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 a thousand posts here about all sorts of topics – please have a good look around before leaving.

If you are looking for an article about the Birth of Experimental Science recently 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 recently 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 recently 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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Turkey orders secondary schools to stop teaching evolution

Why Evolution Is True

According to both the Guardian and The Independentthe Turkish government, with the approval of President Recep Tayyip Erdoğan, has just stopped the teaching of evolution in secondary schools, saying that students in the ninth grade aren’t able to understand the idea. Although—according to a friend who teaches evolution in a Turkish university—evolution is often left out of the secondary school curriculum (as it often is in the U.S.), now it won’t be offered in any secondary schools.

According to the Guardian, the announcement was made here, and if you understand Turkish, do tell us what this guy is saying (click screenshot to go to video):

Alpaslan Durmuş, who chairs the board of education, said evolution was debatable, controversial and too complicated for students.

“We believe that these subjects are beyond their [students] comprehension,” said Durmuş in a video published on the education ministry’s website.

Durmuş said a…

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Restricting bail and parole for those with terror links is no cure-all

The Conversation

File 20170621 2627 1xpyd2r
The new anti-terror laws COAG has proposed for Australia go far beyond those in the UK. AAP/Rob Blakers

Jessie Blackbourn, University of Oxford

Earlier this month, the Council of Australian Governments (COAG) agreed that the states and territories should enact new anti-terrorism laws. This came in the wake of a siege in the Melbourne suburb of Brighton, during which Yacqub Khayre killed a man and took a woman hostage.

At the time of the siege, Khayre was on parole for violent – but not terrorist – crimes. Shortly before Khayre was killed by police at the scene of the siege, he is alleged to have called the Seven Network and said:

This is for IS. This is for al-Qaeda.

Islamic State (IS) subsequently claimed the attack.

Khayre’s background is important in understanding why this attack produced a counter-terrorism response. In 2009, he was arrested and charged with terrorism offences in relation to the Holsworthy Barracks plot. Even though he was acquitted at trial, Khayre was tainted by the perceived association with terrorism.

COAG’s proposed new laws will capture this type of person. As Prime Minister Malcom Turnbull put it:

Violent criminals with terrorist links should not be walking the streets. They belong in jail.

The COAG proposals

Under the COAG proposals, states and territories will be required to:

… strengthen their laws to ensure that there will be a presumption that neither bail nor parole will be granted to those who have demonstrated support for or have links to terrorist activity.

Decisions on parole for those with a terrorism link will be taken out of the hands of the parole authorities. Instead, they will be the responsibility of state attorneys-general.

There are no clear details yet on how the legislation will define “links to” terrorist activity, or what behaviours will be captured by “demonstrating support for terrorist activity”. However, it seems likely that having associated with known or convicted terrorists in the past, or having been investigated for terrorism offences, will be covered.

So, had these measures been in existence when Khayre came up for parole, he would not have been released early from his sentence for violent crimes, and could not have carried out his attack.

Restricting bail and parole

Restrictions on bail and parole are not unusual in the terrorism context.

In the UK, bail is automatically denied to those arrested without warrant on suspicion of being a terrorist.

The blanket ban on bail is relatively uncontroversial. But both the two former independent reviewers of terrorism legislation, and the UK’s Joint Committee on Human Rights, have called for changes to allow terrorist suspects to apply for bail. The government has consistently rejected these calls on the grounds that denying bail to terrorist suspects is operationally useful, and has not been found to breach the right to liberty and security guaranteed in the European Convention on Human Rights.

Under a new law enacted in the UK in 2015, terrorist prisoners are no longer automatically entitled to receive parole once they have served 50% of their prison sentence.

Those convicted of terrorism offences are now required to undergo a risk assessment prior to parole being granted. They will only be released early on parole if the Parole Board decides they no longer represent a risk to the public.

However, the new laws COAG has proposed for Australia go far beyond those in the UK. They will restrict parole and bail to those merely associated in some way with terrorism, even when they have not be arrested for – or convicted of – a specific terrorism offence.

This is a significant expansion of Australia’s already extensive anti-terrorism regime.

Existing post-sentence restrictions

Two regimes already exist to prevent convicted terrorists from being released unsupervised back into the Australian community.

The control order regime, which was introduced in 2005, was amended in 2014 to enable a control order to be issued on the ground that a person has been convicted of a terrorism offence.

Once a control order has been issued, controlees are subject to a range of obligations, prohibitions and restrictions. This includes restrictions on movement and communications. Controlees can also be required to wear a tracking device and report to the police at regular intervals.

Second, under a newly commenced regime, a terrorist offender can be detained in prison under a continuing detention order at the end of their sentence if the court is “satisfied to a high degree of probability, on the basis of admissible evidence, that the offender poses an unacceptable risk of committing a serious [terrorism] offence if the offender is released into the community”, and:

… there is no other less restrictive measure that would be effective in preventing the unacceptable risk.

A continuing detention order can last for up to three years, and may be renewed at the end of its duration. It is a possibility that a convicted terrorist may never be released from prison.

Delaying the inevitable?

Neither of these regimes would have been applicable to Khayre, as he was not on parole for a terrorism offence. However, the police also had no specific intelligence that he posed a terrorist threat.

It is possible that his attack was spontaneous, rather than planned. It is also possible therefore, that Khayre would always have carried out this tragic act.

So, even if COAG’s proposed new laws had been in effect and Khayre had been refused parole, he would eventually have been released from prison after having served his full sentence.

Turnbull has said the new laws will be:

… a vital element in keeping these people who are a threat to our safety, and the safety of our families, off the streets.

But they will only do this during the relatively short period of time after someone would have been released, either on bail or parole. Once they have served their full sentence, they will be released into the community without any supervision.

It is important, therefore, that the government pays as much attention to the provision of rehabilitation and deradicalisation programs for those with potential terrorist links inside prison as it does on measures that appear tough on terrorism.

The ConversationRestricting bail and parole to people like Khayre who have links to terrorist activity, but who have not been convicted of terrorist offences, only delays their inevitable release. If they pose a threat during the parole period, then without rehabilitation and deradicalisation, they will still pose a threat when released at the end of their sentence.

Jessie Blackbourn, Research Fellow, Centre for Socio-Legal Studies, University of Oxford

This article was originally published on The Conversation. (Reblogged by permission). Read the original article.

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“We’re still waiting for a march against honor killings”: Ayaan Hirsi Ali and Asra Nomani in NYT on religion and women’s rights

Why Evolution Is True

Well cut off my legs and call me Shorty! (Is that ableist?) I was astounded to see that Ayaan Hirsi Ali and Asra Nomani, both feminist Muslim reformers, were given a whole op-ed in the New York Times to testify about women’s rights vs religion (click on screenshot to see it):

As I wrote five days ago, when Hirsi Ali and Nomani testified about terrorism (along with two men) before a mixed panel of Senators at the Senate’s Homeland Security Committee, the two women were allowed to speak, but the Democrats ignored them during questioning (see the four-hour hearing at the link at the beginning of this sentence). In fact, as Hirsi Ali and Nomani write in their op-ed, the one male and three Democratic Senators didn’t ask either of them a single question. Why? I explained that in my earlier post:

I don’t think the behavior of…

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“Show some damn respect for people’s religous beliefs”: Piers Morgan and the osculation of Islam

Why Evolution Is True

Tommy Robinson (real name Stephen Christopher Yaxley-Lennon, born 1982) is a shady character and almost certainly a bigot, though his rhetoric has tamed since he used to incite the masses against Muslims. (I’ve learned about him only recently.) He was head of the far-right English Defense League (EDL),  is now advisor and former UK leader of Pegida (Patriotic Europeans against the Islamisation of the West). His main goal seems to be embodied in the Pegida acronym, but I’ve bridled at hearing his rants, and I think he’s not just anti-Islam, but anti-Muslim; that is, it seems that he wants to stop Muslim immigration into the UK. That’s bigotry. And I don’t really believe his claims that he despises Islam, not Muslims.  (See his comment in Part 2 of the video series below that all Muslims listening to his speech are complicit in the 7/7 attacks.) Robinson’s also been jailed several times for…

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The origin and migration of domestic cats: a genetic study

Why Evolution Is True

I think about fifty people sent me articles about a new genetic study of domestic cats and their ancestor, Felis silvestris—an analysis published in a paper in Nature Ecology & Evolution by Claudio Ottoni et al. Thanks to all for calling this to my attention, as it combines two of my favorite subjects, cats and genetics; but excuse me if I can’t thank you all by name.

The reference and free link to the paper (if you have “Unpaywall”) is at the bottom, as well as a link to the study’s supplementary material. The paper was also summarized in articles in The Guardian and in a Nature News and Views piece, and got tons of attention in the press because, well, cats.

In truth, the results can be summarized briefly; they’re a bit surprising but not earthshaking. First, if you want a video presentation and don’t want…

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The professional model of representative democracy

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You have vestigial muscles that moved the whiskers of your ancestors

Why Evolution Is True

This is the kind of post I envisioned writing—once every few weeks or so—when I started this website. My intention was to use the site to publicize new evidence for evolution. Not that we need any to show that that well evidenced theory is true, of course but to support the book and alert people to cool new findings. But, as I’ve said, things got out of hand, and so we have cats, food, travels, religion, and so on. So let’s go back to our roots today. . .

Matthew, on the job as always, sent me this tw**t and asked me if I’d mentioned this in the “vestigial structures” section of Why Evolution is True.

I told him I hadn’t…

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Washington Post writer dishonestly calculated death toll from terrorism vs other forms of murder

Why Evolution Is True

I’m not sure exactly why Tung Yin (described as “a professor at Lewis & Clark Law School in Portland, Oregon [with an] academic specialty [in] national security law and terrorism”) wrote a new essay in the Washington Post—”Is it terrorism or mass murder? That depends on our biases.“—but I have a few ideas. What Yin does is to claim that our definition of terrorism depends largely on the pigmentation of the perpetrator, and that that is a form of bias.

And it would be if that were the case. I’m not sure it is. But Yin, who apparently is unbiased, offers his own definition of terrorism, which he claims is a better one—though I think he’s dead wrong. His definition is based on body counts rather than motivation of the killers.

First, though, Yin gives the Federal legal definition of terrorism, which comprises violent acts that “appear…

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Decoding the music masterpieces: Liszt’s Piano Sonata in B minor

The Conversation

Image 20170412 25870 wo5mpn
Franz Liszt in his home in Weimar, 1884. Bergen Public Library Norway/Flickr

Zoltan Szabo, University of Sydney

Clara Schumann, the wife of the great composer Robert Schumann, wrote in her diary on 25 May 1854:

Liszt sent Robert today a sonata dedicated to him and several other things with a friendly letter to me. But the things are dreadful! [Johannes] Brahms played them for me, but they made me utterly wretched … This is nothing but sheer racket – not a single healthy idea, everything confused, no longer a clear harmonic sequence to be detected there! And now I still have to thank him – it’s really awful.

                   Clara Schumann circa 1850.

She was referring, of course, to Franz Liszt, the Hungarian composer, and his Piano Sonata in B minor, which soon became one of the most popular and influential works of the piano repertoire.

Proof of this is that, despite its mammoth technical difficulties, there are over 50 recordings of the Sonata listed in the catalogues. As a somewhat odd measure of success in our times, the Sonata is even featured in an award-winning iPad app.

A “sonata” in the 19th-century sense would generally refer to a three or four movement composition. Unlike most traditional piano sonatas, Liszt’s work consists of one giant arch of a single movement, lasting almost half an hour. While this was unusual in the middle of the Romantic era, it was not without precedent.

Liszt knew Austrian composer Franz Schubert’s Wanderer Fantasie in C major well. Although Schubert’s themes in the Wanderer Fantasy run through four movements in varied forms, these four movements are played without a break – the parallels with Liszt’s later Sonata are obvious.

Robert Schumann’s own Fantasie in C major, was also written to be played through, more or less hiding its three individual movements. Schumann dedicated this work to Liszt. Thus Liszt’s dedication of the B minor Sonata was a reciprocal gesture, which Schumann, sadly, could no longer appreciate.

Nor could Schumann play the Sonata as, by 1854, he was rather tragically committed to an asylum for the insane.

‘Nothing but sheer racket’

Liszt’s Sonata was publicly played for the first time a few years later in 1857, by one of his students, Hans von Bülow. The two of them grew even closer in the same year, when Bülow married Liszt’s daughter, Cosima. (Bülow was a great champion of compositions said to be unplayable. He also premiered Tschaikovsky’s famous first Piano Concerto in B flat minor in Boston.)

How Liszt, or for that matter, Bülow would have played the Sonata, we do not know. Fortunately though, two of Liszt’s students recorded the Sonata late in their lives and their performances survive on piano rolls (a form of music storage commonly used in the first part of the 20th century).

We can gain a wealth of information about late 19th century performance practice, intriguing technical solutions, tempos, dynamics and other musical ideas through the recordings of these Liszt students, Arthur Friedheim and Eugene d’Albert.

Friedheim’s 1905 recording is the first complete one of the Sonata; his deeply musical, if often unusual playing of the first few minutes of this work is well worth listening to:

Source: Liszt ~ Piano Sonata in B Minor ~ Premier recording by Arthur Friedheim ~ Leipzig 1905

Still, like Clara Schumann, others also had difficulties comprehending the astonishing musical journey of Liszt’s Sonata.

Upon hearing it for the first time, the enormously influential Viennese critic, Eduard Hanslick, opined

whoever has heard that, and finds it beautiful, is beyond help.

Fortunately, such sentiments did not prevail for long.

Liszt as painted by Henri Lehmann in 1839.

The Sonata conquered, yet kept some of its secrets, despite numerous attempts to explain its enigmatic meaning. Among other theories, it has been suggested that it presents a musical portrait of the Faust legend; or that it is, in fact, autobiographical, and the musical contrasts within spring from the conflicts of Liszt’s own personality.

Others propose that it is about the divine and the diabolical, as depicted in the Bible and, specifically, in John Milton’s Paradise Lost, or that it is merely an allegory, set in the Garden of Eden, dealing with the Fall of Man and contains individual themes for “God”, “Lucifer”, “Serpent”, “Adam” and “Eve”.

On a simpler scale, it has also been said that the Sonata has no programmatic allusions at all and it is a piece of “expressive form” with no meaning beyond itself.

Any of these may appeal; whether they are true or not we’ll never know, as Liszt himself never offered an opinion.

Stirring emotions

Whatever its meaning, the Sonata is an incredibly powerful work, inspiring some performers to excessively emotional performances. One of the most vehement of them was recorded by the German Ludwig Hoffmann in 1977.

Here is his playing beginning from the same D major theme where we left off in the previous example, all the way to a tumultuous section that some analysts call the development section of the Sonata. (The main themes of a sonata movement are elaborated in various ways and keys in its middle section, called “development”)


Hoffmann’s is one of the fastest recordings, clocking just under 24 minutes.

In absolute contrast to that, the Croatian enfant terrible of piano stars, Ivo Pogorelich, played the same work a few years ago at a bewilderingly slow speed, taking almost exactly twice as long – an astonishing feat.

Some might call this performance a parody. Others admire it, and often for the very same reasons! The next example shows the same segment already heard on Hoffmann’s recording:

Excerpt 3 – Sonata in B Minor.
Ivo Pogorelich plays Liszt Sonata – live 201211.4 MB (download)
Source: Ivo Pogorelich plays Liszt Sonata – live 2012

Whatever our opinion, time seems to stand still at times in this recording, while Pogorelich’s extreme attention to minutiae brings out harmonic clashes, hidden internal melodies and many other particulars seldom audible in other recordings. Whether the listener needs to be conscious of these details is another question altogether.

Four movements or one?

One of the most fascinating aspects of Liszt’s Sonata is that, depending on how we look at the score (and more importantly, listen to the music), it can be convincingly argued that it abides by two completely different structures – and does so simultaneously!

Viewed from one angle, it can be explained as one giant movement in traditional “sonata form”, containing the three traditional sections of exposition, development and return (or recapitulation) of the themes.

But looking at it from a different perspective, some listeners can discover the hallmarks of a four-movement composition, albeit played without a break. The beginning and end are the usual movements of a sonata, which bookend a conventional slow movement and a scherzo – a fast, light movement.

One of Liszt’s pianos from his apartment in Budapest. Tamcgath/Flickr, CC BY-SA

Does a non-expert music lover have to know about this conundrum? Probably not. Yet listening to such details can be as mesmerising as the discussions they may provoke after the performance.

The intriguing problem of a two-dimensional form surfaces in other compositions of the Romantic period (lasting for most of the 19th century) and it is symptomatic with that era’s growing fascination with ambiguity in musical form.

The surviving manuscript of the Sonata reveals that Liszt originally composed a mighty, almost pretentious finish to it. Fortunately, at a later stage, he changed his mind and after a triumphant climax in B major, he returned to the melody of the “slow movement” and the Sonata not so much finishes but seems to evaporate through the last three ethereal chords.

One of the most moving performances of this final section (called a “coda”) was recorded by the Russian pianist, Sviatoslav Richter:

Excerpt 4 – Sonata in B Minor.
Liszt: Sonata in B minor – Sviatoslav Richter6.77 MB (download)
Source: Liszt: Sonata in B minor – Sviatoslav Richter

Nowadays, it is possible to follow the music of Liszt’s Sonata in B minor with the score, for example, on the following recording with Alfred Brendel as the pianist. This will also provide a chance to listen to the whole Sonata without interruption.

The ConversationRead more here in our series on classical music.

Zoltan Szabo, Ph.d candidate and lecturer, University of Sydney

This article was originally published on The Conversation. (Reblogged by permission). Read the original article.

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FIRE, censorship, and the disturbing Constitutional ignorance of college students

Why Evolution Is True

The Foundation for Individual Rights in Education (FIRE) was founded in 1999, with its founders expecting that it would last only ten years. But you probably know that the organization is still going strong. In fact, it’s going stronger than ever due to the rise of the Authoritarian Left and student Offense Culture, as well as Obama’s “urging” campuses to expand how Title IX, the sexual harassment regulation, is construed—an expansion that has come into conflict with First Amendment rights and thrown many campuses into a turmoil (see an example here).

In fact, only a few years ago I remember FIRE being widely regarded as a right-wing fringe organization, largely because it took on the thankless task of defending free speech and expression on campuses—something that often required them to counter liberal attempts to censor “hate speech.” And FIRE is still supported generously by right-wing groups like the Koch Foundation. That’s…

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