Tag Archive | Logic

Project Logicality | The Non Sequitur Fallacy

What’s going on when the reasons we give to support or refute a statement have no relation to it at all? What is the fundamental error of reasoning underpinning almost all logical fallacies, and when does this represent special cases?

Here we discuss the general fallacy of the Non Sequitur, Latin for does not follow.

This can generally refer to any sort of logical fallacy, any argument where a logical connection between premises is implied that just isn’t there.

This fallacy is often found with other forms of invalid reasoning in the very same statement. Here’s a couple of handy examples of the most common form:

Our cult shall be feared by all, for Azathoth is freakin’ scary when annoyed.

Human-caused global warming is impossible, because it’s cyclical, the ozone hole over the antarctic is closing, cow farts, and Mars is warming too, not just the earth.

But there are more specific named forms of this fallacy as well:

The Fallacy of the Undistributed Middle:

In which a conclusion is incorrectly drawn from two given or assumed premises, and takes the form of:

All Xs are Cs.

A is a C.

So, A is an X.

An obviously ridiculous example would be:

All birds generate their own body heat.

My cats generate their own body heat.

My cats are birds.

There is…

…Denying the Antecedent:

Which takes the form of:

If C is true, then D is true.

C is false.

So, D is also false.

A good example would be:

If I am in ancient Athens, I’m in Greece.

I’m not in ancient Athens.

So, I’m not in Greece.

This is absurd, as there are many locations and times in Greece other than Athens or the Ancient period. There is also…

…Affirming the Consequent:

which takes the form:

If C is true then D is true.

D is true.

So C is true.

An example:

If my Senior Technician intends to transfer me to another project, she’ll have a talk with the Program Director.

My Senior Technician is going to talk with the Program Director.

She wants to get me transferred to another project.

This last is clearly an example of invalid reasoning because the Senior Tech could be seeing the Program Director for entirely different reasons than those given.

One problem people sometimes have with this fallacy is that it can be subtle, and they are often too proud to speak out when they cannot see how an argument follows, or are too polite to point out its lack of relevance to the speaker.

It’s important to more specifically pick out what is being said even as a less general sort of fallacy, including the non sequitur’s aforementioned variants.

So be careful that what facts you bring to an argument are actually relevant to the point you’re trying to make. Otherwise, it may just fail the application of the “so what” test!

Tf. Tk. Tts.

(Fully Updated, Retitled, Broken Links Removed on 2017.06.06)

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Project Logicality | The Appeal to Nature

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This entry deals with an error in reasoning known as The Appeal to Nature, often confused with the Naturalistic Fallacy, and its reverse, the Moralistic Fallacy.

To keeps things short n’ simple, the Naturalistic Fallacy is the confusing of a statement of fact with a statement of subjective worth, a value judgment, an ought from an is, without sound justification, while the Moralistic Fallacy is the confusion of a value judgment with a statement of fact, an is from an ought with an equal lack of good reason.

Is does not by necessity imply Should be, nor does Should be imply Is.

Either of these is an informal fallacy.

The Appeal to Nature typically takes the form of an argument that because something is natural, and of similar use are the familiar marketing buzzwords organic and holistic it is therefore right, good, safe or better than something that is artificial or more efficiently produced, or because something is artificial, it is therefore implied to be inferior, undesirable, bad or wrong…

…For example:

  • Someone tripped over an invisible turtle and staved in his skull on a rock. It is therefore correct to assume that the natural causation (gravity, and impact with a large piece of rock, a naturally-occurring substance…) of the damage to his cranium means that the damage is therefore right or desirable, and should thus not be treated by a physician.

The above is perhaps an extreme example, and then there is the following:

  • Vitamin A, when artificial, is harmful to the body, though not when it is natural, in any arbitrary amount for either.

The above is fallacious because whether natural or synthetic, vitamin A is exactly the same molecule regardless of how or where it is produced, and whether it is safe or harmful depends entirely on the dosage.

Because these last two examples are concerned with the goodness/badness or rightness/wrongness of something based on its origins they also constitute variations of a genetic fallacy.

There are a great many things of completely natural origin that are nonetheless rather unsafe. A few are below:

  • Arsenic, Cadmium, and Uranium are three highly toxic natural elements…
  • There are the herbs Hemlock, Foxglove, and Belladonna
  • …in addition to all other animal, mineral, and plant toxins, such as the venom of certain species of trapdoor spiders, curare, rattlesnake venom, platypus venom, a huge host of poisonous fungi such as species Amanita muscaria

A common argument using this fallacy is the assertion that behaviors and practices “found in nature” are good or more desirable than modern behaviors, such as some of our more detrimental evolved social instincts being “right,” even though in our modern technological society they no longer convey the survival benefits they did to our ancestors on the plains of Africa, now that we are a global species. The following is one such argument…

  • Before we were a technological species we were one with the natural world, but soon we shall pay for our continuous crimes against nature. For every illness we’ve bought temporary respite from through modern medicine, another, more resistant strain takes its place. How long can we keep at our unnatural and invasive medical procedures, when all we are doing is living longer and longer and getting sicker and sicker with each new ‘advance’ in treatment. The only way we can be truly healthy is to return to our roots, to return to nature and relinquish the evils of science and technology.

First, humans have always been a technological species, and we’ve been that even before we were human.

Second, we were then mostly ignorant about the natural world, and saw the supernatural everywhere.

As a species that better understands Nature now than we once did, instead of attributing everything to mystical influences in our ignorance, praying and chanting to invisible and probably nonexistent spirits in invariably failed attempts to cure horrible illnesses, with that better understanding comes a closeness to nature unparalleled by our ancestors even a century ago.

We understand better how nature works, and our scientific and medical advances, limited though they may be in some areas, have given those with access to them greater health and quality of life, and the greater modern life-expectancy and standards of living are reliable indicators of this.

Those belonging to a typical middle-class family live longer and in greater luxury on the average than a medieval king, though perhaps with less gold stashed in the cellar.

Yes, scientific advances are a double-edged sword, but we can’t solve the problems brought about by knowledge by replacing it with ignorance. A problem caused by misuse of knowledge can only be remedied by the use of better knowledge than that which caused the original problem.

Have fun looking for this fallacy in everyday discussions and in the media, especially advertisements for questionable ‘food supplements’ and medical products using the previously mentioned buzzwords, products which tend more often than not to have a high price tag, at least in cash if not in possible health consequences.

Consider: Despite what mystics and quacks will tell you, it pays to be skeptical.

Project Logicality | Zikky the Imp & The Inconsistency Fallacy

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Objects-of-faith themselves are now outside the scope of my blogging. But arguments regardless of original purpose are fair game as they are logically testable. Thus do they open themselves to meaningful critique.

First, the laws of logic demand consistency in their use. You do not get to cherry-pick what reasoning supports your conclusion nor dismiss as silly or absurd what doesn’t. Absurdity is often claimed through the use of disingenuous rhetoric. The claim that actual infinities are impossible because they lead to absurdity are a case in point. Asserted most often by Dr. William Lane Craig, the claim is easily falsified merely by consulting a book by any professional mathematician who regularly works and writes on set theory. The fact that infinities can lead to absurdities in certain arithmetic operations does not prove their actuality impossible, only that you cannot perform those operations using infinities. There is dangerous equivocation to be committed by toying with the semantics of words like ‘actual.’ There is much difference between ‘actual’ in a physical context, and ‘actual’ in a mathematical one. Also, if you declare actual infinities impossible, you must declare all actual infinities impossible including those that favor your argument. You do not get to invoke nonsense, such as ad hoc ‘qualitative infinities’ to save your claims from your own line of reasoning. This is why I refuse to debate apologists; I’ve little patience with dishonest argumentation in a debate partner, and I find it annoying and frustrating. The trouble here is, they just don’t seem to know, or possibly know and don’t care. It matters little. That’s bad for keeping my stress levels down, so no.

Onward, then…

So, let’s say there’s a mischievous imp. We’ll call him Zikky. Zikky (not to be confused with Zippy of pinhead fame…) is a very special sort of imp, a Cartesian demon. He’s a diabolical master of illusion and delusion who can make anyone see and think whatever he likes them to. He’s a virtuoso at mucking with peoples’ heads. He can create whole, self-consistent virtual worlds in any and all minds he wants to. For all functional purposes these virtual worlds cannot be told from ‘the real thing.’ Let’s assume an agnostic position as to whether Zikky really exists. Let’s also assume he has a following, a fan club who idolizes their hero and collects his trading cards.

Despite those pesky doubters who require his existence be shown to some reasonable standard of logic and evidence, Zikky’s fans claim that those are all completely irrelevant to his existence. ‘We don’t need evidence, or logic,’ they say. They also argue that there is both rational and empirical evidence for this; supposedly self-evident reasoning and evidence throughout the natural world. Many of his fans say they’ve met and talked to him personally at conventions. And there is the allegedly rock-solid proof of personally signed Zikky the Imp collector’s cards. Hmmm. It looks as though they are trying to have their chapattis and eat them too!

Fallacy! But while the fact of a fallacy doesn’t show a claim false, it does show that a claim does not follow from the arguments given. Throw those arguments out; they’re at cross-purposes, and so no good!

Relevance works both ways, not just in one direction. If X is relevant to Y, then Y must be relevant to X. The same for irrelevance. They are symmetrical. There is a causal chain that necessarily links both ways even when moving in only one direction.

So if logic and evidence are irrelevant to Zikky, then Zikky is irrelevant to them. Just as you cannot absolutely disprove Zikky’s reality using reason or facts, you also cannot use them to show that he’s real. After all, he’s a master of fiddling around with peoples’ minds not bound by any natural laws. How could anyone possibly know? How would a world with or without Zikky in it appear? No conceivable observation, no knowable brute fact, is inconsistent with either possibility. It cannot be tested, and philosophically, it’s not useful in any practical sense. Whatever you perceive looks and feels real no matter what’s perceived. So it doesn’t really matter whether Zikky exists or not.

Sure, the arguments for his reality are fairly weak on their own, but what if we offer them together to make our case? Can we prove our case with reason alone, using allegedly true premises and a lot of quotations as our evidence? But in fact, while argument is useful to explain evidence, it cannot substitute for it, even with supposedly true premises. Especially in formal logic, determining the actual truth of the premises is the hardest part of evaluating any argument, however valid we find its structure. It’s easy to bamboozle with out-of-context quotes and dubious factoids.

That’s why science uses logical argument in its explanations for natural and human phenomena, and carefully gathered evidential data to support those explanations. Logic alone, outside of a context of maths or pure logic is empty. For claims about anything existing in the real world, you need the data to show it. That’s what counts. Reason serves to organize and make sense of the data, but it cannot replace it. This should not be news. It’s been obvious since modern science began, and our reasoning and data-gathering have only gotten better over the centuries. Science no longer adheres to the naive overconfidence in pure reason of even a few hundred years ago. If the data don’t support it, it’s of no scientific use. No matter how persuasive the reasoning, or rationalizations, as the case may be. That’s why we’ve moved on.

It’s why science has made genuine progress, while apologetics and pseudoscience have not. If there’s no actual data supporting one’s claims, if one’s forced to make a case using the same fallacies dressed up, retooled, and rebranded with questionable data points, then they’ve not come very far at all.

Good luck convincing anyone who doesn’t already accept those claims, no matter their nature. Any fallacy, formal or informal, is enough to disqualify an argument as reliable support for any claim. But the inconsistency fallacy is among the most obvious, and among the most egregious.

Avoid it whenever possible. It will save you the effort of making up excuse after excuse to explain away those same inconsistencies.

Tf. Tk. Tts.

References:

Philosophy of Religion: Lecture 25: Evidence is Irrelevant to Faith

The God Distraction, Chapter One: Arguments

The Big Questions of Philosophy: Lecture 3: How Do We Reason Carefully?

Project Logicality | Labeling Argument Strategies & The Fallacist’s Fallacy

There are many ways to argue deceptively or mistakenly, and often these ways involve logical fallacies–flaws in arguments that come in two general sorts, formal and informal.

The former are defects in structure, errors in the pattern of the argument that render it invalid, usually independent of the argument’s specific content.

The latter are often breaches of procedure rather than structure, attempts to thwart the goal of a critical discussion, often to merely ‘win’ the argument than to achieve better understanding, to obscure truth rather than reach it. Many informal fallacies are not always fallacious.

Fallacy theory is a complex subject, and not all logicians agree on the definitions I’ve just given, but that’s cool. Fallacies can be used to distract and mislead, or they can be used in reverse, in labeling argumentative strategies, to reduce their effectiveness by calling attention to them when abused.

In some debates, such labeling will be done fairly frequently, in others, more subtle counterstrategies will be used rather than explicitly pointing out the fallacies. In this case, knowing thine enemy and naming it is useful, subjecting the flawed argument to scrutiny, and lessening its sting.

But that is not enough. And it pays to not be a dick when debating.

To argue that naming a fallacy shows the claim of an argument false is to commit the fallacists’ fallacy, as it it entirely possible for an argument may be weak, its claims not following from the premises, but the claim made can still be correct despite the argument made for it.

It is also committing the fallacist’s fallacy to falsely accuse one’s opponent of arguing fallaciously, when a fair evaluation of their argument and its context would clearly show the argument valid. Context matters with argumentation!

So it is not enough merely to label an argument. In fact, it’s advised that you don’t, at least not in an arrogant manner. What’s needed is to use your knowledge of how the argument goes wrong to craft an even better counterargument, assuming that it’s even important enough to refute. Not all arguments are, as some may be simply ignored if not worth the time spent ‘attacking’ them.

There’s a military metaphor in that, an unfortunate artifact of the history of argumentation that has given the entire field of study a reputation for quarrelsomeness and bickering.

That’s especially the case with logical inconsistencies and outright contradictions. If two or more arguments work at cross-purposes, logically at least one of them must be rejected, but the natural human inclination is to throw them all out, as reflecting poorly on the arguer’s credibility and even resulting in loss of the argument.

Even fallacious arguments sometimes assert things that are true, being right for the wrong reasons, but they cannot reliably show those things to be the case. Logic alone proves nothing, even if the argument is formally or informally valid or uses strong inference.

For that, we need objective data as well.

We need the best evidence available to support our premises, which must not only be true, but which must also be acceptable, clear, relevant, as non-circular as possible, and as free from unwarranted assumptions and presumptions as can be had.

Tf. Tk. Tts.

Project Logicality | Reducing to Absurdity

What happens when we carry a train of reasoning to its ultimate extreme, far past the reaches of sanity to the realm of the patently absurd? Here, we discuss such an argument in informal logic, borrowed from formal mathematical reasoning, and here known as the Reductio ad Absurdum.

In formal logic it may be used to show an argument’s claim to be false by following it to its ultimate logical conclusion, revealing a contradiction, an absurdity, or it may be used as a form of Straw-Man argument, known here as the False Reductio. I’ll deal first with the latter.

This works by forcing a conclusion that while absurd, doesn’t use the actual reasoning of the original argument, such as:

If you’re skeptical of the existence of UFOs, Bigfoot, and ancient aliens, then you must also be skeptical of the existence of the Taj Mahal, the Sydney Opera House, and the Empire State Building, since you’ve never been there to see those places.

This is fallacious because the proportional nature of the claims requires proportional standards of evidence. The criteria for each differ, and the argument itself ignores the use of evidence other than anecdotal testimony and grainy, low-resolution, or obviously photoshopped videos and photos.

Here is one of my favorites:

If you don’t believe in psychic abilities then you also disbelieve in dark matter and dark energy, so 90% of the Universe does not exist to you because you haven’t seen those either.

Again with ignoring evidence other than personally witnessing something. Also, it fails to consider the fact that though there is some question as to what dark matter and dark energy are, they have been reliably observed by their effects on the visible universe itself, and the evidence shows that they are real. Clearly, elusive supernormal psychic abilities and invisible but indirectly observable astrophysical phenomena are not analogous.

But all is not without a ray of light in the dark. There is an informally valid and intellectually honest use of this as well, to highlight the fallaciousness of some extraordinary claims. Here, the actual train of logic of the original argument is kept intact.

Here are a couple of silly claims I’ve come across:

The ancient Egyptians could not have built the pyramids without alien or Atlantean help. They were far too primitive a civilization.

 

In order to know what a human skeleton looks like, the Maya and Aztecs must have been given X-ray machines by ancient astronauts.

Such claims reek not only of thinly disguised racism and colonialist arrogance, but stupidity and historical shortsightedness as well. Typical of most of the claims of pseudo-archaeology, especially where ancient non-whites are not given due credit for their accomplishments.

And skeletons? Come on, that’s just silly!

Meh!

Here, we may apply the same train of logic to what the proponents of these ideas, mostly whites of Western descent, dare not apply it to: historical Europeans:

How could the Medievals possibly have had the intelligence to invent such marvels as the crossbow, stained glass windows, steel armor and weapons, and those massive cathedrals! They had to get their technology from aliens, because they were too inept to come up with them on their own! They must have gotten medical imaging technology from the aliens too, because Medieval art has lots of skeletons in it, and how could they have possibly known what those looked like without using it?

Absurd? Clearly it is, and in retaining as closely as can be the reasoning of the original applied to another subject, it shows that.

A side note: Technology is cumulative, and evolves over time, with earlier, precursor technologies leading to better, more advanced ones, with archaeological remnants to show this progression, no matter the location, or ethnic and cultural makeup of the civilization. This is true even dating as far back as the Paleolithic with stone tools.

Never underestimate human genius. There exists brilliance in every human era, with no need to gift early peoples with technology from super-civilizations for such tasks as constructing even impressive monuments, which require only engineering, tools, and social organization which we know they had, as opposed to the claims of pseudo-historians in massive, and dare I say, monumental, arguments from ignorance.

But I digress.

Reason is a tool. Use it well and it will serve you reliably, leading to the acquisition of more true conclusions than false ones. But abuse it, and the content of the claims you accept and promote becomes much more prone to error. Especially when you misrepresent the chain of another’s reasoning for ideological ends.

Tf. Tk. Tts.

(Last Update: 2017.06.06)

Project Logicality | Slippery Slopes & False Continua

Are chains of causation inexorable and dire? Does a continuum between extremes mean that neither extreme differs, or that one of those extremes doesn’t exist?

Here, we’ll discuss the Slippery Slope, and the two False Continua, similar arguments though representing causal and semantic versions respectively.

But first I’ll deal with its causal version, the Fallacy of the Beard, also the Camel’s Nose fallacy. The first name comes from an analogy with the greying of a man’s beard, in which the amount of grey is small at first, but inevitably progresses until the entire beard is grey. The second name comes from a fable in which a camel is permitted by its owner to stick its nose in the tent for warmth from the cold desert night air, quickly followed by the entire camel, who crowds its owner out of the tent and into the cold.

The slippery slope asserts that a position or claim is unacceptable because if accepted, its worst extreme must inevitably follow, without sound reasons as to how or why this must be.

It’s a fallacy that’s both committed and labels itself as an argument strategy at the same time, with the use of such opening phrases as “It’s a slippery slope if…” or “It sets a bad precedent when…” and so on.

A superficially similar form of argument can be a strong line of reasoning when the chain of inference is laid out and each link logically follows, but the fallacy refers to the specious usage, as below:

The public teaching of comparative religion leads to awareness of religious diversity, then to religious doubt, then to agnosticism, then to atheism, then to anti-theism, then to nihilism, then to moral degeneracy, then inevitably to the disintegration of a society in total anarchy, so we don’t want comparative religion courses taught in our public schools.

Beside the fact that the evidence just doesn’t bear this ridiculous chain of consequences out, note here that no supporting reasons or other justification are ever provided as to why this chain must be true.

The Vagueness, or False Continuum, is below, used in two ways:

One version attempts to argue that concepts B and E shade into each other along a continuum without any fine dividing line between them, so they are the same thing, that no distinction exists.

But it just doesn’t follow that:

There is no difference between blue light and yellow light, despite no sharp dividing point in wavelengths in the visible spectrum.

Nor does it follow that:

There is no separation between humid or dry weather when the moisture in the air at any one time and place varies in degree from high to low.

The second variant is used to argue that concept B differs so little from concept E with no fine line between them, that concept E simply doesn’t exist. As for this one, it doesn’t follow that:

Truth doesn’t exist because of the continuum between truth and falsehood. The concept of truth is without any objective reference. It’s all falsehood, and we don’t know a thing!

These two fallacies, causal and semantic, are distinct, but they are mentioned together here as the use of the semantic version can and does often lead to the commission of the causal version. Their joint use implies that a slip from position or claim B to E is inevitable because of the lack of a fine point of separation between them.

The tricky thing about fallacies like these, often used by postmodernists and political buffs with conspiratorial leanings, is that they are common in social discourse, especially in academic settings like the Humanities, and oddly hard to recognize as specious while committing them oneself.

Learn to note them, and picking them out reliably becomes easier with practice, even to avoiding the temptation to use them in your own arguments, which is always a plus.

Tf. Tk. Tts.

(Last Update 2017.06.06)

Project Logicality | Reducing to Absurdity

What happens when we carry a train of reasoning to its ultimate extreme, far past the reaches of sanity to the realm of the patently absurd? Here, we discuss such an argument in informal logic, borrowed from formal mathematical reasoning, and here known as the Reductio ad Absurdum.

In formal logic it may be used to show an argument’s claim to be false by following it to its ultimate logical conclusion, revealing a contradiction, an absurdity, or it may be used as a form of Straw-Man argument, known here as the False Reductio. I’ll deal first with the latter.

This works by forcing a conclusion that while absurd, doesn’t use the actual reasoning of the original argument, such as:

If you’re skeptical of the existence of UFOs, Bigfoot, and ancient aliens, then you must also be skeptical of the existence of the Taj Mahal, the Sydney Opera House, and the Empire State Building, since you’ve never been there to see those places.

This is fallacious because the proportional nature of the claims requires proportional standards of evidence. The criteria for each differ, and the argument itself ignores the use of evidence other than anecdotal testimony and grainy, low-resolution, or obviously photoshopped videos and photos.

Here is one of my favorites:

If you don’t believe in psychic abilities then you also disbelieve in dark matter and dark energy, so 90% of the Universe does not exist to you because you haven’t seen those either.

Again with ignoring evidence other than personally witnessing something. Also, it fails to consider the fact that though there is some question as to what dark matter and dark energy are, they have been reliably observed by their effects on the visible universe itself, and the evidence shows that they are real. Clearly, elusive supernormal psychic abilities and invisible but indirectly observable astrophysical phenomena are not analogous.

But all is not without a ray of light in the dark. There is an informally valid and intellectually honest use of this as well, to highlight the fallaciousness of some extraordinary claims. Here, the actual train of logic of the original argument is kept intact.

Here are a couple of silly claims I’ve come across:

The ancient Egyptians could not have built the pyramids without alien or Atlantean help. They were far too primitive a civilization.

 

In order to know what a human skeleton looks like, the Maya and Aztecs must have been given X-ray machines by ancient astronauts.

Such claims reek not only of thinly disguised racism and colonialist arrogance, but stupidity and historical shortsightedness as well. Typical of most of the claims of pseudo-archaeology, especially where ancient non-whites are not given due credit for their accomplishments.

And skeletons? Come on, that’s just silly!

Meh!

Here, we may apply the same train of logic to what the proponents of these ideas, mostly whites of Western descent, dare not apply it to: historical Europeans:

How could the Medievals possibly have had the intelligence to invent such marvels as the crossbow, stained glass windows, steel armor and weapons, and those massive cathedrals! They had to get their technology from aliens, because they were too inept to come up with them on their own! They must have gotten medical imaging technology from the aliens too, because Medieval art has lots of skeletons in it, and how could they have possibly known what those looked like without using it?

Absurd? Clearly it is, and in retaining as closely as can be the reasoning of the original applied to another subject, it shows that.

A side note: Technology is cumulative, and evolves over time, with earlier, precursor technologies leading to better, more advanced ones, with archaeological remnants to show this progression, no matter the location, or ethnic and cultural makeup of the civilization. This is true even dating as far back as the Paleolithic with stone tools.

Never underestimate human genius. There exists brilliance in every human era, with no need to gift early peoples with technology from super-civilizations for such tasks as constructing even impressive monuments, which require only engineering, tools, and social organization which we know they had, as opposed to the claims of pseudo-historians in massive, and dare I say, monumental, arguments from ignorance.

But I digress.

Reason is a tool. Use it well and it will serve you reliably, leading to the acquisition of more true conclusions than false ones. But abuse it, and the content of the claims you accept and promote becomes much more prone to error. Especially when you misrepresent the chain of another’s reasoning for ideological ends.

Tf. Tk. Tts.

(Last Update: 2017.06.06)