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Five Laws Of Logic In Critical Thinking

0:14Skip to 0 minutes and 14 secondsIn the last video, we saw how we reason analogically. We proceed from the observation that two or more things are similar in some respects, to the conclusion that they are probably similar in some other respect, as well. Here's how this applies in law. In August, 1928, Mrs. May Donaghue and a friend went into the Wellmeadow Cafe in Paisley, Scotland. The friend bought her ice cream and ginger beer to make a soda. The ginger beer came in an opaque glass bottle. The shopkeeper poured some of the ginger beer into a glass over the ice cream. Mrs. Donahue drank some, and her friend poured the rest of the ginger beer in the glass for her.

1:03Skip to 1 minute and 3 secondsBut, as she did so, a partially decomposed snail floated out of the bottle. "In sequence of the nauseating sight of the snail in such circumstances, and of the noxious condition of the said snail-tainted ginger beer consumed by her, Mrs. Donaghue sustained shock, and indeed, illness." Mrs. Donaghue sued the ginger beer manufacturer, Stevenson, climbing 500 pound. Now most lawyers would probably have told her that she was wasting her time and money. You could then sue in negligence only if you had a contract under which someone owed you a duty of care. And Mrs. Donaghue had no contract-- not with the shopkeeper-- her friend had bought the ginger beer-- or with the manufacturer, whose contract was with the shopkeeper. But remarkably, Mrs.

1:55Skip to 1 minute and 55 secondsDonaghue won. And in one of the most important cases in western legal history, the tort of negligence was born. Now the judgement in Donaghue and Stevenson, itself involves complex analogical reasoning, as the judge, Lord Atkin, finds authority for his decision in various proceeding cases and extra legal material, including the Bible. But we see the mode of reasoning more clearly in decisions that follow the snail in the ginger beer case. Donaghue itself might have been read as establishing a fairly narrow principle.

2:34Skip to 2 minutes and 34 secondsOn one reading, just this-- "A manufacturer of products, which he sells in such a form as to show that he intends them to reach the ultimate consumer in the form in which they left him with no reasonable possibility of intermediate examination, and with the knowledge that the absence of reasonable care in the preparation or putting up of the products will result in an injury to the consumer's life or property, owes a duty to the consumer to take that reasonable care." Analogical reasoning, however, allowed the courts to quickly move beyond that narrow principle. In the early 1930s, around the same time that Mrs. Donahue was enjoying-- or not enjoying-- her soda in Paisley, a Dr.

3:20Skip to 3 minutes and 20 secondsGrant was buying a pair of woollen underpants in Adelaide, Australia. The underpants came wrapped in paper. Unfortunately, for Doctor Grant, the manufacturer hadn't washed a caustic solution out of the underpants. And he, having apparently worn them for an entire week without washing them, developed a very serious, almost fatal, dermatitis. The Court in Grant and the Australian Knitting Mills, lists the features they take to be central in the then recent and revolutionary Donaghue's case. A manufacturer had to sell products in a form in which he intended them to reach the ultimate consumer. There had to be no reasonable opportunity for the consumer to examine the product before consumption.

4:15Skip to 4 minutes and 15 secondsThe manufacturer had to know that if he didn't take reasonable care, his product posed a risk to the consumer. And if features one, two, and three were present, so was a new feature-- a legal duty of care to the consumer. And, say the Australian Court, Grant's case resembles Donaghue's. One, Australian Knitting Mills sold the underpants in the form they intended them to be worn. Two, though they were wrapped in paper, and not sealed in a bottle, the consumer couldn't have seen the caustic solution by looking at the underpants. Three, the manufacturer knew, or ought to have known that wearing caustic underpants might be very, very bad for you.

5:04Skip to 5 minutes and 4 secondsAnd so since Grant resembled Donahue in those respects, it also had the further feature-- a duty of care and so liability. Putting it in our schema-- one, Grant's case is similar to Donaghue's case-- it shares features one to three. Two, Donaghue's case has the further feature-- a duty of care and liability. Three, therefore, Grant's case also has that further feature. The judges in the caustic underpants case, in other words, reasoned by analogy. Looking for similarities, interpreting or setting aside some-- the fact the underpants weren't in a sealed container and weren't food didn't matter. They were like the colour of the car.

5:54Skip to 5 minutes and 54 secondsBefore saying, this case is similar to that one, and therefore the extra property-- a duty of care-- applies in Grant because it applied in the ginger beer case. Reasoning by analogy is central to legal reasoning. It allows lawyers and judges to pay proper regard to previous decisions, while also allowing them to extend those decisions, to work out which similarities really matter. And it can do that in a logical and critical thinking outside the law as well.

3. Contradictions (A and not-A)

The concept of a contradiction is very important in logic. In this lecture we’ll look at the standard logical definition of a contradiction.

Here’s the standard definition. A contradiction is a conjunction of the form “A and not-A”, where not-A is the contradictory of A.

So, a contradiction is a compound claim, where you’re simultaneously asserting that a proposition is both true and false.

Given the logic of the conjunction and the contradictory that we’ve looked at in this course, we can see that the defining feature of a contradiction is that for all possible combinations of truth values, the conjunction comes out false, since a conjunction is only true when both of the conjuncts are true, but by definition, if the conjuncts are contradictories, they can never be true at the same time:


So, propositional logic requires that all contradictions be interpreted as false. It’s logically impossible for a claim to be both true and false in the same sense at the same time.ALWAYS FALSE

This is known as the “principle of non-contradiction”, and some people have argued that this is the most fundamental principle of logical reasoning, in that no argument could be rationally persuasive to anyone if they were consciously willing to embrace contradictory beliefs.

There’s a minor subtlety in the definition of a contradiction that I want to mention.

Here’s a pair of claims:

John is at the movies.” and “John is not at the movies.

This is clearly a contradiction, since these are contradictories of one another. John can’t be both at the movies and not at the movies at the same time.

Now, what about this pair?

John is at the movies.” and “John is at the store.

Recall, now, that these are contraries of one another, not contradictories. They can’t both be true at the same time, but they can both be false at the same time.

Our question is: Does this form a contradiction?

This is actually an interesting case from a formal point of view. Let’s assume that being at the store implies that you’re not at the movies (so we’re excluding the odd possibility where a movie theater might actually be in a store).

Then, it seems appropriate to say that, since they both can’t be true at the same time, it would be contradictory to assert that John is both at the movies and at the store. And that’s the way most logicians would interpret this. They’d say that the law of non-contradiction applies to this conjunction even though, strictly speaking, these aren’t logical contradictories of one another. The key property that it has, is that it’s a claim that is false for all possible truth values.

Here’s another way to look at it.

This is the truth table for the conjunction:


But in our case, the top line of the truth table doesn’t apply, since our two claims are contraries — they can’t both be true at the same time. So this case never applies.A conjunction is true only when both conjuncts are true. For all other truth values it’s false.


This kind of example raises a question that logicians might debate — whether, on the one hand, a contradiction should be defined as a conjunction of contradictory claims, or, on the other hand, whether it should be defined as any claim that is false in all logically possible worlds.The remaining three lines give you all the possible truth values for contraries, and now we see that the conjunction comes out false for all of them.

Examples like these suggest to some people that it is this latter definition which is more fundamental, that’s it more fundamental to say that a contradiction is a claim that is logically false, false in all possible worlds.

This issue isn’t something you’ll have to worry about, though. If you’re a philosopher or a logician this may be interesting, but for solving logic problems and analyzing arguments, it doesn’t make any difference.