Welcome to Tim Harding’s blog of writings and talks about logic, rationality, philosophy and skepticism. There are also some reblogs of some of Tim’s favourite posts by other writers, plus some of his favourite quotations and videos This blog has a Facebook connection at The Logical Place.

There are over 2,300 posts here about all sorts of topics – please have a good look around before leaving.

If you are looking for an article about Skepticism, Science and Scientism published in The Skeptic magazine titled ”A Step Too Far?’, it is available here.

If you are looking for an article about the Birth of Experimental Science published in The Skeptic magazine titled ‘Out of the Dark’, it is available here.

If you are looking for an article about the Dark Ages published in The Skeptic magazine titled ‘In the Dark’, it is available here.

If you are looking for an article about the Traditional Chinese Medicine vs. Endangered Species published in The Skeptic magazine titled ‘Bad Medicine’, it is available here.

If you are looking for an article about the rejection of expertise published in The Skeptic magazine titled ‘Who needs to Know?’, it is available here.

If you are looking for an article about Charles Darwin published in The Skeptic magazine titled ‘Darwin’s Missing Link“, it is available here.

If you are looking for an article about the Astronomical Renaissance published in The Skeptic magazine titled ‘Rebirth of the Universe‘, it is available here.

If you are looking for an article about DNA and GM foods published in The Skeptic magazine titled ‘The Good Oil‘, it is available here.

If you are looking for an article about animal welfare published in The Skeptic magazine titled ‘Creature Features‘, it is available here.

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What is logic?

The word ‘logic‘ is not easy to define, because it has slightly different meanings in various applications ranging from philosophy, to mathematics to computer science. In philosophy, logic’s main concern is with the validity or cogency of arguments. The essential difference between informal logic and formal logic is that informal logic uses natural language, whereas formal logic (also known as symbolic logic) is more complex and uses mathematical symbols to overcome the frequent ambiguity or imprecision of natural language.

So what is an argument? In everyday life, we use the word ‘argument’ to mean a verbal dispute or disagreement (which is actually a clash between two or more arguments put forward by different people). This is not the way this word is usually used in philosophical logic, where arguments are those statements a person makes in the attempt to convince someone of something, or present reasons for accepting a given conclusion. In this sense, an argument consist of statements or propositions, called its premises, from which a conclusion is claimed to follow (in the case of a deductive argument) or be inferred (in the case of an inductive argument). Deductive conclusions usually begin with a word like ‘therefore’, ‘thus’, ‘so’ or ‘it follows that’.

A good argument is one that has two virtues: good form and all true premises. Arguments can be either deductiveinductive  or abductive. A deductive argument with valid form and true premises is said to be sound. An inductive argument based on strong evidence is said to be cogent. The term ‘good argument’ covers all three of these types of arguments.

Deductive arguments

A valid argument is a deductive argument where the conclusion necessarily follows from the premises, because of the logical structure of the argument. That is, if the premises are true, then the conclusion must also be true. Conversely, an invalid argument is one where the conclusion does not logically follow from the premises. However, the validity or invalidity of arguments must be clearly distinguished from the truth or falsity of its premises. It is possible for the conclusion of a valid argument to be true, even though one or more of its premises are false. For example, consider the following argument:

Premise 1: Napoleon was German
Premise 2: All Germans are Europeans
Conclusion: Therefore, Napoleon was European

The conclusion that Napoleon was European is true, even though Premise 1 is false. This argument is valid because of its logical structure, not because its premises and conclusion are all true (which they are not). Even if the premises and conclusion were all true, it wouldn’t necessarily mean that the argument was valid. If an argument has true premises and its form is valid, then its conclusion must be true.

Deductive logic is essentially about consistency. The rules of logic are not arbitrary, like the rules for a game of chess. They exist to avoid internal contradictions within an argument. For example, if we have an argument with the following premises:

Premise 1: Napoleon was either German or French
Premise 2: Napoleon was not German

The conclusion cannot logically be “Therefore, Napoleon was German” because that would directly contradict Premise 2. So the logical conclusion can only be: “Therefore, Napoleon was French”, not because we know that it happens to be true, but because it is the only possible conclusion if both the premises are true. This is admittedly a simple and self-evident example, but similar reasoning applies to more complex arguments where the rules of logic are not so self-evident. In summary, the rules of logic exist because breaking the rules would entail internal contradictions within the argument.

Inductive arguments

An inductive argument is one where the premises seek to supply strong evidence for (not absolute proof of) the truth of the conclusion. While the conclusion of a sound deductive argument is supposed to be certain, the conclusion of a cogent inductive argument is supposed to be probable, based upon the evidence given. An example of an inductive argument is: 

Premise 1: Almost all people are taller than 26 inches
Premise 2: George is a person
Conclusion: Therefore, George is almost certainly taller than 26 inches

Whilst an inductive argument based on strong evidence can be cogent, there is some dispute amongst philosophers as to the reliability of induction as a scientific method. For example, by the problem of induction, no number of confirming observations can verify a universal generalization, such as ‘All swans are white’, yet it is logically possible to falsify it by observing a single black swan.

Abductive arguments

Abduction may be described as an “inference to the best explanation”, and whilst not as reliable as deduction or induction, it can still be a useful form of reasoning. For example, a typical abductive reasoning process used by doctors in diagnosis might be: “this set of symptoms could be caused by illnesses X, Y or Z. If I ask some more questions or conduct some tests I can rule out X and Y, so it must be Z.

Incidentally, the doctor is the one who is doing the abduction here, not the patient. By accepting the doctor’s diagnosis, the patient is using inductive reasoning that the doctor has a sufficiently high probability of being right that it is rational to accept the diagnosis. This is actually an acceptable form of the Argument from Authority (only the deductive form is fallacious).


Hodges, W. (1977) Logic – an introduction to elementary logic (2nd ed. 2001) Penguin, London.
Lemmon, E.J. (1987) Beginning Logic. Hackett Publishing Company, Indianapolis.

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Rationality may be defined as as the quality of being consistent with or using reason, which is further defined as the mental ability to draw inferences or conclusions from premises (the ‘if – then’ connection). The application of reason is known as reasoning; the main categories of which are deductive and inductive reasoning. A deductive argument with valid form and true premises is said to be sound. An inductive argument based on strong evidence is said to be cogent. It is rational to accept the conclusions of arguments that are sound or cogent, unless and until they are effectively refuted.

A fallacy is an error of reasoning resulting in a misconception or false conclusion. A fallacious argument can be deductively invalid or one that has insufficient inductive strength. A deductively invalid argument is one where the conclusion does not logically follow from the premises. That is , the conclusion can be false even if the premises are true. An example of an inductively invalid argument is a conclusion that smoking does not cause cancer based on the anecdotal evidence of only one healthy smoker.

By accident or design, fallacies may exploit emotional triggers in the listener (e.g. appeal to emotion), or take advantage of social relationships between people (e.g. argument from authority). By definition, a belief arising from a logical fallacy is contrary to reason and is therefore irrational, even though a small number of such beliefs might possibly be true by coincidence.

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Innumeracy by John Allen Paulos (1988)

Books & Boots

Our innate desire for meaning and pattern can lead us astray… (p.81)

Giving due weight to the fortuitous nature of the world is, I think, a mark of maturity and balance. (p.133)

John Allen Paulos is an American professor of mathematics who won fame beyond his academic milieu with the publication of this short (134-page) but devastating book thirty years ago, the first of a series of books popularising mathematics in a range of spheres from playing the stock market to jokes.

As Paulos explains in the introduction, the world is full of humanities graduates who blow a fuse if you misuse ‘infer’ and ‘imply’, or end a sentence with a dangling participle, but are quite happy to believe and repeat the most hair-raising errors in maths, statistics and probability.

The aim of this book was:

  • to lay out examples of classic maths howlers and correct them
  • to teach readers…

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New Zealand bans semiautomatic and “military style” weapons

Why Evolution Is True

On March 13, 1996, the Dunblane Massacre took place in Scotland. A man named Thomas Hamilton assaulted a school with four legally-owned handguns, killing 16 children and a teacher (and wounding another 16) before committing suicide. Reaction was swift, and within two years the government had passed two acts banning all handguns in England, Scotland and Wales; the exceptions are “historic and muzzle-loading guns” and a few other types of large “sporting” handguns that are large.

Following the two mosque shootings on March 15, New Zealand has acted even faster. Prime Minister Jacinda Ardern, whom I much admire, just announced that New Zealand is banning not only the sale of semiautomatic weapons, but ownership of them, which will end via a government buyback scheme. (The weapons used in the mosque shootings had, as I recall, been bought legally but modified illegally.)

Tvnz reports (click on screenshot):

Ms Ardern had previously…

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Is the Pope Catholic?

Why Evolution Is True

Here’s a video from the British comedy game show QI (“Quite Interesting”) about the official title of the Pope Francis. It turns out that it’s not “Pope”. Further, you’ll learn that THE POPE IS NOT A CATHOLIC! In fact, the man who is officially the Pope is also NOT a Catholic. Listen and learn.

h/t: Michael

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New York Times changes headline to make Israel seem more culpable

Why Evolution Is True

On March 14, two rockets were fired at Tel Aviv, Israel, from Gaza. Fortunately, although the missiles weren’t intercepted by the Iron Dome, nobody was hurt. It was the first rocket attack on Tel Aviv since 2014, and Israel retaliated with air attacks on terrorist military sites. Hamas denied responsibility, but it’s clear that some Palestinian militant group was responsible. It is of course a war crime to fire missiles at civilian targets.

What’s interesting—and I noticed this at the time—was that mainstream (or anti-Israel) Western media almost invariably began its stories with headlines like “Israel retaliates after rockets strike Tel Aviv”, switching the temporal order of events to make Israel seem more culpable. Here, for example, is what I just got when I Googled “rockets fired at Tel Aviv from Gaza”:

But in an even more telling media switch, Honest Reporting notes that the New York Times, which…

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Harald Sohlberg: Painting Norway @ Dulwich Picture Gallery

Books & Boots

Harald Sohlberg (1869 to 1935) was one of Norway’s greatest painters. He is best known for works which evoke the wildness of the Nordic landscape, brooding scenery illuminated by midwinter light, and realistic depictions of the wood buildings of old Norwegian towns.

This is the first major UK exhibition of Sohlberg’s works, celebrating 150 years since the artist’s birth, and it reveals that there’s much more variety, in subject matter, treatment and quality, than a first glance suggests.

Self Portrait (1896) by Harald Sohlberg. Private collection Self Portrait (1896) by Harald Sohlberg. Private collection

The exhibition proceeds in sensible chronological order. Born the eighth of 12 children, Sohlberg early wanted to be a painter but his father insisted he learn a craft and apprenticed him to a master scene painter and decorator, Wilhelm Krogh. When he went on the National College of Art and Design, where he developed his printmaking skills, it was also to discover the great…

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Titania McGrath outed!

Why Evolution Is True

There’s nothing that can debunk stupidity or irrationality more strongly than satire. And that’s why, as “wokeness” floods across college campuses then spills into the workplace as members of the Offense Culture graduate, Titania McGrath, through her tweets and now in an upcoming book, has shown up the craziness of that culture. And she’s done it by pretending to be one of The Woke. She did it so effectively, even on Twitter, that she was accepted as one of them and demonized by the Right and those reasonable Leftists who didn’t get the joke.

But who was she/he/hir/it/zir? Everybody knew that Titania (and her “male” counterpart Godfrey Elfwick) were pseudonyms, but who had a sense of humor that good?

Well, as revealed in the two pieces below, one from Spiked and the other from the Torygraph, Titania is none other than Spiked columnist and humorist Andrew Doyle.

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Readers’ wildlife photos

Why Evolution Is True

It’s Saturday, and time to gather the singletons, doubletons, and tripletons that I’ve been sent.  The first three are from reader Diana MacPherson. As usual, readers’ captions are indented.

The birds are wanting seeds lately – even the poor, nervous cardinal, worried about his redness, has been on my deck. Here are some pictures of the male Northern Cardinal (Cardinalis cardinalis) on the deck and a White-breasted Nuthatch (Sitta carolinensis) on the fat.

From Gary Womble:

A Tri-Colored Heron (Egretta tricolor) dragging a wing tip through the water while holding the other wing above its head to influence the movements of underwater prey.  A Roseate Spoonbill (Platalea ajaja) observes the technique.

And two photos from John Avise’s “Birds of the World” collection:

Snow goose (Chen caerulescens), California:

Laysan albatross (Phoebastria immutabilis), Hawaii:

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From Secret Ballot to Democracy Sausage: How Australia Got Compulsory Voting, by Judith Brett

Much to my astonishment, I was singing the praises of this book the other day, when it transpired that my friend did not know what a democracy sausage was.  So for the edification of those unfortunate citizens who do not enjoy the same privilege as we do here in Australia, an explanation is in order.

Because we are almost unique in the world in having compulsory voting, and because impecunious state schools are very often the place for polling booths all over the country, and because enterprising Parents and Friends associations can spot a good fundraiser when they see one, it has become routine practice for there to be a sausage sizzle so that voters can assuage their hunger pangs in a worthy cause.  Indeed on election day there is a dedicated website where you can even scout around for the best democracy sausage options.  They don’t all offer fried onions or chilli sauce, you know, and some of them have a cake stall as well!



March 16, 2019 · 4:05 pm

NYT goes soft on astrology

Why Evolution Is True

“It is wrong, everywhere and for every one, to believe anything on insufficient evidence”.
—W.K. Clifford, The Ethics of Belief

If a newspaper has an astrology column, write it off. Unsubscribe. It may be justified as a form of amusement, but many people accept astrology, and such a justification feeds into the acceptance of woo and faith. And a lot of people spend a lot of money on astrological advice, just as they do on psychics. The two phenomena are, after all, related.

The New York Times doesn’t have an astrology column, but it just published an article that could be seen as soft on astrology, for while it points out that many people don’t accept astrology, it doesn’t point out that scientific tests also debunk it. (For a very good test of astrology, see this pdf.) And the article (below) copiously quotes those who accept it. It’s like…

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Why is Pinker demonized?

Why Evolution Is True

The Chronicle of Higher Education has a new and longish article by Tom Bartlett about the character, achievements, and demonization of Steve Pinker. Click on the screenshot below to read it.

Let me give my own take on Pinker first. It’s no secret that I consider him a friend and admire him hugely. Among all those in the atheist-sphere with whom I’ve interacted, he’s the most empathic, the most intellectually productive, and the most thoughtful. Dawkins is a marginally better writer, but not by much. I’ve never seen Steve commit a shoddy act nor engage in ad hominem arguments. I’ve read nearly all his books (save the linguistic ones except The Language Instinct), and can’t find much to quibble with.

But people still dislike him—even hate him. This is puzzling to me as he’s a nice guy and can’t be accused of Misogyny and Nazism Through Tweeting. As best…

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