As my first contribution to the growing list of basic terms and concepts, I'm going to explain a few things no one asked about when I opened the request line. But, these are ideas that are crucial building blocks for things people actually did ask about, like falsifiability and critical thinking, so there will be a payoff here.
Philosophers talk a lot about arguments. What do they mean?
An argument is a set of claims. One of those claims is the conclusion which the other claims are supposed to support. While logicians, geometers, and that crowd customarily give you the conclusion as the last claim in the argument, arguments in novels and op-ed pieces may give you the conclusion at the very start of the argument.
The non-conclusion claims in the argument are generally referred to as premises or assumptions. These claims are the reasons being offered to support the conclusion of the argument. Note that some of the claims labeled as "assumptions" feel like certainties.
The point of an argument is to give good reasons for accepting the conclusion. An argument is something stronger and more persuasive than a mere opinion. What makes an argument more persuasive is that it makes its assumptions clear and then shows how these assumptions lead logically to the conclusion.
A valid argument is one where the truth of the premises guarantees the truth of the conclusion. In other words, if your argument is valid, someone who accepts your premises as true will have to accept your conclusion or else embrace a logical contradiction.
Do you like Ps and Qs (and upside down As and backward Es)? If so, you'll find a wide selection of symbolic logic textbooks that set out a dizzying array of valid patterns of inference. Many philosophers manage to set out arguments without talking in Ps and Qs and upside down As and backward Es, though. There are some patterns of inference that careful thinkers will recognize as valid (even if they can't whip out the old school name of the syllogism) and others that they will recognize as not guaranteeing a true conclusion even if the premises are true.
Here's an example of an invalid argument:
- If my battery is dead, my car won't start. (premise)
- My car won't start. (premise)
- Thus, my battery must be dead. (conclusion)
It's perfectly possible for both premises to be true, yet for the conclusion to be false (because something else is wrong with my car that is keeping it from starting). In other words, we shouldn't take (1) and (2) as sufficient reasons for accepting (3).
Here's an example of a valid argument:
- Britney Spears is from Mars. (premise)
- Martians have astounding vocal range and are great dancers. (premise)
- Hence, Britney Spears has astounding vocal range and is a great dancer. (conclusion)
If claims (1) and (2) were true here, there is no way that claim (3) could fail to be true. Accepting the assumptions commits you to the conclusion -- unless, of course, you choose to opt out of the shared rules of valid inference we've been trained to accept. That's always an option, but it's not one that puts you in a very good place to engage with others who accept those rules (which is something you'd want to do to persuade them to accept some of your conclusions)!
Valid or not, most of you are not accepting my argument's conclusion, that Britney Spears has astounding vocal range and is a great dancer. Why not? Perhaps because you reject my premise that Britney Spears is from Mars and/or my premise that Martians have astounding vocal range and are great dancers. Even if the logical connections between my premises and my conclusion are good, if any of my assumptions are false, you're entitled to reject my argument as giving good reasons to believe the conclusion. (By the way, even people who accept the truth of the claim that Britney Spears has astounding vocal range and is a great dancer will reject the argument offered here in favor of that conclusion -- they won't want to endorse the false premises about Martians.)
An argument that is valid and whose premises are true is a sound argument. Not only does it have the right kind of logical connections between the conclusion and the reasons offered to support the conclusion, but all those reasons are true claims. The challenge, of course, is in being sure of the truth of your premises. "All men are mortal" sure sounds like a true claim, but given that there are scads of people who haven't yet demonstrated their mortality by kicking off, can we be certain that one of them won't turn out to be immortal?
Don't go whipping out data on all the humans who have dies so far, thus proving themselves to be mortal and making it a good bet that we are all mortal, too. The argument:
- Guy 1 died.
- Guy 2 died.
- Guy 3 died.
- Guy 4 died.
- Guy 5 died. ...
Thus, we're all going to die eventually.
looks like an appealing argument, but it is not a valid argument -- at least, there's no guarantee that the truth of the conclusion follows from the truth of the premises. Rather than being a deductive argument, it's an inductive argument.
Inductive inference can be plenty useful, but as any broker -- or any kid who plays a lot of Duck Duck Goose -- will tell you, there is a real danger in inferring future outcomes from past performance. More about this when we take up "falsifiability".
Vladimir Nabokov parodied unsound syllogisms as follows (from memory, may not be 100% accurate):
(1) All men are mortal.
(2) Socrates was a man.
(3) Therefore Socrates was mortal.
(4) But I am not Socrates.
(5) Therefore, I am immortal.
A nice refresher, Janet. I've been away from the academic side of this for too long.
Why do we assume (or argue) that the universe will obey logic? Isn't that assumption itself an inductive one?
When you set up the assumption that the universe is subjected to our logic, it does become an inductive one. However, if we logically look at the universe, logic becomes a tool to guide our reasoning. Then, reasoning counter checks our logic to make sure it's up to par. (An argument that is valid and whose premises are true is a sound argument.) Then, the spagetti monster comes and makes it all better.
Logic doesn't have to have anything to do with "truth" any more than mathematics does. All it needs is a self-consistent set of rules. You can judge an argument based on those rules and determine whether it is logical without regard to any underlying truth.
If one of the purposes of defining terms like this is to move toward a greater public awareness of what scientists generally mean when they call something scientific, it might be useful to incorporate Toulmin's notion of "warrants" in the discussion (a warrant is an assumption that underlies one's view of a piece of information as counting or not counting as support for a claim).
Scientific argumentation rests on a shared set of included and excluded warrants -- for example, we don't count an assertion made in a religious text, be it the Bible or the Popol Vuh, as automatically eligible for use to support claims of fact (except for a limited set of claims that might be made about the text itself, e.g. "The use of a word for obsidian, which is not found in the area of the text's creators, can be taken as potential evidence of trade relationships with areas in which it is found").
Warrants are implicit in the typical presentation of arguments as assertions and conclusions, but making them explicit can aid in pointing out where points of difference lie. Many of the students I work with come in with what I'd call a notion of "scienciness" rather than of science -- it's based on what the argument *sounds* like, including whether it does or does not use a lot of grecoroman jargon terms. I've found explicit discussions of differences in warrants to be particularly useful in clarifying the distinction.
"Logic doesn't have to have anything to do with "truth" any more than mathematics does."
Well... All so-called "standard" logics are so designated precisely because their rules of transformation are truth preserving. A logical system where allowed patterns of inference don't preserve truth is ipso facto "aberrant."
And just what does it mean to call a set of rules "self-consistent?"
"Truth" in "truth preserving" is not the kind of truth I mean. I mean what is normally accepted in everyday use. The kind of truth you refer to can mean something else as long as you abide by your accepted rules. "Self consistent" means exactly what it appears to mean: no rule contradicts any other rule.
>And just what does it mean to call a set of rules "self-consistent?"
Why not ask GÃ¶del?
"Why not ask GÃ¶del?"
Just give me a chance to finish my wayback machine. In the meantime, I wonder how many people think his incompleteness theorems apply to logic as well as to mathematics.