Category Archives: Miscellaneous

Deductive Soundness and Validity (How to win arguments part 2)

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validity and soundness

In my last post, I explained what a deductive argument is and looked at conditional statements, which play a central role in deductive reasoning. Now I’d like to talk about soundness and validity. Being able to establish quickly whether a deductive argument is valid or not allows you to work out if you need to devote more time and energy to unpacking it. If it’s invalid, you don’t have to examine it any further; you can put it aside and focus your attention on other arguments. But if it’s valid, it’s time to start the arduous process of working out whether it’s sound (and, thus, whether you have to accept its conclusion).

But what do these terms mean? We use them in various ways in our every day life, but in the realm of critical thinking they have specific definitions. Validity refers to an argument’s form; a deductively valid argument is one that has one of two forms. Basically, the premises need to guarantee the conclusion. You may remember from my previous post that this is the definition of a deductive argument. So, when we’re saying that an argument is deductively valid, all we’re really saying is that it actually is successfully deductive. To determine whether it is or isn’t, we have to look at the conditionals.

A conditional deductive argument will always contain a conditional statement, some kind of follow-up statement, and a conclusion. An example of this would be: “If something is a green plant, it photosynthesizes. My cactus is a green plant. Therefore, it photosynthesizes.” The follow-up statement in this case is affirming the sufficient condition. This is one valid form of deductive argument, also known as a modus ponens argument. The other form of valid deductive argument is known as a modus tollens argument – this is an argument in which the second premise denies the necessary condition. An example of this might be “If something is a green plant, it photosynthesizes. My cat does not photosynthesize, therefore it’s not a green plant.” In each of these arguments, the premises guarantee the conclusion. If a conditional deductive argument denies the sufficient condition or affirms the necessary condition, the result is an invalid argument: “If something is a green plant, it photosynthesizes. My cat is not a green plant, therefore it doesn’t photosynthesize.” The way I was taught to remember this is to look for matching letters – affirming the sufficient and denying the necessary are the valid forms. It’s possible for an invalid argument to have only true premises and a true conclusion, as in the example just given – validity refers only to whether or not the conclusion is guaranteed by the truth of the premises.

What about soundness? A sound deductive argument is a valid deductive argument with only true premises (and, thus, has a true conclusion – if a deductive argument is shown to be sound, you can’t disagree with its conclusion). This is what people want to achieve when they construct a deductive argument. But it’s hard to establish whether an argument really is sound, because determining whether it’s premises are true can be difficult and may involve subjective reasoning. Note that validity and soundness are two different things; an argument can be valid without being sound (though it can’t be sound without being valid). Consider my first example in the paragraph above. Cacti are indeed green plants. And they do photosynthesize. But it’s not true that all green plants photosynthesize; dodder, a kind of parasitic plant, can have a green colour but does not photosynthesize. So the first premise and the conclusion are true, but the second premise is false. The argument is valid, but it isn’t sound.

Knowing how to identify valid deductive arguments can allow you to have far more fruitful discussions with people; you can get straight to the work of examining the premises of their valid arguments to determine whether they’re true, without wasting time on arguments that are structurally flawed. Hopefully this post will help you learn how to do so.

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Conditionals (How to win arguments part 1)

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argumentillustration

Being able to argue properly, with yourself and others, is an incredibly valuable skill. Being able to critically evaluate arguments is not only extremely useful in the workplace – it can help you make better life choices for yourself and the people around you. This skill is generally known as “critical thinking”, and it is a philosopher’s bread and butter. Now, there’s no point in denying that we all use our brains differently, and that some of us are naturally good at this kind of thinking. But anyone can get better at thinking critically by studying arguments, including those to whom it comes naturally. So, for your entertainment and edification, I’ve decided to put together a few posts on the topic.

Let’s start with deduction. A deductive argument, simply speaking, is one in which the premises (if true) guarantee the conclusion. In other words, if the premises of a valid deductive argument are true, the conclusion can’t possibly be false. An example of this could be; “If I don’t study for my philosophy exam on wednesday, I will not get a good mark on it (first premise). I’m not studying for my philosophy exam on wednesday (second premise), therefore I will not get a good mark on it (conclusion)”. As you can see, if the premises of this argument are true, the conclusion must also be true. Note that this doesn’t mean that the conclusion actually is true, because the premises might be false. Compare this to; “If I don’t study for my philosophy exam on wednesday, I will not get a good mark on it. I will study for my philosophy exam on wednesday, therefore I will get a good mark on it”. This is a bad argument, deductively speaking, because the premises don’t guarantee the conclusion. This is because the form of the argument is invalid. I’ll get to validity later, but for now I want to focus on conditionals.

Conditional statements (often shortened to “conditionals”) are statements like the first premise in the example arguments above. “If then” statements, essentially. Conditional statements contain two different conditions (hence the name): a necessary condition and a sufficient condition. To put it very simply, the sufficient condition is the one that comes after the “if”, and the necessary condition is the one that comes after the “then”. In the examples above, “not studying for my philosophy exam” is the sufficient condition and “not getting a good mark on it” is the necessary condition. The “if” and “then” are not part of the conditions. Knowing the difference between these different kinds of condition, and being able to identify them, is an essential skill when it comes to evaluating deductive arguments.

However, identifying them can be difficult, because conditional statements are often not given in the standard “if then” form. In such sentences, it’s possible to work out which is which by looking at the meaning of the statement (what is necessary and what is sufficient), but it’s also possible to translate it into “if then” form. Consider this statement: “only people who don’t study for their philosophy exam will get a bad mark on it.” This translates into: “if you get a bad mark on your philosophy exam, then you didn’t study for it.” The original sentence does not say that everyone who doesn’t study for their philosophy exam will get a bad mark on it; rather, it says that those who do get a bad mark will not have studied. This becomes a lot clearer when the sentence has been translated, because it’s easier to identify the conditionals.

There are various different ways in which you can go about translating conditional statements, such as memorizing certain key words and phrases (“only if”, for instance, usually precedes a necessary condition), but I’ve found that the easiest way is to use a conditional statement that you know is true (preferably one that’s very obviously true), and seeing how it would be rearranged in the form of the sentence you’re translating. I tend to use “if you’re a father, then you’re a parent”, which was the example given to me when I was learning how to do this. Consider the example sentence I gave you earlier. If I translate my “if then” sentence into the form it has, I get “only parents are fathers” (since the “if then” sentence is true, it must still be true when it’s rearranged – that’s how I know where to put the “father” and where to put the “parent” – “only fathers are parents” would be a false statement). I can now see that the necessary condition and sufficient condition have changed place, with the necessary condition coming first. All I have to do now is identify what the original conditions were (“not studying for your philosophy exam” and “getting a bad mark on it”) and lable them as necessary and sufficient.

Translating conditional statements like this is a skill, and as such you have to practice doing it. There’s a great little game on Khan Academy that let’s you do just this (don’t worry, it’s not too mathsy): https://www.khanacademy.org/math/geometry/logical-reasoning/e/conditional_statements_2

You can also find more information on conditional statements and deductive arguments on that page – I’ll be following up on this post with one on deductive validity in the near future. Until then, I hope you are well, and as always if you have any questions or suggestions please leave a comment below!

Say hello to a new blogger!

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Hi folks!

I’m afraid this isn’t going to be a proper post, just a little note to anyone who happens to stop by. I will start posting again soon, as my university studies will be starting in just under a month, whereupon I’ll be learning about the “philosophy of happiness”, and hopefully sharing that learning with you. I might actually write a couple of posts before that, just to get my brain back in gear. If you have any suggestions for good topics, give ’em up in the comments!

Anyway, what I wanted to say was this; my friend just started a blog! Now, the similarities between our blogs are not great. This is a philosophy blog, and his is a gaming blog. However, he’s a clever guy and his first post on the controversial ending of the third installment of the Mass Effect series is highly philosophical. I encourage anyone with an interest in gaming to go check out his blog, pixelpub.wordpress.com, and maybe leave a pleasant comment or two for him to read. He’s got a wonderfully weird sense of humour, too.

Hej svej!

Aside

I’ve noticed that this blog is still receiving a decent amount of traffic. I’m very glad this is the case, as it means my efforts are not for naught (I do wish people would try to start more discussions, though!). However, as those who are still coming here may have realized, I’m not updating the blog very frequently. In other words, I’ve all but abandoned it.

I’m terribly sorry for that! Fear not, though, I will start posting again in the relatively near future, when I finally start to attend my university studies. As followers of my other blog, the Musings of an Imaginative Mind (also discontinued for the time being, not entirely sure why though I suspect it has something to do with laziness), will know, I’ve moved to Australia with my family. This means that my university studies won’t start up until March. When that time comes, however, I’ll start posting again. The idea with this blog is for it to serve as a study aid to myself and others studying philosophy, and so it’s been temporarily discontinued due to the fact that I’m not currently studying anything. I attempted to keep it going for a while, but I felt like I was trying to pass myself off as a teacher when I’m not yet at all ready to take on such a role. So, while you’re waiting for new material, I encourage you to read my old posts, and start as many discussions as possible to pass the time. Do you agree or disagree with the ideas I’ve talked about in my posts? Do you have any favourite philosophers? Do you feel that I’ve left important information out of some of my posts? Etc.

If you want to talk about some general philosophical problem that doesn’t quite fit into any of my posts, feel free to start it up here!

Cheerio!

To Those Still Coming Here

Stoicism

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Stoicism was a philosophical school of thought founded by Zeno of Citium (not to be confused with Zeno of Elea, a pre-Socratic philosopher perhaps best known for his paradoxes). Zeno of Citium was a pupil of Crates of Thebes (among others). Considering the fact that this Crates was a Cynic, it’s not surprising that many aspects of Cynicism – the idea of living a virtuous life, for instance, as well as the rejection of material wealth – were absorbed into Stoic philosophy.

Stoicism became immensely popular in both Greece and Rome, with many illustrious thinkers refining and defining it over the years. The central focus of Stoicism lies in the idea of always maintaining a will that “works in accordance with nature”. According to the Stoics, a person who does this can be considered virtuous and should be able to overcome suffering and thereby live a happy life. So what, exactly, does it mean to have such a will? Well, the Stoics had a deterministic view on nature, and felt that it was inevitable that things should occasionally not go our way. If a person accepts this fact, and doesn’t get angry when it happens (which rarely does any good anyway), they have managed to cultivate a will that does, indeed, work in accordance with nature. In other words (and I do hope I’ve got this right); “go with the flow”. It’s important to note, however, that Stoicism was more than just a bit of theory, it was a way of life. It can be compared to forms of spirituality like Buddhism, and involved a lot of practical elements such as daily meditation and self-reflection. It’s not enough to force yourself to stay calm when bad things happen if you want to call yourself a Stoic – there’s much more to it than that.

Much like the Cynics, the Stoics placed more emphasis on what people did than what they said. It’s easy enough to say that you’re not going to throw a fit the next time you end up in a traffic jam, but it’s considerably harder to actually keep your cool when the theoretical traffic congestion becomes a reality.

P.S. Unlike the term “cynic”, the modern definition of “stoic” hasn’t deviated too far from the origins of the word. The Stoics felt that happiness could be obtained not by fulfilling desires but by removing them, and so a slight lack of passion is characteristic of the practicing Stoic. Stoicism does not, however, have anything to do with repressing emotions.

Check out these links to learn more (open in a new window/tab):

http://en.wikipedia.org/wiki/Stoicism

http://plato.stanford.edu/entries/stoicism/

Related articles

Cynicism

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Right, so I thought I’d do some quick posts on three of the main schools of thought that came out of Ancient Greece and Rome back in the good old days. First up, Cynicism.

Cynicism was a philosophical way of thinking created by Antisthenes, a pupil of Socrates. The term “Cynic” comes from Ancient Greek and translates roughly to “dog-like” – it seems this name was given to the Cynics due to their canine approach to life; they were shameless and animalistic, but also loyal to their own and to their cause. Diogenes, perhaps the most infamous of the classical Cynics, was known as “the dog-man”.

The Cynics were concerned with virtue, honesty and integrity. Socrates was himself concerned with virtuous existence, but Antisthenes took his theories regarding this subject to their logical extreme, and founded an entire life-philosophy on them. The Cynics were concerned with analyzing society and the people living in it, and finding the flaws therein. They believed that civilization had taken a sort of wrong turn and was leading people away from a virtuous, natural life. Diogenes focused the Cynical “goal” or “vision” by adding that it was important to study basic human nature, and to see where civilization was leading people away from this natural state. Most Cynics lived rough, denouncing wealth, eating and even copulating on the streets – like dogs (I’d say a good way to understand the essence of Cynicism is to remember its literal meaning, as stated above). They were concerned with man returning to a natural existence, and thought that only when people gave up their desire for things like wealth, fame and power could they be happy. They were evangelical, striving at all times to show people the error of their ways. They taught by example and were known to preach in public places. Diogenes apparently walked the streets during the day with a lantern, saying that he was looking for a virtuous man. It’s important to note that the Cynics were not saying we should live like primitive beasts – they saw humans as “rational animals” and thought we should live as such.

Many of the Cynical ideas and theories later went into the making of Stoicism, another Hellenistic “way of life”. In the 19th century, academics began to focus on the negative aspects of Cynicism, which is how we arrived at the contemporary definition of the term “cynic”: an unpleasantly critical and excessively negative person.

Check out these links to learn more (open in a new window/tab):

http://en.wikipedia.org/wiki/Cynicism

http://www.i-cynic.com/whatis.asp

On Frustration – because a better title eludes me

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A long time ago in a galaxy far, far away I watched a series of YouTube videos featuring Alain de Botton’s documentary based on his book “The Consolations of Philosophy”. Anyone who, like me, is interested in those aspects of philosophy that help us live happier, fuller lives should watch these – he discusses a lot of interesting points. Each video is centred around a particular philosopher and his or her work, and each one deals with a particular topic. As an example, there’s one on Epicurus and his ideas regarding happiness and how to attain it. Another one, which I found very interesting, was focused on Seneca, a Roman Stoic philosopher, and his thoughts on frustration.

I found this video intriguing because frustration is something I deal with on a daily basis, both my own and that of other people. Being a slow, pensive person, I tend to cause a lot of it. Seneca, apparently, was also dealing with quite a bit of frustration, working as the tutor of the emperor’s son, and frustration in that time and place was a dangerous thing. So it’s only natural that he ended up spending quite a bit of time trying to figure out how to prevent it. What he came up with is that frustration is caused by excessive optimism. It’s when we expect things to turn out well and they don’t that we get frustrated. Just think about it; imagine you have a friend who has a tendency to show up late to things. If you fully expect that said friend will arrive late to your party, and plan things accordingly, then you’ll be fine if he is late, and pleasantly surprised if he’s on time. However, if you don’t expect him to be late, but believe he’ll be on time on this occasion, and if you plan according to that, then you’ll be frustrated when he is late. We only ever become frustrated when things don’t work out the way we expect them to. Think back; can you remember a single occasion where you’ve genuinely said to yourself “oh, I’m sure this or that will happen, and if it does I’ll just have to deal with it in such and such a way” and then become frustrated when it did happen? Generally speaking, if we’re pessimistic about something from the start we’ll only find adversity mildly amusing. I, for one, think this is true. It’s that tried and true bit of advice; if your expectations are low you won’t be disappointed.

There is, however, one problem with this theory. Its conclusion is that we should adopt a more pessimistic attitude in order to avoid disappointment. We should be cynical, always expecting the worst. Many people believe that the opposite is better, that being optimistic is the best approach. I think a lot of people genuinely believe that if they’re positive and are sending out positive “vibes”, good things will come to them. Now, this might actually be the case. After all, if you wake up in the morning and convince yourself from the start that you’re going to have a good day, chances are it will be a good day. It’s a self-fulfilling prophecy, since you’ll get a kick of energy and will be more prepared to be active, and you’ll erect a sort of “bubble” of good-will and humour around yourself, dealing with problems more effectively. If you’re good at being optimistic, I think it’s possible to be quite content even on a fairly bad day. I recon it might even be possible to combat frustration with optimism. However, eventually you’ll hit a wall. Life has a way of keeping our feet firmly planted on the ground. If you’re pessimistic, on the other hand, you may be less happy in the short-term but you probably won’t be disappointed. It is, in many ways, an easier frame of mind to adopt and maintain than its opposite.

And yet, the idea that we’ll be more content if we’re cynical and pessimistic all the time seems counter intuitive, at least to me. It just doesn’t seem right. But maybe it’s not a question of being pessimistic. In fact, I don’t believe it is. What Seneca was saying was that we should always be prepared for the worst, but that doesn’t mean we can’t hope for the best. What he was advocating was realism, a simple acceptance of the fact that things really don’t always work out and that we’re bound to bump into problems from time to time. When we do, we should be prepared to say “ah well, that’s just the way of the world” and move on, rather than becoming angry and indignant. We should steep ourselves in reality, always ready to take the good with the bad. And when something goes wrong, we should try to take it philosophically. When the emperor ordered Seneca to kill himself, the man didn’t so much as complain. He took the knife, and then his life. Perhaps the perfect – if a tad lugubrious – illustration of what he was talking about.

On a side note, Alain de Botton has been criticized for popularising philosophy, over simplifying it to make it more accessible to “the masses”. To be frank, I’m not sure this is such a bad idea. I think philosophy has become a little too esoteric, a little too academic, and a little too lofty. Reading a philosophical text can be like trying to decipher some strange code. I believe it’s fully possible to express even the most complex philosophical theories in a simple manner. But I’ve only studied the subject for a while and can’t claim to be an expert. If you happen to have any thoughts on the matter, please share them!