions.

Some such arguments are called Enthymemes, arguments in which one of the premises, or the conclusion, is not stated but implied and needed for the argument to follow.

Why leave these out?

It depends on the situation, and upon the shared understanding of those involved in the discussion.

Generally, one part of an argument may be unspoken because it’s assumed by both and doesn’t need to be stated. So these parts will need to be teased out by a third-party analyst of the argument to determine fully what is being argued.

This can be an intellectually honest form of argument, and I offer some examples here.

I’m using standard form deductive syllogisms — conditionally certain three-part arguments with two premises and a conclusion — for ease of presentation. The first is a 1st order, or unstated major premise, argument:

  • The Magna is a mutant.
  • So the Magna is radioactive.

With the major premise being:

  • All mutants are radioactive.

This one has a hidden minor premise, or 2nd order enthymeme structure.

  • Not giving the proper homage to the Nine Who are One will endanger all our lives.
  • So we should not fail to give proper homage to the Nine.

With the hidden premise given as:

  • The Nine would wish us to do that which preserves our lives.

Finally, we have one in which the conclusion is left unstated, of the 3rd order:

  • We must deal ruthlessly with all freakishly powerful threats.
  • The Mirus is a freakishly powerful threat.

It’s not hard to see where this one will go… The conclusion, though unstated, should be obvious.

In some situations this sort of argument is less than intellectually honest, when the assumptions are NOT shared, or need to be fully expressed, this may be used to obscure matters as a rhetorical fallacy, as a tactic that obscures the meaning of an argument and makes misdirection and confusion easy.

This happens when the aim intended, or not attempted to avoid, is thwarting the goal of honest critical discussion. I’ll provide an example of this as a fallacy, this one from a hypothetical creationism/evolution debate in which the major premise is obscured:

  • No fossil meeting my (impossible to satisfy) criterion as a transitional form has ever been found,
  • So there are no transitional fossils, so evolution is false.

But here is the missing major premise, NOT shared or expressed, and assumed only by the creationist:

  • To count as transitional, a fossil must be an impossible, half-formed monstrosity combining unlikely features of dissimilar species or ‘kinds,’ like a lizard/bird hybrid with incomplete, useless wings… (or a crocoduck)

‘Enthymeme’ has also been used to refer to probabilistic arguments, such as those used in inductive reasoning or in informal argumentation with language bound up with an argument’s content, and the conclusion follows from the premises more or less strongly depending on the audience.

One such maxim may be “Present-day Continental philosophy is not credible,” which could elicit different responses and have differing levels of credibility depending on the chosen philosophical schools of those hearing or reading it.

As can be seen, some of the very same sort of statements used in ordinary argumentation can be fallacies, and indeed, when informal, their fallaciousness depends on their misuse as argument strategies, not so much the the structure of the argument; they are more often violations of procedure than logical form.

Many fallacies are not always such, but even otherwise effective arguments, when they are put to specious use, are pure argumentative poison no matter their rational structure.

Talotaa frang.

Project Logicality: Generalizing & Classifying both Deductively & Inductively

Isaac Newton (Bolton, Sarah K. Famous Men of S...

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It’s often said that the distinction between deductive and inductive reasoning is that one argues from the general to the specific, and that the other does so from specific to the general, but this is not correct across all forms of these sorts of reasoning.

Each can work both ways. Whoa. That’s quite an assertion, so I’ll attempt to show why here…

In deductive reasoning, the truth of an argument’s conclusion automatically follows from the truth of its supporting statements if it’s valid. Also, it’s possible for one or more of such an argument’s supporting statements to be false, and this renders it unsound even when valid. Valid but knowingly unsound arguments are not persuasive, and cannot ethically be used as though they were compelling.

Deductive arguments reorganize what we know rather than providing any new data. Deductive conclusions cannot go beyond what’s expressed or implied in their supporting statements.

Inductive reasoning, such as some of the informal sort more typically used in everyday life, can only justify conclusions as more or less probable, depending on the strength of the argument and the prior adherence of an audience to its evidence. This form of reasoning does provide new knowledge, by moving us from the known to the unknown, unstated, and not implied.

In generalizing from particular examples, I’ll show how it may be deductive and then inductive:

If I were to be on the shoreline of my local beach, and noted that the pebbles found there were worn smooth and comfortable to the touch by the actions of water and sand, and were to completely and perfectly enumerate each and every such pebble on the shore, to find them all worn smooth, an unlikely and difficult task at best, I would know with certainty that all of these pebbles were smooth and comfortable to the touch. Each and every one. The argument would then follow deductively.

If, though, I were to find one smooth pebble, and then another, and so on, and after noting from a large enough but limited sample of such stones that they are almost all smooth to the touch, though I may find a few which are not, I could conclude inductively that they are more often smooth and worn than not. The argument follows to a high degree of probability based on the size and representativeness of the sample examined, and it is an acceptable substitute for the certainty we cannot usually get in measuring things in the real world.

The things to look out for when generalizing are known as the fallacy of composition, and the hasty generalization, these errors made when we attempt to apply deductive certainty where it does not belong, the first in assuming that the whole of a population is necessarily like the parts, and the second in drawing an unfounded general conclusion on the basis of too little sample data.

Now from general to specific, classifying rather than generalizing.

If I were to get a perfect count of all sand-ground stones on this hypothetical beach, not over-counting or skipping some, and they all were worn smooth, then I could conclude certainly that any one of these stones was going to be smooth in texture just like all the others. The argument would follow deductively.

But if I were to do the more likely thing, and count a fairly sizable number of these pebbles, all showing signs of wear and smoothness, then I could argue with a good chance of being correct in saying that any one of the stones I pick up would be ground and smooth. It would then be an inductive argument.

The error to avoid committing here is the very opposite of the fallacy of composition, the fallacy of division, in which one misapplies deductive certainty by claiming that the part is necessarily like the whole.

To close out, the examples I used in this post come from a quote attributed to Sir Isaac Newton, that cranky and brilliant English guy, which goes:

I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me. ~ Memoirs of the Life, Writings, and Discoveries of Sir Isaac Newton (1855) by Sir David Brewster (Volume II. Ch. 27).

Project Logicality: The Reductio Ad Absurdum – Invalid & Valid

Let’s suppose that there are two men engaged in an argument, we’ll call them Mr. A and Mr. B.

They’re engaged in a rather spirited discussion on psi-phenomena, and Mr. A argues that psi is unlikely to exist because truly compelling evidence, in the form of successful replications of psi, regardless of the beliefs or level of enthusiasm of those attempting the replication of the initial studies, does not currently exist.

Note that he is not saying he doesn’t think it’s real because he hasn’t personally experienced it nor seen concrete, direct evidence of its existence, but that despite the immense volume of evidence in the literature, it just isn’t very convincing by reasonable scientific standards, and so one should remain skeptical for the time being.

Nor is he arguing that it’s impossible, only unlikely to exist until convincing evidence under reasonable conditions by reasonably objective research workers indicates otherwise.

In his rebuttal, Mr. B argues that Mr. A, in thinking that psi probably isn’t real, must also believe that dark energy and dark matter must not exist, because Mr. A hasn’t seen them either, and that he must therefore believe that 90% of the universe must not exist.

But wait…

Mr. A said nothing about needing to see psi himself, only that convincing evidence obtained under adequate conditions by non-believers in psi is not there, not yet, saying nothing at all about the evidence needed to establish dark matter or dark energy, both of which have different evidential requirements than psi does, for which almost the entire body of data consists of statistical quirks, convincing or not.

Mr. A’s argument has, as can be seen, been misrepresented, and in such a way as to carry it to an absurd conclusion, the claim that by his own reasoning, most of the universe doesn’t exist.

That last was an example of a fallacious Reductio ad absurdum, and of course there was probably much more said than simply the above. But Mr. B’s argument was fallacious because it led to an absurd conclusion without using the actual chain of reasoning of Mr. A’s argument, by misrepresenting that argument as a straw person.

Later, Mr. A and Mr. B get into a discussion of the nature of reality, in which Mr. B, not liking the direction of the argument, responds to what he feels are the overly absolutist statements of his opponent, in exasperation saying in a rather postmodern fashion, “Reality is nothing!”

There are several ways that this can be interpreted, but in this case, a clarification is not offered, and Mr. A cannot read minds nor thinks at the time to ask for a clarification, so the most likely interpretation, that B is claiming reality doesn’t exist, will have to do.

What does this mean? Can we carry this claim to it’s ultimate conclusion without merely misrepresenting it?

Let’s see…

What is reality? And I don’t mean what is its ultimate nature in fact, but what is the meaning of the word? How is it used?

Reality, by definition, is that which can truly be said to exist, no matter it’s nature or other properties:

a=a: reality is real.

To be real, this quality of existing is essential, whether the thing existing is directly observable or not. If something doesn’t exist, then it’s not part of reality, and if it’s not even imagined, it’s not fantasy either.

What is everything that is real?

We call it the Universe, or the Cosmos, take your pick, though myself, I’m partial to the latter, though for this discussion I’ll use “universe” for the totality of existence.

To say that reality is nothing, in this context implies that the universe doesn’t exist, 100% of it, not just 90% in the straw person argument above, since the universe is everything, with or without any supplementation to it by anything allegedly supernatural.

But if the universe is everything that exists, and everything currently within and originating within the universe, by definition existing as part of its totality, and therefore part of all reality…

Hmmm… I smell something funny about this, don’t you?..

If the ‘reality does not exist’ interpretation holds and the claim were true, then the claim could never be made, since neither of the two persons would even exist themselves in order to have their argument.

But if Mr. B exists to make his argument to Mr. A, and Mr. A exists to hear the argument, then the claim, assuming this interpretation, is simply, obviously, and demonstrably false.

Clearly this is an unacceptable conclusion, at least until such time as Mr. B offers a clarification of his statement that requires a different interpretation of what he said, we must assume what we did know and thus consider this a valid Reductio ad absurdum.

But personal debates among argumentative friends are often messy, impromptu, with little if any ‘rehearsal’ or ‘practice’ beforehand, and unless both are skilled arguers, it is unlikely that normative standards or ideals will reasonably be met without time and practice.

This is just one of the hazards of personal arguments, but it’s something that can be improved if done systematically and with time, skillfully and instinctively, but the rewards of rich and confident testing of our knowledge by argumentation far outstrip any annoyance that may result in the beginning.

Project Logicality: Argumentation’s Basic Assumptions

An argument is a connected series of statement...

An argument is a connected series of statements intended to establish a definite proposition. (Photo credit: harold.lloyd)

This is the second re-release in my Project Logicality series, and it was posted in its original form in April of 2011. I’ve corrected and re-written this and reposted it here, hopefully clearer and to the point. May all your arguments be rational and all your disputes be resolved. ~ Troythulu

We persuade others through our arguments, to get them to accept the statements and claims we make as likely true of their own free choice, justified on the basis of the reasons we give rather than prove them absolutely. Argumentation contributes to healthy discussion and debate, to let those so arguing find common ground, and to make easier a willingness to compromise.

People argue daily, though seldom with skill, and in my view, argumentation as a well-honed tool of a functional democratic republic is needed more than ever with the increasing decay of social discourse, political polarization and interpersonal conflicts that ever more are seen as irreconcilable.

In this post, I’ll describe the basic assumptions and basic conditions that go into any attempt at constructive argument, and before I do, I’ll note as before that good argument is intellectual in force, not coercive or deceptive. It is an ethical means of influencing others, limiting their freedom of action without imposing on their freedom of will.

First, argument is carried out under conditions of uncertainty: We generally don’t argue about things we think certain, though that doesn’t prevent us from talking about them.

We argue about things because we think it important enough to convince others of them, and things may well turn out to be otherwise. If things were absolutely self-evident, they would be so to all, and there would be no need to convince anyone of them.

These differences may be implied and apparent to an analyst, concealed in the context of an argument, or explicit, obvious to an audience. Bear in mind that even the concept of certainty can depend on the audience addressed and the assumptions they bring to the table as to what it means.

Second, Argumentation must consider the needs of an audience. people argue about things that matter to them, attempting to resolve what they think are conflicting positions that cannot simply be settled by any non-argumentative means; appealing to common knowledge, or widely-shared empirical methods; things they consider to be non-trivial, matters important enough to need resolution.

This is not to pander to their biases, or to say that one claim is just as good as any other, it’s just that in being ethical, we must consider what is likely to persuade a given audience as if they were exercising their critical judgment on the merits of the arguments we give, and the soundness of the justifications we offer for our claims.

The audience is the final judge of whether an argument is strong or weak, justified or not, assenting to it if it is strong or justified, rejecting it if not.

Third, argumentation is both adversarial and cooperative. we make choices in arguments, choices in what arguments to select, and how to arrange and present them, based upon the audience we are addressing.

The adversarial components of argumentation help the rigor of the discussion; they help us avoid hasty generalizations; they reduce omission of important details. Skilled arguers seek first to find common ground which is itself the bedrock upon which they can meaningfully discuss their disagreement. Ultimately, these enhance our confidence of the outcome, a confidence pending better arguments to be made in future.

Fourth, argumentation involves restrained partisanship. It requires a cooperative effort between arguer and audience, despite the contentiousness often associated with everyday argument.

Arguers must share a common system of terms, assumptions, and meanings. This allows resolution of the dispute, and is needed to permit any meaningful argument at all.

Fifth, and finally, argument involves elements of risk. This is the risk of losing the argument, the risk of being shown wrong, the risk of having to alter one’s views and position, and in either case the emotional disruption of wounding one’s self-esteem or losing face with others.

But the cooperative aspect of argument means that in willingly accepting these risks, each arguer is respecting the rights and personhood of the other, and in so doing, claiming that same privilege of respect from the other for him or herself.

I think that these are good situational benchmarks, and are the optimal conditions, I would argue even necessary conditions, under which can be made any serious attempt to argue constructively, for the purpose of reaching the best possible conclusions given the means at hand.


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Project Logicality: What is Argumentation?

Cropped image of a Socrates bust for use in ph...

Cropped image of a Socrates bust for use in philosophy-related templates etc. Bust carved by by Victor Wager from a model by Paul Montford, University of Western Australia, Crawley, Western Australia. (Photo credit: Wikipedia)

This post was originally published in 2011, and since then I’ve decided to give it new life and clear up difficulties in the text. I decided to use it once for for the pilot entry of my current Project Logicality. I hope it adds to the online discussion of the virtues of reason despite the decidedly unreasonable tendencies of the human species.

What is it that I mean when I say ‘argument?’ When I use this term, I don’t mean quarrelsome bickering accompanied by yelling and screaming, nor do I mean a mere shadow of an argument where debaters try to undermine the legitimacy of each others’ position without attempting to reach a real understanding or settling anything.

When I say, “argument” I mean it in the context of any rational discussion with constructive intent, not an attempt to thwart constructive ends through fallacious means.

Here, I mean that the parties involved act to offer reasons, premises, rationales, and justifications for the statements, the claims, and the ideas that they put forth. They want others to accept these, not merely by pandering to their prejudices or appealing to their biases, nor upon the use of legal or physical force, but by winning the free assent of that audience — an audience treated as though it were in principle intelligent, educated, and capable of exercising rigorous critical judgement.

I refer to argument in the sense of modern argumentation theory, a vibrant field of study involving the making and use of messages to influence others, by appealing to their willingness to cooperate — this is essential for the conditions of a viable free society.

Any coherent social structure, especially a functioning representative democracy with a large number of people needs some means of mutual influence between its members, of and for the viability of its governing system, however imperfect its governing body in practice. Perfection in matters of human endeavor is a chimera.

Argumentation as a field of study crosses paths with three other areas of intellectual endeavor:

First, it converges with Logic, the broader study of the structures we use in all processes of reasoning — this includes formal logic, mathematical and symbolic logic where the conclusion of a valid argument is alleged to be certainly true if the premises used to support it are also true.

But argumentation concerns itself more with informal logic, the everyday reasoning we engage in within typical discussions — in which the statements we wish to support do not follow with certainty, but to a degree of probability depending on the strength of our reasons and the willingness of the audience to accept them.

In argumentation, even the very idea of certainty depends on the audience addressed.

Language is important in informal logic, because informal argumentation depends heavily on the use of language as the content of the argument. Language is more than merely decorative window-dressing for an informal argument, but an essential part of the argument’s inherent meaning. The language that an argument is cast in cannot be taken from the argument itself without rendering it sterile and empty.

Second, argumentation converges with Rhetoric, originally one of the seven Liberal Arts — it is more than just vacuous or bombastic and flowery ornamentation in speech as is commonly supposed, but in the technical sense it is the broader study of how people are influenced by messages.

It is from Rhetoric that argumentation gets the concern with the requirements of an audience — its needs, disposition, and outlook must be considered by the arguer in making their case.

Third, argumentation crosses over with dialectic, a term that many people still associate with the concept of an opposition between grand historical forces, like the opposition of capitalism and communism depicted in Marxist social theory.

This concept has a different meaning, and dates at least since the Socratic method,  given in the dialogues of Plato, and others, in which fictionalized persons are seen to engage in a sort of give and take exchange of questions and answers to resolve a dispute or reveal the truth of a matter.

This sort of questioning is similar to the use of cross-examination of witnesses in modern legal courts by the prosecuting attorneys in a case to uncover inconsistencies in testimony and to reveal possibly questionable motives.

Argumentation is the meeting point of all of these fields, and with it, we can clarify our understanding of our positions, resolve disputes, reach sound decisions for collective actions we may undertake, engage in formal and often productive debates, and, with ourselves as the audience, think through personal problems we may face or get out of a rut.

Argumentation as a process of giving reasons for our claims is one of the most important abilities we have as humans, and no matter our level of education, we can all benefit from the ability to arrive at better answers to questions and make more sound decisions than we otherwise might.

Argumentation isn’t just for egghead academics: Clear thinking and having good reasons for what we believe and do are for everyone. As humans, we are not always rational, but we have a sense of reason, one that once nurtured and practiced can serve us and enfranchise us as informed, effective, and smart voters very well indeed.


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