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!