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Will studying formal logic improves logical reasoning?

Will studying formal logic improves logical reasoning?



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Reason for asking question:

I am looking to see if there is any good empirical evidence or study that shows or suggests that studying former logic or maybe informal logic would actually improve skills at logical reasoning (using deductive or inductive reasoning)?

Here is a study I found but I know nothing about how to assess the validity or interpreting results:

https://dspace.lboro.ac.uk/dspace-jspui/bitstream/2134/21445/5/InglisPME40RR.pdf

Is this an accepted method of testing on this topic or is there a more accepted test? If you could also explain the results to answer my question I would appreciate it?


Bottom Line

It is human nature to make rushed, emotional decisions based on incomplete information, then regret those decisions later on.

You can protect yourself from poor judgment by striving to attain the big picture when careful consideration is called for.

Focus on the consequences of your decision before considering how you feel about it.

Play with the cards you&rsquove been dealt, but look for opportunities in each situation and you will find them.

Ask knowledgeable mentors for advice, but beware of biased people who have an opinion, but do not necessarily have your best interest in mind.

Yet remember, true big picture thinking comes from hard-won experience. Legendary military commanders Napoleon Bonaparte and Mikhail Kutuzov were both injured on the battlefield.

Clear thinking comes from putting your big picture to the test of reality.


Study Philosophy to Improve Thinking—A Case of False Advertising?

A company advertises product X by claiming that it substantially improves memory and staves off dementia. The company provides no convincing evidence for these claims, and scientific studies fail to confirm the existence of the stipulated effects. Would you buy X? Probably not. Would the government and consumer protection agencies allow X to be freely marketed without at least a warning to potential gullible customers? Hardly, it seems.

Yet there is a similar product X, which has been sold to tens of thousands of people for decades without a murmur. I am talking here about studying philosophy at a university as a way of improving one’s thinking skills.

Obviously there are different reasons why students choose to study philosophy: they may find it intrinsically interesting or want to become professional philosophers or hope to discover the meaning of life or… But presumably an important reason for investing in studying philosophy—for the majority of students who do not plan to become philosophy professors—is the belief that this will make them better thinkers and perhaps also increase their chances of good employment. Were it discovered that the undergraduate study of philosophy in no way improves thinking or advances career opportunities, at least some parents might be more reluctant to pay a lot of money for their children to get a degree in philosophy. And it may well be that some of the prospective students themselves would be less inclined to incur a large college debt, with no expectation that it would generate some palpable benefit in the real world. The average student loan debt for American university graduates in 2016 was $37,172—which, according to some estimates, can cost borrowers $500,000 in lost retirement savings. Presumably some students might conclude that such a huge financial loss could not be justified by the expected enjoyment of the supervised reading of Plato, Kant and Wittgenstein.

Philosophy departments must be acutely aware of the widespread worry about the lack of practical utility of philosophy, which (if not alleviated) might seriously threaten their enrolment numbers. It is for this reason that departments so often try to reassure potential applicants that studying philosophy does add practical value.

For example, the Princeton philosophy department links to the American Philosophical Association’s list of well-known people from diverse fields who studied philosophy in college and then jumps to the conclusion that “skills acquired by concentrating in philosophy can thus be useful for a variety of careers.” But evidently the mere fact that, over the past century, around one hundred well-known people from different parts of the world studied philosophy cannot show that they became successful because of skills they supposedly acquired in philosophy courses. The inference is completely off-base. Surely the Princeton philosophers must be aware that similar lists of eminent people who majored in, say, English literature, economics, etc. could be (and have been) put together. Can we learn anything about the usefulness of these majors from the mere existence of such lists? Of course not.

The New York University philosophy department (widely regarded as currently the best in the United States, if not the world) asks on its website what a philosophy major is good for, and responds: “Students are right to wonder how their choice of a college major will affect their career prospects. Not to worry: research shows that majoring in philosophy is excellent preparation for a wide range of careers.” Although students are told not to worry, actually they should. The first cause for concern is that no research is actually cited. In fact, no research establishing this kind of beneficial consequence of studying philosophy has ever been cited in self-advertisements of other philosophy departments. Since this kind of research still faces a lot of serious methodological difficulties and obstacles (see below), it seems unlikely that at the present stage studies could unequivocally “show” the result claimed by the NYU philosophy department. Hence, all this gives us excellent reason to suspect that the NYU statement is false and that the research establishing “that majoring in philosophy is excellent preparation for a wide range of careers” simply does not exist.

The Harvard philosophy department says on its website that “the skills you acquire studying philosophy are highly marketable.” It further alleges that in contrast to “many specialized skills [that] eventually become obsolete” philosophy teaches general skills of clear thinking and critical approach and that consequently “these skills that philosophy teaches you will always be in high demand” and that “you can apply [these skills] to any line of work.”

Is this believable? Is it probable that merely by satisfying the basic requirements for a BA in philosophy at Harvard (12 undergraduate courses) you can acquire skills that will always be in high demand and useful to you in any line of work? What evidence is offered in support of this extravagant claim? Perhaps some independent and impartial studies or peer-reviewed research by scholars in psychology, education or other relevant disciplines?

No. The only two sources to which the Harvard philosophy department refers the reader on this matter are a frivolous article “Be Employable, Study Philosophy” originally published in the magazine The Tyee and a web page “Philosophy: What Can It Do for You?” run by a junior philosopher from Pepperdine University. The Tyee article is also recommended by philosophy departments at MIT, UC Davis, Ohio State University, University of Wisconsin-Madison, Middlebury, Northwestern, and Carnegie Mellon. The other source (the web page) is recommended to prospective philosophy students by one of the best philosophy departments in the world, at Rutgers University, and also by the departments at the University of North Carolina at Chapel Hill, City College New York, Middlebury, and George Washington University. According to that web page, what philosophy can do for you is help you get high scores on various tests like the GRE, GMAT, and LSAT, and also “it gets you into medical school.”

Philosophy is awash in optimism about the practical benefits of studying philosophy. Philosophy departments tell potential students that “because studying philosophy improves one’s analytical skills, it affords a greater probability of success on standardized tests such as the GRE, LSAT, and GMAT” (Florida State University), they can be very successful “as a result of majoring in philosophy” and “tend to do well on the GRE and the LSAT” (Notre Dame), since philosophy develops analytical skills “it is no surprise, then, that students who major in philosophy do exceptionally well on tests required for admissions to graduate and professional schools” (University of Michigan), “studying philosophy can also help you get into graduate school [since] philosophy majors excel on standardized tests like the GRE, GMAT, and LSAT” (University of Wisconsin, Madison), given what they are taught in philosophy courses “it is therefore not surprising that philosophy students have historically scored more highly on tests like the LSAT and GRE, on average, than almost any other discipline” (University of Washington), “philosophy provides an excellent foundation for graduate studies” shown by the fact that “GRE and LSAT scores of Philosophy majors exceed those of most other majors” (University of Arizona), “because philosophy teaches students how to analyze difficult problems, philosophy majors almost always have the highest scores on any graduate school exam (MCAT, LSAT, GMAT, GRE) apart from hard science majors” (Claremont McKenna College), “philosophy helps us develop various important skills” and you can “learn more about how a degree in philosophy can give you an advantage in your career path” by acquiring the information that “philosophy majors outperform all other majors on both the Verbal Reasoning and Analytical Writing sections of the GRE” (Carnegie Mellon University), and so on.

All these statements, in one way or the other, amount to the causal claim that studying philosophy produces higher scores on those tests. Many other prestigious philosophy departments (including the two most highly ranked departments in the U.S. at NYU and Princeton) conspicuously emphasize the high scores of philosophy majors on the GRE and other tests. It is hard to see why this information would be given in that particular context if not in order to suggest, again, that studying philosophy will bring about the rise of those scores. At any rate, no one should have any doubt that this will be widely taken to be the intended message. Briefly: if philosophy departments ask “Why study philosophy?” and then say “Philosophy graduates have higher test scores” the public will think that what they want to communicate is: “Studying philosophy leads to higher test scores.”

Finally, even the American Philosophical Association officially endorses the statement that philosophy training raises scores: “That the discipline of philosophy trains students in highly transferable skills is evidenced by the fact that philosophy majors perform exceptionally well on the LSAT, GMAT, and GRE.”

In reality, however, there is no justification for such claims. Getting higher test scores after studying philosophy does not show that higher scores are the result of studying philosophy. For all we know, it may be that philosophy students are brighter than average to begin with, and that this is why they perform so well on the tests. If that were true, their high scores would have nothing to do with their studying philosophy courses. Therefore, as long as this alternative hypothesis is not ruled out, no inference about practical benefits of philosophy is logically permissible.

Notice the irony. In their very attempt to promote philosophy as a great way to improve one’s critical thinking and logic, philosophers have so massively fallen prey to one of the most common and easily detectable logical fallacies—post hoc, ergo propter hoc (that is, A is followed by B, therefore, A caused B). This should give us pause about rushing to accept the idea that philosophy improves thinking.

But wait, doesn’t philosophy focus very heavily on logic, analysis of arguments, fostering a critical approach, etc.? Shouldn’t this fact alone make us expect that exposure to philosophy would almost certainly lead to some improvement in thinking and reasoning skills? Not necessarily.

To establish that studying philosophy improves thinking and that this is useful for a range of careers after university, three conditions must be satisfied: (1) there has to be some improvement, (2) this improvement has to persist over time, and (3) the improved thinking has to be transferable to contexts outside of the learning environment.

With respect to (1), there is a lot of skepticism about the effectiveness of various attempts to teach logic and critical thinking. In a recent overview of this research field, one of the world’s leading experts on the psychology of thinking, Philip N. Johnson-Laird, says that “no one knows whether a course in logic would improve our reasoning in life.” He also mentions the opinion of philosopher Stephen Toulmin that logic is actually inappropriate for the analysis of real arguments. (Princeton philosopher Gilbert Harman defends a similar view.) Speaking about all the proposed strategies of teaching informal logic and critical thinking, Johnson-Laird says that “no one appears to have demonstrated robust improvements in reasoning as a result of any of them.” Not all scholars agree with such a bleak evaluation, of course. However, even those who are more optimistic usually concede that the observed effects of teaching thinking are moderate at best, hence falling far short of transformative improvements that are often advertised as expected effects of studying philosophy.

Concerning (2), the benefits to thinking ability obtained in some studies typically taper off after a few months or years. But if the improvements in thinking disappear after a short time, studying philosophy will not lead to a lasting increase in either the students’ reasoning skills or in their employability because the whole point is always to insure significant improvement that is not restricted just to the learning period or its immediate aftermath.

With respect to (3), the problem is precisely about these “transferable” skills that “can be applied to any line of work” and that are alleged to be taught in philosophy classes. Do such all-purpose or “domain-general” skills exist at all, and if yes, can they be taught? Many psychologists and educationists think they cannot answer these two questions in the affirmative in good faith. For instance, a widely cited article on this very issue ends with the following words: “On the basis of the available evidence, however, drawn from many very different disciplines, we believe that the pursuit of [general transferable] skills is a chimera-hunt, an expensive and disastrous exercise in futility.” Another highly influential education researcher insists that “critical thinking is not a skill” and that “there is not a set of critical thinking skills that can be acquired and deployed regardless of context.”

The central problem for philosophers’ aspirations to teach thinking is that it is supposed to be about transferring what is learned in a philosophy class to a wide variety of very different real-life situations and in highly diverse jobs and careers. Empirical research has not found much support for this kind of transfer (so-called “general transfer”). In a well-known book about transfer of learning we read: “Again, beyond a minimal level, the literature clearly shows that we’ve failed to achieve significant transfer of learning, historically or currently, on any level of education.” In a highly influential article on transfer the author concludes: “Transfer has been studied since the turn of the [twentieth] century. Still, there is very little empirical evidence showing meaningful transfer to occur and much less evidence for showing it under experimental control.”

To see the disconnect between philosophers’ chutzpah of advertising their poorly articulated thinking-improvement method and the gloomy assessment of such prospects by many scholars who conduct research on this matter, consider (as an illustration) the following contrast. On one hand, prominent Yale philosopher Shelly Kagan writes that “of all the various fields and disciplines, there is one field that most centrally emphasizes the skills in question [improved critical thinking, communicating and being creative and original], and it is, indeed, philosophy” and that “one reason to study philosophy is that there is nothing better at improving your ability to think for yourself…” (He offers no justification for these claims.)

On the other hand, in the chapter “Learning to Think: The Challenges of Teaching Thinking” in the Cambridge Handbook of Thinking and Reasoning, the authors review the literature, point to strong reasons for skepticism about thinking-improvement efforts, and then conclude: “These limitations are signs that the grandest ambitions regarding the teaching of thinking are yet to be realized.” Also, according to the Macmillan Encyclopedia of Education “research has shown that it is very difficult to improve people’s reasoning, with instruction in logical reasoning being notoriously difficult.” Furthermore, a recent meta-analysis of studies examining whether college really teaches critical thinking ends with a pessimistic conclusion that “the central limitation of the literature … is the inability to make clear causal conclusions,” mainly because “the studies reviewed do not distinguish the effects of college from ordinary maturation effects, a persistent problem in this body of research.” A widely cited article from 2002 also expresses skepticism about transfer: “The issue of whether generalizable reasoning skills transfer to reasoning contexts outside of formal schooling remains an open question in the opinions of leading researchers.” And so on.

Now since all this is public and easily accessible information, why do so many philosophers and philosophical institutions blissfully continue with their thinking-improvement advertisements, in the face of the accumulated research that gives ample grounds for skepticism or at least caution? And why do philosophers almost never find fault with these unrealistic promises of philosophy’s marvellous accomplishments? (One of the very few exceptions is Georgetown philosopher Jason Brennan who offered a clear and cogent criticism in two posts on a libertarian blog. I myself raised the same issue repeatedly in the course “Morality and Markets” that I taught in Hong Kong from 2012 until 2015, and also in an article and a book.)

Why so little resistance to the peddling of false hopes? A possible answer is that some philosophers must be aware that the prevailing optimism is unjustified but that they have not been willing to speak up and thereby harm their own discipline by destroying an important rationale for the existence and funding of philosophy departments in their current form and size.

This whole situation is quite an embarrassment for philosophy as a field. Kant famously called it “a scandal of philosophy” that it had to “assume, as an article of mere belief, the existence of things external to ourselves, and not to be able to oppose a satisfactory proof to anyone who may call it in question.” But philosophy publicly advertising that it can massively improve people’s thinking is in some ways a bigger scandal. For in this case there is no clear indication that philosophers are even aware that their promise rests on a mere article of faith. They apparently feel no need to provide any evidence that they can achieve their professed goal or overcome numerous difficulties that worry education experts. Out of the top 20 philosophy departments (according to the well-known Philosophical Gourmet Report), 17 of them put out unsubstantiated claims about important practical effects of studying philosophy. It appears that the disease has reached an advanced stage.

There is a moral problem here as well. With many leading philosophy departments and philosophy associations repeatedly assuring us that those who study philosophy will become much better thinkers, many students may conclude that even a huge investment of money and time in this kind of self-improvement would eventually pay off. If no goods are delivered these people will be harmed in a way that could have easily been anticipated.

This connects back to the company selling product X, mentioned at the beginning of this article. The example was not fictitious. The company’s name is Lumosity and it indeed advertised that its “brain training” games have the effect of fending off memory loss and dementia. The Federal Trade Commission (FTC) was not satisfied with the evidence given for this claim and consequently charged Lumosity with “deceptive advertising.”

The FTC explained further: “Lumosity preyed on consumers’ fears about age-related cognitive decline, suggesting their games could stave off memory loss, dementia, and even Alzheimer’s disease. But Lumosity simply did not have the science to back up its ads.” The case was later settled under the agreement that any future claims about the efficacy of Lumosity’s products would have to rely on human clinical testing that “shall be (1) randomized, adequately controlled, and blinded to the maximum extent practicable and (2) be conducted by researchers qualified by training and experience to conduct such testing.”

Question: if Lumosity ran into such legal problems because of the poor evidence it had offered in support of the efficacy of its brain training games, could then philosophy departments be also charged on similar grounds, namely that their “mind training” practices, too, violate the “truth in advertising” laws because they are not backed by proper scientific evidence? It is hard to give a resolute answer without more detailed exploration, but the two cases do display worrying similarities.

By Neven Sesardic

Neven Sesardić has taught philosophy at universities in Croatia, the United States, Japan, England and Hong Kong. His books include "When Reason Goes on Holiday: Philosophers in Politics" (Encounter, 2016) and "Making Sense of Heritability" (Cambridge, 2005). He has also published articles in leading philosophy journals like Journal of Philosophy, Ethics, Philosophy of Science, and the British Journal for the Philosophy of Science.


The Importance of Logic and Critical Thinking

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Real or fake? Tilt shift photography pushes the limits of visible logic.

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"Critical thinking is a desire to seek, patience to doubt, fondness to meditate, slowness to assert, readiness to consider, carefulness to dispose and set in order and hatred for every kind of imposture." - Francis Bacon (1605)

As parents, we are tasked with instilling a plethora of different values into our children. While some parents in the world choose to instill a lack of values in their kids, those of us that don't want our children growing up to be criminals and various misfits try a bit harder. Values and morality are one piece of the pie. These are important things to mold into a child's mind, but there are also other items in life to focus on as well. It starts with looking both ways to cross the street and either progresses from there, or stops.

If you stopped explaining the world to your children after they learned to cross the street, then perhaps you should stop reading and go back to surfing for funny pictures of cats. I may use some larger words that you might not understand, making you angry and causing you to leave troll-like comments full of bad grammar and moronic thought processes. However, if you looked at the crossing the street issue as I did – as a logical problem with cause and effect and a probable solution – then carry on. You are my target audience.

Or perhaps the opposite is true, as the former are the people that could benefit from letting some critical thinking into their lives. So what exactly is critical thinking? This bit by Linda Elder in a paper on CriticalThinking.org pretty much sums it up:

Through critical thinking, as I understand it, we acquire a means of assessing and upgrading our ability to judge well. It enables us to go into virtually any situation and to figure out the logic of whatever is happening in that situation. It provides a way for us to learn from new experiences through the process of continual self-assessment. Critical thinking, then, enables us to form sound beliefs and judgments, and in doing so, provides us with a basis for a 'rational and reasonable' emotional life. — Inquiry: Critical Thinking Across the Disciplines, Winter, 1996. Vol. XVI, No. 2.

The rationality of the world is what is at risk. Too many people are taken advantage of because of their lack of critical thinking, logic and deductive reasoning. These same people are raising children without these same skills, creating a whole new generation of clueless people.

To wit, a personal tale of deductive reasoning:

Recently I needed a new transmission for the family van. The warranty on the power train covers the transmission up to 100,000 miles. The van has around 68,000 miles on it. Therefore, even the logic-less dimwit could easily figure that the transmission was covered. Well, this was true until the dealership told me that it wasn't, stating that because we didn't get the scheduled transmission service (which is basically a fluid change) at 30,000 and 60,000 miles the warranty was no longer valid. Now, there are many people that would argue this point, but many more that would shrug, panic, and accept the full cost of repairs.

I read the warranty book. I had a receipt that said the fluid was checked at 60,000 but not replaced. A friend on Twitter pointed out the fact that they were using 100,000 mile transmission fluid. So logically, the fluid would not have to be replaced under 100,000 miles if it wasn't needed, right? So why the stipulation that it needed to be replaced at 60,000 and the loose assumption that not doing that would void the warranty? So I asked the warranty guy to show me in the book where the two items are related. Where it explicitly says that if you don't get the service, the transmission isn't covered. There were portions where it said the service was recommended, but never connecting to actual repairs. Finally the warranty guy shrugged, admitted I was right and said the service was covered.

In this case, valid logic equaled truth and a sound argument. I used very simple reasoning and logic to determine that I was being inadvertently screwed. I say "inadvertently" because I truly believe based on their behavior that they were not intentionally trying to screw me. They believed the two items were related, they had had this argument many times before and were not prepared to be questioned. While both the service manager and the warranty guy seemed at least junior college educated, proving my argument to them took longer than it should have between three adults.

However, valid logic does not always guarantee truth or a sound argument. This is where it gets a little funky. Valid logic is when the structure of logic is correct in the way of syntax and semantics rather than truth. Truth comes from deductive reasoning of said logic. For example:

All transmissions are covered parts. All covered parts are free. Therefore, all transmissions are free. This logic is technically valid, and if the premises are true, then of course the conclusion must be true. You can see here however that it's not always true, though in some situations it could be. While the logic is valid, not all transmissions are free, only those covered by the warranty. So based on that, saying all transmissions are free is not sound logic.

To take it one step further:

All Daleks are brown. Some brown things are Cylons. Therefore, some Daleks are Cylons. Sci-fi fan or not, you probably know that this is not true. The basic lesson here is that, while the logic above might seem valid because of the structure of the statement, it takes a further understanding to figure out why it's not necessarily true: That is, based on the first two statements it's possible that some Daleks are Cylons, but it's not logically concludable. That's where deductive reasoning comes on top of the logic. The underlying lesson here is not to immediately assume everything you read or are told is true, something all children need to and should learn.

This is the direct lesson that needs to be passed on to our children: that of not accepting the immediately visible logic. While not all problems are complex enough to require the scientific method, some of them need some deduction to determine if they are true. Take the example above — how many kids would immediately be satisfied with the false conclusion? Sure, it's a bit geeky with the examples, but switch out bears for Daleks and puppies for Cylons. That makes it easier, and takes the actual research out of it (to find out what Daleks and Cylons are respectively) but many people would just accept that in fact some bears are puppies, if presented with this problem in the context of a textbook or word problem.

Maybe I'm being paranoid or thinking too doomsday, whatever, but I think this is an epidemic. Children are becoming lazier and not as self sufficient because their parents have a problem with watching a three year old cry after they tell her to remove her own jeans, or ask her to put away her own toys (yes, organizational logic falls under the main topic). These are the same parents who do their kid's science project while the kid is playing video games. These kids grow up lacking the simple problem solving skills that make navigating life much easier. Remember when you were growing up and you had the plastic stacking toys? Well, instead of toys for early development like that, parents are just plopping their kids down in front of the television. While there is some educational type programming on television, it's just not the same as hands-on experience.

My father is an engineer, and he taught me logic and reasoning by making me solve simple, then complex, problems on my own. Or at least giving me the opportunity to solve them on my own. This helped develop critical thinking and problem solving skills, something a lot of children lack these days. Too often I see children that are not allowed to solve problems on their own instead their parents simply do it for them without argument or discussion. Hell, I am surrounded by adults every day that are unable to solve simple problems, instead choosing to immediately ask me at which point I have to fill the role that their parents never did and – knowing the solution – tell them to solve it themselves, or at least try first.

One of the things I like to work on with my kids is math. There is nothing that teaches deductive reasoning and logic better than math word problems. They are at the age where basic algebra can come into play, which sharpens their reasoning skills because they start to view real world issues with algebraic solutions. Another thing is logic puzzles, crossword puzzles and first person shooters. Actually, not that last one. That's just the reward.

Since I weeded out the folks that don't teach their kids logic in the first two paragraphs, as representatives of the real world it's up to the rest of us to spread the knowledge. It won't be easy. The best thing we can do is teach these thought processes to our children, so that they may look at other children with looks of bewilderment when other children are unable to solve simple tasks. Hopefully, they will not simply do the task for them, but teach them to think. I'm not saying we need to build a whole new generation of project managers and analysts, but it would be better than a generation of task-oriented mindless office drones with untied shoelaces, shoving on a door at the Midvale School for the Gifted.


7 - Informal Logical Fallacies

Premise 1: All good chapters begin with a pithy quote.

Premise 2: We do not begin with a pithy quote.

Conclusion: This is not a good chapter.

Is this a valid conclusion? According to formal logic, it is. Formally, an argument is valid if the conclusion follows from the premises (whether or not the premises are true) and is invalid if it does not. Thus, formal logic is only concerned with the rules for drawing conclusions from a given set of premises (Baron, 1994). It does not specify a standard for evaluating the premises themselves (except, of course, to the extent that the premises were derived as conclusions from other premises).

This chapter focuses on informal logic. Unlike formal logic, informal logic seeks standards for the generation and evaluation of premises. Thus, if Premise 1 is not supported by sufficient evidence, then, according to informal logic, the conclusion about the chapter is not valid. So don't despair: This chapter may have more promise than our opening syllogism would compel you to conclude.

A second difference between formal logic and informal logic is that formal logic deals with certainty, and therefore does not offer a way to weigh the reasonableness of multiple valid or invalid conclusions (Baron, 1994). For instance, if the first premise were, “Some good chapters begin with pithy quotes,” the conclusion would be invalid.


§4. Necessity in logic

A second feature of the principles of logic is that they are non-contingent, in the sense that they do not depend on any particular accidental features of the world. Physics and the other empirical sciences investigate the way the world actually is. Physicists might tell us that no signal can travel faster than the speed of light, but if the laws of physics have been different, then perhaps this would not have been true. Similarly, biologists might study how dolphins communicate with each other, but if the course of evolution had been different, then perhaps dolphins might not have existed. So the theories in the empirical sciences are contingent in the sense that they could have been otherwise. The principles of logic, on the other hand, are derived using reasoning only, and their validity does not depend on any contingent features of the world.

For example, logic tells us that any statement of the form "If P then P." is necessarily true. This is a principle of the second kind that logician study. This principle tells us that a statement such as "if it is raining, then it is raining" must be true. We can easily see that this is indeed the case, whether or not it is actually raining. Furthermore, even if the laws of physics or weather patterns were to change, this statement will remain true. Thus we say that scientific truths (mathematics aside) are contingent whereas logical truths are necessary. Again this shows how logic is different from the empirical sciences like physics, chemistry or biology.


Deductive Reasoning

The study of reasoning is very important because it pertains to the heart of the question of whether people think logically and rationally. Do people follow the basic rules of logic when they make inferences? Some researchers highlight the flaws of human reasoning and its irrationality others stress the enormous flexibility and rationality of human reasoning.

Reasoning can be distinguished in inductive reasoning and deductive reasoning. Inductive reasoning refers to moving from the specific to the general, for example, “You can find the whole of nature within one flower.” Studying the details of a flower can lead to general hypotheses and rules about nature. This is an inductive approach. On the other hand, deductive reasoning means taking a general rule or theory and making inferences about a specific example.

Deductive reasoning has been widely studied using propositions in the form of “If… then” statements and using deductive arguments, also called syllogisms. Let us take the following example for a proposition: “If A, and B, but not C at the same time of E, then F in order to avoid G.” This example is quite abstract. An example of this proposition is, “If you have a car (A) which runs on diesel (B), but not a car which runs on regular gasoline (C), when you want to start the car (E), then you have to wait a bit and let it glow before you start (F), otherwise you damage the motor (G).”

An example for a syllogism is the following: “All cats love sausages. Fluffy is a cat. Therefore, Fluffy loves sausages.” The syllogism consists of two arguments, also called premises, and one conclusion. According to rules of logic, if the premises are true, the conclusion is also true. In our example, the two premises are true therefore, the conclusion is also true. The presented syllogism only consists of two premises. Syllogisms become difficult, however, when they consist of many premises, when they include the quantifier “some” instead of “all,” or when one premise is negated.

Several theoretical approaches have been developed that try to explain how people deal with syllogisms, that is, what cognitive processes occur when people solve syllogisms. A first approach, according to Sternberg, for example, distinguishes several components: encoding the information presented, mentally representing the meaning of the words in the premises, and controlling one’s own mental processes. A second approach, following Braine, for example, stresses the mental rules or inferences people use to draw conclusions. People might not be aware of these rules. These rules are often implicit like the rules of grammar we use to build sentences. A third approach, developed by Johnson-Laird, understands deductive reasoning as the building of mental models. Similar to understanding language by constructing mental models, people construct mental models when they read premises and draw conclusions. Recent neuropsychological studies of Goel and colleagues find initial support for the mental models approach. However, one might see these approaches not as mutually exclusive or contradictory, but as complementing one another.

In the context of cognitive development, the ability of deductive reasoning starts with the concrete operational stage (labeled by Jean Piaget) at around the age of 6 or 7 years. One prerequisite for deductive reasoning is the ability of the child to build groups and hierarchies of groups on different levels of abstraction, for example, the ability to know and differentiate dogs from cats and birds, and in greater complexity, differentiating German shepherds from poodles and bulldogs. This ability allows children to categorize objects correctly using necessary and sufficient criteria. Children at the preoperational stage of cognitive development, however, classify objects if they merely look similar (e.g., for them a carp and a whale are both fish). Although children in the preoperational stage can classify objects, children in the concrete operational stage are able to do this with more complexity and sophistication.

In the earlier years of childhood, some mistakes of deductive reasoning can be evident and observed. Many children, for example, overgeneralize and label every animal they see as “dog.” The implicit argument might be the following: “All objects that move, that have two eyes, two ears, a nose, and four legs are dogs. This concrete object that moves in the park has two eyes, two ears, a nose, and four legs. Therefore, it is a dog.” However, the object might not be a dog, but a sheep or a cat. In most cases, when the child then says “dog” and it is not a dog, other persons present might correct the child and help the child to differentiate and further refine his or her schemata.

Another error in deductive reasoning is undergeneralization. A child might call only one specific brand of cereal, Cheerios, for instance, as “cereal” and not apply the category “cereal” to all other brands. The implicit argument might be the following: “This food which is round, small, and has a whole in the middle is cereal. This food is flat. Therefore, it is not cereal.” It is common knowledge to most adults that Cheerios and corn flakes are both cereal. However, the child only labels the Cheerios as cereal. In both examples regarding overgeneralization and undergeneralization, the mistake lies in the first premise, that is, that all objects that have two eyes, two ears, a nose, four legs, and move are dogs and that only Cheerios are cereal. The child is not yet able to distinguish appropriately between groups and is not able to differentiate between levels of abstraction.

One way to help children improve their deductive reasoning is visualization, for example, using Venndiagrams. Venn-diagrams are geometric figures (e.g., circles or rectangles) that show similarities by overlapping figures. When drawing a Venn diagram about dogs and German shepherds, it becomes visually quite obvious that the group of dogs is bigger and more encompassing than the group of German shepherds and that the group of German shepherds is all included and a part of the group of dogs.

The ability of deductive and inductive reasoning acquired during the concrete operational stage is further developed during the stage of formal operational thinking. The abstract quality of formal operational thinking helps adolescents step back from the concrete content and judge the validity of the inferences. Let us consider the following syllogism: “All scorpions are mammals. Mammals are warm blooded. Therefore, scorpions are warm blooded.” One might say this conclusion is true another one might say this conclusion is not true. And both answers are right! The conclusion is logically correct and valid just following the abstract rules of logic and temporarily assuming the truth of the premises. However, the content of the first premise is untrue. In reality, scorpions are not mammals. Therefore, considering world knowledge about scorpions and mammals, people might think this is nonsense, and therefore might choose the answer “not true.” Similarly, one might abstract from the content of the two previous examples on dogs and cereals and only judge the logical validity of the conclusions.

Premises conflicting with world knowledge are one difficulty in working with syllogisms. We already mentioned that syllogisms with negated premises or abstract formulated syllogisms are more difficult then syllogisms that are not negated and concrete. There are still other factors that influence the accuracy of solving syllogisms. Researchers such as Luria, Scribner, and Cole presented syllogisms to people from different educational backgrounds in different cultures in Africa, America, and Asia. In all cultures, participants who have a formal education, attend school, or have gone to school were able to solve syllogisms better than participants who did not go to school. Participants without formal school education gave correct answers in about 50% of the cases, which is not better than chance. This result does not necessarily mean that people who go to school think more rationally than those who do not go to school. They might just be more familiar with such kinds of problems. Looking not just at right or wrong answers, but at the kinds of answers and justifications of participants without formal school education, shows their way of thinking. In one study, Scribner presented the following syllogism: “All children like candy. Mary is a child. Does Mary like candy?” Someone without formal education might answer: “How would I know if Mary likes candy. I don’t even know her!” or “Who is Mary?” These answers show that participants without formal school education interpret the syllogisms personally, using their world knowledge. They often refused to accept initial premises that contradicted their own experiences and they refused to treat general premises as truly general. It seems like they were not able or willing to stay within the problem boundaries. Interestingly, they could solve syllogisms easily that referred to familiar content.

To summarize, deductive reasoning is the ability to draw specific conclusions from general information. It is a key ability that children start acquiring in the concrete operational stage and that adolescents and adults further develop in the formal operational stage. Prerequisites for deductive reasoning are elaborated mental concepts on different levels of abstraction, as well as certain rules of inference. Research shows that in most cultures, formal schooling as well as familiarity with the material presented facilitate success on formal reasoning tasks.


Multitasking Video Game Improves Cognition in 79-year-olds!

Today, Nature published evidence that training on a multitasking video game improved older adults' cognitive ability beyond the scope of the game to untrained aspects of cognition. The article featured a four-year research led by Drs. Adam Gazzaley and Joaquin Anguera at UCSF. They utilised a relatively simple video game, NeuroRacer to train older adults on multitasking. NeuroRacer requires participants to drive a cartoon car, and to respond to relevant signs as they appear: simulating a day-to-day scenario of driving and responding to traffic signals or street signs.

A long-lasting plight for cognitive ageing scientists has been the lack of "Transfer" in training tools. That is, training can reliably improve older adults' performance on the tasks they are trained on sometimes they even exceed their younger counterparts. However, these changes all too often do not transfer to other tasks that utilise different aspects of cognition ("Cognitive Domains").

By comparing participants' brainwaves and test scores on various cognitive domains the were recorded before-, after-training, and 6 months later, Drs. Gazzlaey and Anguera were able to see whether the game's benefits transferred to untrained domains. These tests included sustained attention, inhibition, working and long-term memory, logical and visual reasoning/memory, motor control, etc.

They found that training on NeuroRacer's multitasking version benefited cognitive control abilities, such as sustained attention and working memory. After training, older participants' brainwave activities were more similar to those of younger adults. Additionally, these changes were still there after six months. Moreover, they reported evidence that these improvements were related to training-induced neuro-plasticity, and that they were not present if participants were trained on the drive and the sign tasks separately.

What's Next?

The same research group is extending NeuroRacer to the following projects at various stages

- NeuroRacer and Autism - NeuroGrocer: NeuroRacer under working memory load (See "Disclosure" section below) - Clinical trial of a consumer version of the NeuroRacer - Brainwave-computer interface: to use real time neural signals to adjust video game difficulty for maximum training effectiveness - Closed-loop non-invasive brain stimulation + EEG to increase plasticity of specific brain regions and networks

Brain Training Games?

Many consumer games claim to "improve the brain". Many of them lack empirical testing, and others showed mixed results in the ability to promote transferable benefits.

In my opinion, NeuroRacer stands out from the crowd because of its immersive environment and that it forces the brain to do multiple things at once. If I were in the market for "brain games", I would look for to select training games that reproduce these strengths.

More Information

Peer-Reviewed NeuroRacer Article Video game training enhances cognitive control in older adults. Anguera, J.A., Boccanfuso, J., Rintoul, J.L., Al-Hashimi, O., Faraji, F., Janowich, J., Kong E., Laraburro, Y., Rolle, C., Johnston, E., & Gazzaley, A. Nature 501: 97-101 (2013)

Disclosure of professional connection to featured research

Joey Essoe is the investigator for the aforementioned NeuroGrocer study (an offspring of NeuroRacer), under the supervision of Drs. Anguera and Gazzaley.


Study Philosophy to Improve Thinking—A Case of False Advertising?

A company advertises product X by claiming that it substantially improves memory and staves off dementia. The company provides no convincing evidence for these claims, and scientific studies fail to confirm the existence of the stipulated effects. Would you buy X? Probably not. Would the government and consumer protection agencies allow X to be freely marketed without at least a warning to potential gullible customers? Hardly, it seems.

Yet there is a similar product X, which has been sold to tens of thousands of people for decades without a murmur. I am talking here about studying philosophy at a university as a way of improving one’s thinking skills.

Obviously there are different reasons why students choose to study philosophy: they may find it intrinsically interesting or want to become professional philosophers or hope to discover the meaning of life or… But presumably an important reason for investing in studying philosophy—for the majority of students who do not plan to become philosophy professors—is the belief that this will make them better thinkers and perhaps also increase their chances of good employment. Were it discovered that the undergraduate study of philosophy in no way improves thinking or advances career opportunities, at least some parents might be more reluctant to pay a lot of money for their children to get a degree in philosophy. And it may well be that some of the prospective students themselves would be less inclined to incur a large college debt, with no expectation that it would generate some palpable benefit in the real world. The average student loan debt for American university graduates in 2016 was $37,172—which, according to some estimates, can cost borrowers $500,000 in lost retirement savings. Presumably some students might conclude that such a huge financial loss could not be justified by the expected enjoyment of the supervised reading of Plato, Kant and Wittgenstein.

Philosophy departments must be acutely aware of the widespread worry about the lack of practical utility of philosophy, which (if not alleviated) might seriously threaten their enrolment numbers. It is for this reason that departments so often try to reassure potential applicants that studying philosophy does add practical value.

For example, the Princeton philosophy department links to the American Philosophical Association’s list of well-known people from diverse fields who studied philosophy in college and then jumps to the conclusion that “skills acquired by concentrating in philosophy can thus be useful for a variety of careers.” But evidently the mere fact that, over the past century, around one hundred well-known people from different parts of the world studied philosophy cannot show that they became successful because of skills they supposedly acquired in philosophy courses. The inference is completely off-base. Surely the Princeton philosophers must be aware that similar lists of eminent people who majored in, say, English literature, economics, etc. could be (and have been) put together. Can we learn anything about the usefulness of these majors from the mere existence of such lists? Of course not.

The New York University philosophy department (widely regarded as currently the best in the United States, if not the world) asks on its website what a philosophy major is good for, and responds: “Students are right to wonder how their choice of a college major will affect their career prospects. Not to worry: research shows that majoring in philosophy is excellent preparation for a wide range of careers.” Although students are told not to worry, actually they should. The first cause for concern is that no research is actually cited. In fact, no research establishing this kind of beneficial consequence of studying philosophy has ever been cited in self-advertisements of other philosophy departments. Since this kind of research still faces a lot of serious methodological difficulties and obstacles (see below), it seems unlikely that at the present stage studies could unequivocally “show” the result claimed by the NYU philosophy department. Hence, all this gives us excellent reason to suspect that the NYU statement is false and that the research establishing “that majoring in philosophy is excellent preparation for a wide range of careers” simply does not exist.

The Harvard philosophy department says on its website that “the skills you acquire studying philosophy are highly marketable.” It further alleges that in contrast to “many specialized skills [that] eventually become obsolete” philosophy teaches general skills of clear thinking and critical approach and that consequently “these skills that philosophy teaches you will always be in high demand” and that “you can apply [these skills] to any line of work.”

Is this believable? Is it probable that merely by satisfying the basic requirements for a BA in philosophy at Harvard (12 undergraduate courses) you can acquire skills that will always be in high demand and useful to you in any line of work? What evidence is offered in support of this extravagant claim? Perhaps some independent and impartial studies or peer-reviewed research by scholars in psychology, education or other relevant disciplines?

No. The only two sources to which the Harvard philosophy department refers the reader on this matter are a frivolous article “Be Employable, Study Philosophy” originally published in the magazine The Tyee and a web page “Philosophy: What Can It Do for You?” run by a junior philosopher from Pepperdine University. The Tyee article is also recommended by philosophy departments at MIT, UC Davis, Ohio State University, University of Wisconsin-Madison, Middlebury, Northwestern, and Carnegie Mellon. The other source (the web page) is recommended to prospective philosophy students by one of the best philosophy departments in the world, at Rutgers University, and also by the departments at the University of North Carolina at Chapel Hill, City College New York, Middlebury, and George Washington University. According to that web page, what philosophy can do for you is help you get high scores on various tests like the GRE, GMAT, and LSAT, and also “it gets you into medical school.”

Philosophy is awash in optimism about the practical benefits of studying philosophy. Philosophy departments tell potential students that “because studying philosophy improves one’s analytical skills, it affords a greater probability of success on standardized tests such as the GRE, LSAT, and GMAT” (Florida State University), they can be very successful “as a result of majoring in philosophy” and “tend to do well on the GRE and the LSAT” (Notre Dame), since philosophy develops analytical skills “it is no surprise, then, that students who major in philosophy do exceptionally well on tests required for admissions to graduate and professional schools” (University of Michigan), “studying philosophy can also help you get into graduate school [since] philosophy majors excel on standardized tests like the GRE, GMAT, and LSAT” (University of Wisconsin, Madison), given what they are taught in philosophy courses “it is therefore not surprising that philosophy students have historically scored more highly on tests like the LSAT and GRE, on average, than almost any other discipline” (University of Washington), “philosophy provides an excellent foundation for graduate studies” shown by the fact that “GRE and LSAT scores of Philosophy majors exceed those of most other majors” (University of Arizona), “because philosophy teaches students how to analyze difficult problems, philosophy majors almost always have the highest scores on any graduate school exam (MCAT, LSAT, GMAT, GRE) apart from hard science majors” (Claremont McKenna College), “philosophy helps us develop various important skills” and you can “learn more about how a degree in philosophy can give you an advantage in your career path” by acquiring the information that “philosophy majors outperform all other majors on both the Verbal Reasoning and Analytical Writing sections of the GRE” (Carnegie Mellon University), and so on.

All these statements, in one way or the other, amount to the causal claim that studying philosophy produces higher scores on those tests. Many other prestigious philosophy departments (including the two most highly ranked departments in the U.S. at NYU and Princeton) conspicuously emphasize the high scores of philosophy majors on the GRE and other tests. It is hard to see why this information would be given in that particular context if not in order to suggest, again, that studying philosophy will bring about the rise of those scores. At any rate, no one should have any doubt that this will be widely taken to be the intended message. Briefly: if philosophy departments ask “Why study philosophy?” and then say “Philosophy graduates have higher test scores” the public will think that what they want to communicate is: “Studying philosophy leads to higher test scores.”

Finally, even the American Philosophical Association officially endorses the statement that philosophy training raises scores: “That the discipline of philosophy trains students in highly transferable skills is evidenced by the fact that philosophy majors perform exceptionally well on the LSAT, GMAT, and GRE.”

In reality, however, there is no justification for such claims. Getting higher test scores after studying philosophy does not show that higher scores are the result of studying philosophy. For all we know, it may be that philosophy students are brighter than average to begin with, and that this is why they perform so well on the tests. If that were true, their high scores would have nothing to do with their studying philosophy courses. Therefore, as long as this alternative hypothesis is not ruled out, no inference about practical benefits of philosophy is logically permissible.

Notice the irony. In their very attempt to promote philosophy as a great way to improve one’s critical thinking and logic, philosophers have so massively fallen prey to one of the most common and easily detectable logical fallacies—post hoc, ergo propter hoc (that is, A is followed by B, therefore, A caused B). This should give us pause about rushing to accept the idea that philosophy improves thinking.

But wait, doesn’t philosophy focus very heavily on logic, analysis of arguments, fostering a critical approach, etc.? Shouldn’t this fact alone make us expect that exposure to philosophy would almost certainly lead to some improvement in thinking and reasoning skills? Not necessarily.

To establish that studying philosophy improves thinking and that this is useful for a range of careers after university, three conditions must be satisfied: (1) there has to be some improvement, (2) this improvement has to persist over time, and (3) the improved thinking has to be transferable to contexts outside of the learning environment.

With respect to (1), there is a lot of skepticism about the effectiveness of various attempts to teach logic and critical thinking. In a recent overview of this research field, one of the world’s leading experts on the psychology of thinking, Philip N. Johnson-Laird, says that “no one knows whether a course in logic would improve our reasoning in life.” He also mentions the opinion of philosopher Stephen Toulmin that logic is actually inappropriate for the analysis of real arguments. (Princeton philosopher Gilbert Harman defends a similar view.) Speaking about all the proposed strategies of teaching informal logic and critical thinking, Johnson-Laird says that “no one appears to have demonstrated robust improvements in reasoning as a result of any of them.” Not all scholars agree with such a bleak evaluation, of course. However, even those who are more optimistic usually concede that the observed effects of teaching thinking are moderate at best, hence falling far short of transformative improvements that are often advertised as expected effects of studying philosophy.

Concerning (2), the benefits to thinking ability obtained in some studies typically taper off after a few months or years. But if the improvements in thinking disappear after a short time, studying philosophy will not lead to a lasting increase in either the students’ reasoning skills or in their employability because the whole point is always to insure significant improvement that is not restricted just to the learning period or its immediate aftermath.

With respect to (3), the problem is precisely about these “transferable” skills that “can be applied to any line of work” and that are alleged to be taught in philosophy classes. Do such all-purpose or “domain-general” skills exist at all, and if yes, can they be taught? Many psychologists and educationists think they cannot answer these two questions in the affirmative in good faith. For instance, a widely cited article on this very issue ends with the following words: “On the basis of the available evidence, however, drawn from many very different disciplines, we believe that the pursuit of [general transferable] skills is a chimera-hunt, an expensive and disastrous exercise in futility.” Another highly influential education researcher insists that “critical thinking is not a skill” and that “there is not a set of critical thinking skills that can be acquired and deployed regardless of context.”

The central problem for philosophers’ aspirations to teach thinking is that it is supposed to be about transferring what is learned in a philosophy class to a wide variety of very different real-life situations and in highly diverse jobs and careers. Empirical research has not found much support for this kind of transfer (so-called “general transfer”). In a well-known book about transfer of learning we read: “Again, beyond a minimal level, the literature clearly shows that we’ve failed to achieve significant transfer of learning, historically or currently, on any level of education.” In a highly influential article on transfer the author concludes: “Transfer has been studied since the turn of the [twentieth] century. Still, there is very little empirical evidence showing meaningful transfer to occur and much less evidence for showing it under experimental control.”

To see the disconnect between philosophers’ chutzpah of advertising their poorly articulated thinking-improvement method and the gloomy assessment of such prospects by many scholars who conduct research on this matter, consider (as an illustration) the following contrast. On one hand, prominent Yale philosopher Shelly Kagan writes that “of all the various fields and disciplines, there is one field that most centrally emphasizes the skills in question [improved critical thinking, communicating and being creative and original], and it is, indeed, philosophy” and that “one reason to study philosophy is that there is nothing better at improving your ability to think for yourself…” (He offers no justification for these claims.)

On the other hand, in the chapter “Learning to Think: The Challenges of Teaching Thinking” in the Cambridge Handbook of Thinking and Reasoning, the authors review the literature, point to strong reasons for skepticism about thinking-improvement efforts, and then conclude: “These limitations are signs that the grandest ambitions regarding the teaching of thinking are yet to be realized.” Also, according to the Macmillan Encyclopedia of Education “research has shown that it is very difficult to improve people’s reasoning, with instruction in logical reasoning being notoriously difficult.” Furthermore, a recent meta-analysis of studies examining whether college really teaches critical thinking ends with a pessimistic conclusion that “the central limitation of the literature … is the inability to make clear causal conclusions,” mainly because “the studies reviewed do not distinguish the effects of college from ordinary maturation effects, a persistent problem in this body of research.” A widely cited article from 2002 also expresses skepticism about transfer: “The issue of whether generalizable reasoning skills transfer to reasoning contexts outside of formal schooling remains an open question in the opinions of leading researchers.” And so on.

Now since all this is public and easily accessible information, why do so many philosophers and philosophical institutions blissfully continue with their thinking-improvement advertisements, in the face of the accumulated research that gives ample grounds for skepticism or at least caution? And why do philosophers almost never find fault with these unrealistic promises of philosophy’s marvellous accomplishments? (One of the very few exceptions is Georgetown philosopher Jason Brennan who offered a clear and cogent criticism in two posts on a libertarian blog. I myself raised the same issue repeatedly in the course “Morality and Markets” that I taught in Hong Kong from 2012 until 2015, and also in an article and a book.)

Why so little resistance to the peddling of false hopes? A possible answer is that some philosophers must be aware that the prevailing optimism is unjustified but that they have not been willing to speak up and thereby harm their own discipline by destroying an important rationale for the existence and funding of philosophy departments in their current form and size.

This whole situation is quite an embarrassment for philosophy as a field. Kant famously called it “a scandal of philosophy” that it had to “assume, as an article of mere belief, the existence of things external to ourselves, and not to be able to oppose a satisfactory proof to anyone who may call it in question.” But philosophy publicly advertising that it can massively improve people’s thinking is in some ways a bigger scandal. For in this case there is no clear indication that philosophers are even aware that their promise rests on a mere article of faith. They apparently feel no need to provide any evidence that they can achieve their professed goal or overcome numerous difficulties that worry education experts. Out of the top 20 philosophy departments (according to the well-known Philosophical Gourmet Report), 17 of them put out unsubstantiated claims about important practical effects of studying philosophy. It appears that the disease has reached an advanced stage.

There is a moral problem here as well. With many leading philosophy departments and philosophy associations repeatedly assuring us that those who study philosophy will become much better thinkers, many students may conclude that even a huge investment of money and time in this kind of self-improvement would eventually pay off. If no goods are delivered these people will be harmed in a way that could have easily been anticipated.

This connects back to the company selling product X, mentioned at the beginning of this article. The example was not fictitious. The company’s name is Lumosity and it indeed advertised that its “brain training” games have the effect of fending off memory loss and dementia. The Federal Trade Commission (FTC) was not satisfied with the evidence given for this claim and consequently charged Lumosity with “deceptive advertising.”

The FTC explained further: “Lumosity preyed on consumers’ fears about age-related cognitive decline, suggesting their games could stave off memory loss, dementia, and even Alzheimer’s disease. But Lumosity simply did not have the science to back up its ads.” The case was later settled under the agreement that any future claims about the efficacy of Lumosity’s products would have to rely on human clinical testing that “shall be (1) randomized, adequately controlled, and blinded to the maximum extent practicable and (2) be conducted by researchers qualified by training and experience to conduct such testing.”

Question: if Lumosity ran into such legal problems because of the poor evidence it had offered in support of the efficacy of its brain training games, could then philosophy departments be also charged on similar grounds, namely that their “mind training” practices, too, violate the “truth in advertising” laws because they are not backed by proper scientific evidence? It is hard to give a resolute answer without more detailed exploration, but the two cases do display worrying similarities.

By Neven Sesardic

Neven Sesardić has taught philosophy at universities in Croatia, the United States, Japan, England and Hong Kong. His books include "When Reason Goes on Holiday: Philosophers in Politics" (Encounter, 2016) and "Making Sense of Heritability" (Cambridge, 2005). He has also published articles in leading philosophy journals like Journal of Philosophy, Ethics, Philosophy of Science, and the British Journal for the Philosophy of Science.


Bottom Line

It is human nature to make rushed, emotional decisions based on incomplete information, then regret those decisions later on.

You can protect yourself from poor judgment by striving to attain the big picture when careful consideration is called for.

Focus on the consequences of your decision before considering how you feel about it.

Play with the cards you&rsquove been dealt, but look for opportunities in each situation and you will find them.

Ask knowledgeable mentors for advice, but beware of biased people who have an opinion, but do not necessarily have your best interest in mind.

Yet remember, true big picture thinking comes from hard-won experience. Legendary military commanders Napoleon Bonaparte and Mikhail Kutuzov were both injured on the battlefield.

Clear thinking comes from putting your big picture to the test of reality.


Score higher on your logical reasoning test.

So, take this logical reasoning test online. Use your logical reasoning skills to identify the correct answers. In the results you'll see your answers, all correct answers and explanations.

Logical reasoning tests are almost always a part of any job assessment or intelligence testing setup. You can use this test as part of aptitude test practice to make sure you are maximally prepared. The format of this test is similar to Raven's progressive matrices.

If you want an extensive and professional assessment or job test preparation, make sure to check out our logical reasoning practice package.

So, improve your IQ score with this free online logical reasoning test. Use your logical reasoning skills to complete the grid. In the results you'll see your answers, all correct answers and full explanations.


Does Mathematical Study Develop Logical Thinking? Testing the Theory of Formal Discipline

Are advanced mathematics students more prepared for logical thinking, careers, and life in general? Are they just naturally &ldquobetter&rdquo at logic and drawn to it, leading them to study a field that is supremely logical? This book attempts to address questions such as these.

For many years I have heard that majoring, or getting a doctorate, in mathematics is considered desirable by employers. When students ask me what career options are open to them through a mathematics major I respond in kind, along the lines of &ldquoStudying math trains your brain to think critically and logically. You could get lots of jobs!&rdquo As a pure mathematician, I have been told that the National Security Agency loves to hire people like me, not because of our particular field of study but because of how we are trained to think. When talking to undergraduates, I tout that math students are known to perform well on logical tests like the LSAT, making mathematics majors prime candidates for law schools. (This is actually true, as physics/math majors score at the top out of 29 disciplines, seen in Nieswiadomy, Michael, &ldquoLSAT Scores of Economics Majors: The 2008&ndash2009 Class Update.&rdquo Available at SSRN.)

Despite my willingness to believe that my chosen field developed my general thinking skills, I had no real evidence to back up this claim. For that reason, I was excited to read this book and learn whether mathematicians&rsquo hubris is well-founded. Inglis and Attridge begin with a bit of history, describing how the belief in the usefulness and transferability of mathematics skills is grounded in classical philosophy and current policy. The Theory of Formal Discipline (TFD) is at one point explained through the words of Plato: &ldquoThose who have a natural talent for calculation are generally quick at every other kind of knowledge and even the dull &hellip become much quicker than they would otherwise have been&rdquo (p. 3). I found it especially interesting how the TFD influenced the formation of early schools in countries like the US and England. Even now students are generally required to learn mathematics, often leading to jokes about how people never actually use algebra in real life. (Math, the only place where people can buy 60 watermelons and no one wonders why&hellip).

Apparently the TFD is not as universally accepted today, despite the prominence that mathematics maintains as a compulsory subject. Inglis and Attridge strive to determine whether there is truth to the theory by collecting data about the conditional reasoning of advanced mathematics students in the UK and Cyprus. In chapter two, the researchers select tasks based on the reasoning gains expected by proponents of the TFD. These tasks revolve around conditional reasoning and students&rsquo understanding of &ldquoif&hellip, then&hellip&rdquo statements. At this point in the book I actually found myself in suspense about what the results would show, as if it were a novel. Although I had some concerns about basing general thinking skills on investigations of conditional reasoning, I understood the authors&rsquo basis for choosing this direction and felt that it allowed for a decent foundation of evaluating broader logical thinking.

A series of studies were conducted. The first couple focus on comparing mathematics and literature students in the UK. Following that came a longitudinal study of high-level and low-level mathematics students in Cyprus. More research followed in the UK, some involving psychology students. I was impressed by the authors&rsquo research methodology and frequent consideration of alternative explanations of results. On the other hand, I was surprised at what was considered to be &ldquoadvanced&rdquo mathematics. I always assumed that most of the benefits to studying mathematics, when it comes to logical thinking, derived from exposure to proof-based mathematics. The research participants in this book were not often in proof-based courses, with the exception of some Cyprus students who took geometry. It would be interesting to extend the research to include students who have seen advanced algebra or analysis, or perhaps even doctoral mathematics students.

The conclusions of the various studies in this book were interesting but not always satisfying. I won&rsquot spoil future readers&rsquo suspense by describing all of the results. I will mention, however, that there is convincing evidence that studying mathematics helps students reject invalid inferences. This outcome holds through longitudinal studies where there was no initial difference between the reasoning skills of different groups of students, or where those differences were controlled. When I first mentioned to a colleague that I was reading this book their response was to point out that mathematics students probably go into the subject because they are naturally more inclined to logical thinking. Inglis and Attridge are mostly successful in contradicting such a &ldquofiltering&rdquo theory through longitudinal studies. To summarize in the words of the authors, &ldquowe found that mathematicians and non-mathematicians do appear to reason differently, and that this cannot easily be explained by group differences in intelligence&rdquo (p. 102).

There are two less satisfying results. One is that the benefits of mathematical study extend mainly to abstract tasks and not to thematic thinking. Another is that mathematics students did not become better at accepting valid modus tollens inferences (from (pLongrightarrow q) and not-(q), infer not-(p)). In fact, the students sometimes became worse at judging these statements. This negative finding was followed-up and reiterated through another study the authors spend considerable time explaining why mathematics students persistently made this mistake.

In all, I felt that this book was interesting and well-written. Their research methods were explained clearly and conclusions were summarized nicely. It is a relatively quick read at only 130 pages (before appendices). There were no definitive conclusions about the TFD, which is to be expected with such a difficult research project, but there were convincing results. I think that anyone who has been told, or who has told others, that mathematicians make better thinkers should read this book.

Mindy Capaldi is an associate professor at Valparaiso University. Her current research area is mathematics education, but she enjoys the Scholarship of Teaching and Learning realm. Her favorite area of mathematics is Abstract Algebra. She is a fan of reading fiction and doing math, and spends much of her time on these two activities.


III. Quotes About Logical Reasoning

Quote 1

“I am convinced that the act of thinking logically cannot possibly be natural to the human mind. If it were, then mathematics would be everybody’s easiest course at school and our species would not have taken several millennia to figure out the scientific method.” (Neil Degrasse Tyson)

Neil Degrasse Tyson is an astrophysicist and TV personality who passionately advocates for science and critical thinking. In this quote, he suggests that science and logical reasoning are inherently difficult tasks for the human mind, an organ that evolved to perform a very different set of tasks under very different conditions from the ones we live in today.

Quote 2

“Logic takes care of itself all we have to do is to look and see how it does it.” (Ludwig Wittgenstein)

Wittgenstein was probably the most influential philosopher of the 20th century, but his views changed dramatically over the course of his life, leading to some controversy as to what he actually thought. This quote is a good example. Early on, Wittgenstein believed that logical reasoning was autonomous — that logical truth was an objective truth, out there in the world for anyone to see if they knew how to look. Later on, though, Wittgenstein started to believe that culture and nature influence the way we see logic, and that logic is therefore not perfectly objective. It’s a tricky question, whether logical reasoning is universal or cultural — it must be tricky if a genius like Wittgenstein couldn’t make up his mind on it!


The Importance of Logic and Critical Thinking

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Real or fake? Tilt shift photography pushes the limits of visible logic.

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"Critical thinking is a desire to seek, patience to doubt, fondness to meditate, slowness to assert, readiness to consider, carefulness to dispose and set in order and hatred for every kind of imposture." - Francis Bacon (1605)

As parents, we are tasked with instilling a plethora of different values into our children. While some parents in the world choose to instill a lack of values in their kids, those of us that don't want our children growing up to be criminals and various misfits try a bit harder. Values and morality are one piece of the pie. These are important things to mold into a child's mind, but there are also other items in life to focus on as well. It starts with looking both ways to cross the street and either progresses from there, or stops.

If you stopped explaining the world to your children after they learned to cross the street, then perhaps you should stop reading and go back to surfing for funny pictures of cats. I may use some larger words that you might not understand, making you angry and causing you to leave troll-like comments full of bad grammar and moronic thought processes. However, if you looked at the crossing the street issue as I did – as a logical problem with cause and effect and a probable solution – then carry on. You are my target audience.

Or perhaps the opposite is true, as the former are the people that could benefit from letting some critical thinking into their lives. So what exactly is critical thinking? This bit by Linda Elder in a paper on CriticalThinking.org pretty much sums it up:

Through critical thinking, as I understand it, we acquire a means of assessing and upgrading our ability to judge well. It enables us to go into virtually any situation and to figure out the logic of whatever is happening in that situation. It provides a way for us to learn from new experiences through the process of continual self-assessment. Critical thinking, then, enables us to form sound beliefs and judgments, and in doing so, provides us with a basis for a 'rational and reasonable' emotional life. — Inquiry: Critical Thinking Across the Disciplines, Winter, 1996. Vol. XVI, No. 2.

The rationality of the world is what is at risk. Too many people are taken advantage of because of their lack of critical thinking, logic and deductive reasoning. These same people are raising children without these same skills, creating a whole new generation of clueless people.

To wit, a personal tale of deductive reasoning:

Recently I needed a new transmission for the family van. The warranty on the power train covers the transmission up to 100,000 miles. The van has around 68,000 miles on it. Therefore, even the logic-less dimwit could easily figure that the transmission was covered. Well, this was true until the dealership told me that it wasn't, stating that because we didn't get the scheduled transmission service (which is basically a fluid change) at 30,000 and 60,000 miles the warranty was no longer valid. Now, there are many people that would argue this point, but many more that would shrug, panic, and accept the full cost of repairs.

I read the warranty book. I had a receipt that said the fluid was checked at 60,000 but not replaced. A friend on Twitter pointed out the fact that they were using 100,000 mile transmission fluid. So logically, the fluid would not have to be replaced under 100,000 miles if it wasn't needed, right? So why the stipulation that it needed to be replaced at 60,000 and the loose assumption that not doing that would void the warranty? So I asked the warranty guy to show me in the book where the two items are related. Where it explicitly says that if you don't get the service, the transmission isn't covered. There were portions where it said the service was recommended, but never connecting to actual repairs. Finally the warranty guy shrugged, admitted I was right and said the service was covered.

In this case, valid logic equaled truth and a sound argument. I used very simple reasoning and logic to determine that I was being inadvertently screwed. I say "inadvertently" because I truly believe based on their behavior that they were not intentionally trying to screw me. They believed the two items were related, they had had this argument many times before and were not prepared to be questioned. While both the service manager and the warranty guy seemed at least junior college educated, proving my argument to them took longer than it should have between three adults.

However, valid logic does not always guarantee truth or a sound argument. This is where it gets a little funky. Valid logic is when the structure of logic is correct in the way of syntax and semantics rather than truth. Truth comes from deductive reasoning of said logic. For example:

All transmissions are covered parts. All covered parts are free. Therefore, all transmissions are free. This logic is technically valid, and if the premises are true, then of course the conclusion must be true. You can see here however that it's not always true, though in some situations it could be. While the logic is valid, not all transmissions are free, only those covered by the warranty. So based on that, saying all transmissions are free is not sound logic.

To take it one step further:

All Daleks are brown. Some brown things are Cylons. Therefore, some Daleks are Cylons. Sci-fi fan or not, you probably know that this is not true. The basic lesson here is that, while the logic above might seem valid because of the structure of the statement, it takes a further understanding to figure out why it's not necessarily true: That is, based on the first two statements it's possible that some Daleks are Cylons, but it's not logically concludable. That's where deductive reasoning comes on top of the logic. The underlying lesson here is not to immediately assume everything you read or are told is true, something all children need to and should learn.

This is the direct lesson that needs to be passed on to our children: that of not accepting the immediately visible logic. While not all problems are complex enough to require the scientific method, some of them need some deduction to determine if they are true. Take the example above — how many kids would immediately be satisfied with the false conclusion? Sure, it's a bit geeky with the examples, but switch out bears for Daleks and puppies for Cylons. That makes it easier, and takes the actual research out of it (to find out what Daleks and Cylons are respectively) but many people would just accept that in fact some bears are puppies, if presented with this problem in the context of a textbook or word problem.

Maybe I'm being paranoid or thinking too doomsday, whatever, but I think this is an epidemic. Children are becoming lazier and not as self sufficient because their parents have a problem with watching a three year old cry after they tell her to remove her own jeans, or ask her to put away her own toys (yes, organizational logic falls under the main topic). These are the same parents who do their kid's science project while the kid is playing video games. These kids grow up lacking the simple problem solving skills that make navigating life much easier. Remember when you were growing up and you had the plastic stacking toys? Well, instead of toys for early development like that, parents are just plopping their kids down in front of the television. While there is some educational type programming on television, it's just not the same as hands-on experience.

My father is an engineer, and he taught me logic and reasoning by making me solve simple, then complex, problems on my own. Or at least giving me the opportunity to solve them on my own. This helped develop critical thinking and problem solving skills, something a lot of children lack these days. Too often I see children that are not allowed to solve problems on their own instead their parents simply do it for them without argument or discussion. Hell, I am surrounded by adults every day that are unable to solve simple problems, instead choosing to immediately ask me at which point I have to fill the role that their parents never did and – knowing the solution – tell them to solve it themselves, or at least try first.

One of the things I like to work on with my kids is math. There is nothing that teaches deductive reasoning and logic better than math word problems. They are at the age where basic algebra can come into play, which sharpens their reasoning skills because they start to view real world issues with algebraic solutions. Another thing is logic puzzles, crossword puzzles and first person shooters. Actually, not that last one. That's just the reward.

Since I weeded out the folks that don't teach their kids logic in the first two paragraphs, as representatives of the real world it's up to the rest of us to spread the knowledge. It won't be easy. The best thing we can do is teach these thought processes to our children, so that they may look at other children with looks of bewilderment when other children are unable to solve simple tasks. Hopefully, they will not simply do the task for them, but teach them to think. I'm not saying we need to build a whole new generation of project managers and analysts, but it would be better than a generation of task-oriented mindless office drones with untied shoelaces, shoving on a door at the Midvale School for the Gifted.