Logic Quiz 2

Here are the answers: 

1. Socrates is a philosopher.
All philosophers are poor.
So Socrates is poor.


2. Whenever Anil is here, Kumar is also here.
Anil is not here.
So Kumar is not here.

Invalid  Kumar is not always with Anil. 

3. Most drug addicts are depressed people.
Most depressed people are lonely.
So most drug addicts are lonely.

Invalid  Compare: Some men are doctors; Some doctors are women; Therefore, some men are women.

4. Nothing that is cheap is good.
So nothing that is good is cheap.


5. If there is an earthquake, the detector will send a message.
No message has been sent.
So there was no earthquake.

Valid   There’s no time dimension here.

6. John said that everyone loves Mary.
Nothing that John has said is true.
So nobody loves Mary.

Invalid   Even if it’s not true that everyone loves Mary, we can’t deduce that nobody does.

7. If there is life on Mars, then Mars contains water.
If Mars has ice, it contains water.
There is ice on Mars.
So there is life on Mars.

Invalid.  It would be valid if line 1 said If there is water on Mars, then there is life on Mars.

8. All roses are flowers.
Some flowers fade quickly.
So some roses fade quickly.

Invalid  Roses might not be part of the set in line 2.

9. Our government should either spend less or raise taxes.
Raising taxes is impossible.
So our government should spend less.

Valid A necessary consequence of either / or.

10. If John is guilty, so is Peter.
If Peter is not guilty, Jeremy is.
So if John is not guilty, Jeremy is.

Invalid   “Jeremy is” means Jeremy is guilty in line 2 and Jeremy is not guilty in line 3.   

In the puzzle, Argument 2 is correct

A few more comments:

Such puzzles are interesting for MA students (they can help to prevent bad interpretation of data collected in their small studies) and essential for those who want to argue that one thing does or doesn’t logically imply another.

Logic is to do with valid argument, not truth. Thus, an argument can be valid but not true – i.e. it doesn’t correspond to the facts.  For example: All cats are black; Tibby is a cat; So Tibby is black.

When it comes to evidence, we should be clear that evidence can’t prove a hypothesis is true: you can’t go from the particular to the general. The famous example is “All swans are white” based on the fact that all the swans we’ve ever observed have been white: while the observations support the claim, they don’t prove it. This is Popper’s great contribution to scientific method, although he’s only following Hume’s devastating critique of inductive reasoning. There’s an asymmetry between truth and falsehood: you can prove a theory is false, but you can’t prove it’s true. That’s why Popper says that the role of empirical evidence is to test a theory (to try to falsify it), not to prove it. We don’t know if any of the theories we hold to be true are actually true, but we allow them (through a very interesting process called inference to the best explanation) for as long as they survive tests.

The worst examples of bad reasoning in discussions of SLA or ELT come from either using circular arguments (Krashen’s 5 hypotheses making up the Monitor Theory are the best-know examples) or non sequiturs ( a blanket term covering most fallacies). Circular arguments make it impossible to disprove them and the usual reason here is that the theoretical constructs used in them have no empirical content. As for non sequiturs, these abound in discussions of SLA and ELT, where conclusions drawn from observations simply don’t follow. In my opinion, those working in the area of sociolinguistics, particularly those adopting post-modernist, ethnographic approaches, are particularly prone to drawing sweeping conclusions from scant evidence and from the use of at times absurd theoretical constructs.  The most blatant recent examples of non-sequiturs I’ve seen are Harmer’s claims that exams are good because knowing he had an exam helped his tuba playing, and that the Pearson test of Academic English is reliable because the research behind its voice recognition software is “massive”; Dellar’s claim that my “insults” and not having read his coursebook adversely affect my argument against coursebooks; Scrivener’s claim that coursebooks are good because they’re better than they were; and Mayne’s  suggestion that Chomsky’s theory is thrown into doubt by the fact that Chomsky’s criticism of Skinner is “nasty”.

In my page on Critical Thinking – see the menu on the right – I suggest a few web sites where those interested in following up my remarks could look further.

Finally, by far the most important part of critical thinking is the attitude of suspicion. Suspicion sounds negative, but here it simply means don’t believe what you’re told. Constantly challenge not just the reasoning but also the so-called facts. On the latter point, Russ has  done a great job in the last year of promoting the question “Where’s the evidence?”

There is, of course, a political dimension to all this. Critical discourse analysis (not one of favourite areas of the MA!!) deliberately focuses on the ideologies and power relations involved in discourse, and tries to uncover these properties of texts. Without overdoing things, it’s surely a good idea to appreciate that when you read stuff published by the British Council, or by CUP (promoters of the upcoming, self-congratulatory, Oscar-type-love-in ELTon event – complete with red carpet just to increase the embarrassing bathos of the whole show) these two powerful bodies have a vested interest in preserving the status quo. Everything you read that’s published by the British Council, by Cambridge English Examination Assessment, and by other major stakeholders in the current ELT industry needs careful scrutiny. Particular careful attention has to given to uncovering the principles which support their approach to ELT practice. In my opinion, the principles on which CELTA and DELTA, and most coursebooks are based are wrong. You might well disagree, but I think it behoves all teachers to critically assess the arguments on both sides.

Critical thinking helps progress. To the extent that more and more teachers sharpen their critical thinking, the old regime will feel increasingly less comfortable in the roost they rule. So, if you’ll allow me to climb onto this flimsy soapbox: Teachers! If you’re inspired by Dogme, teacher cooperatives and other alternatives; if you’re angry at the tawdry treatment of NNESTs and at their own pay and work conditions; if you’re bored by the showcase events mounted by IATEFL and TESOL, where the same old luminaries trot out the same old stuff; and if you’re eager to explore new approaches to teaching and to participate more in decisions affecting your teaching; sharpen your critical thinking tools!


7 thoughts on “Logic Quiz 2

  1. Interesting post, Geoff. I have a question: you say that ‘we should be clear that evidence can’t prove a hypothesis is true’ and that ‘while the observations support the claim, they don’t prove it’. What is the point in asking ‘Where’s the evidence?’ then? Even if I provide all the evidence, it proves nothing (or not very much). As I understand it, it would make more sense to ask: ‘Where’s the evidence *against* the theory?’. But even if the theory survives tests, does that mean/prove it’s valid?


  2. Hi Hana,

    We can’t prove a theory is true, but if it survives tests to falsify it, the empirical evidence used in these tests counts as supporting evidence for it. This is why replication studies are so important in SLA (and why I encourage my students to do such studies, BTW). So we say that the theory we work with is the best explanation we have to date because all the evidence so far supports it. Supporting evidence gives us more reason to work with the theory and to assume that it’s “tentatively true”, as Popper would say – to the best of our present knowledge. A good theory makes daring predictions and we can test those predictions.

    Two caveats. First, theory builders often ignore counter-evidence, and also use bolt-on ad hoc hypotheses to deal with it (even though this is frowned on). So it’s very simplistic to say that falsification is achieved by finding one bit of empirical evidence which contradicts the theory. Second, while an inductive argument is logically invalid, in fact scientists make use of a form of induction, which is where the “inference to the best explanation”, known as abduction, comes in. The most famous example of abduction is when in1818 observations of the orbit of Uranus conflicted with Newton’s theory of gravitation. Strictly, these observations falsified Newton’s theory. Unwilling to give up the theory, Couch Adams and Leverrier, said that the best explanation was that there must be another planet causing the gravitational “deviations” in Uranus’ orbit, although they had no evidence to support the claim. Neptune was discovered soon afterwards. Lipton’s “Inference to the Best Explanation” (Routledge, 2004, 2nd edition) is, in my opinion, the best book on this, but I recommend the always reliable Stanford Encyclopedia of Philosophy for a quick overview. http://plato.stanford.edu/entries/abduction/

    There’s no theory which gives a satisfactory explanation of SLA, and great debates still rage about the best way to get to one. I wrote my book “Theory Construction in SLA” mostly as a reply to the increasing clamour of relativists and post-modernists in the late 90s. in defence of what termed the rationalist approach. I’m writing a new version, which will lean heavily on Lipton.

    Liked by 1 person

    • I forgot to say that supporting evidence alone is no good. Popper gives the example of astrology, where millions of predictions turn out to be true. Ah, you’re a Gemini. Let’s look at the way the planets are aligned. Oh dear, next Tuesday you’ll have an accident. And you do have an accident that Tuesday. But first, the majority of their predictions turn out be false, and second, they refuse to say what evidence would falsify their theory.


    • Hi Mura,

      It’s a curate’s egg – good in parts! The author is absolutely right to say that Krashen’s lack of a neurological explanation for language acquisition is irrelevant. And it’s now generally accepted that comprehensible input (CI) is a necessary condition for SLA. But there are lots of problems with the strident assertions made.

      1. There’s no evidence that CI is a sufficient condition for SLA and it pays too little importance to the role of interaction and output.

      2. Studies (notably the Canadian immersion studies, but others, too) have shown that thousands of hours of exposure to CI does not usually result in high levels of proficiency. As far as instructed SLA is concerned, relying exclusively on CI gives worse results that mixing CI with explicit focus on form.

      3. Krashen started with the rigid distinction between acquisition and learning, and has since back-tracked to allow a more important place for conscious learning. If he abandoned all the rest of his hypotheses (which actually are good examples of what I referred to in my reply to Hana, viz.: bolt-on ad hoc hypotheses aimed at rescuing the main theory), then he would have no critics, but neither would he have anything to contribute these days. The Monitor hypothesis is rescued from counter evidence by the Affective Filter hypothesis and makes it impossible to refute.

      Krashen’s non-interface position regarding explicit and implicit learning is now discredited: there are compelling reasons to believe that learning is enabled and enhanced by negative feedback. What remains is the extremely important claim that SLA is predominantly an implicit process where grammar instruction plays a minor role,

      And, BTW, neurological approaches to SLA have a promising future. Lawson-Freeman’s ridiculous misinterpretation of important work done by MacWhinney and his colleagues on connectionism has done nothing to help MacWhinney’s excellent attempts to dislodge Chomsky’s paradigm status, but it might just turn out that neurological work will, contrary to everybody’s aims and expectations, provide evidence of a monitor at work. Stranger things have happened.


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