by Corry Shores
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[Bracketed commentary and boldface (unless otherwise indicated) are my own.]
Summary of
Graham Priest
Logic: A Very Short Introduction
Ch.1
Validity: What Follows from What?
Brief Summary:
“Logic is the study of what counts as a good reason for what, and why” (Priest, 1). An inference draws a conclusion from premisses (or from a premiss). It is valid if the conclusion follows from those premisses. It is deductively valid if it necessarily follows, that is, if no other conclusion could possibly follow, and it can be determined as such when “there is no situation in which all the premisses are true, but the conclusion is not.” An inductively valid inference is based on reasoning given in the premisses, yet other conclusions could also follow instead.
Summary
After noting how in common usage we say “being illogical” as a form of criticism meaning “to be confused, muddled, irrational,” Priest then asks, “But what is logic?” He then quotes from the Tweedledum and Tweedledee scene in Lewis Carroll’s Through the Looking Glass. Alice becomes “lost for words,” and the twins begin to attack her argumentatively [the following quotes from Carroll]:
‘I know what you are thinking about’, said Tweedledum: ‘but it isn’t so, nohow.’
‘Contrariwise,’ continued Tweedledee, ‘if it was so, it might be; and if it were so, it would be: but as it isn’t, it ain’t. That’s logic.’
(1)
We see Tweedledee reasoning, which is what logic is all about (1).
Priest writes:
We all reason. We try to figure out what is so, reasoning on the basis of what we already know. We try to persuade others that something is so by giving them reasons. Logic is the study of what counts as a good reason for what, and why.
(1)
We need to grasp this claim in a certain way, and to work our way to this understanding, we now examine two inferences [quoting Priest]:
1. Rome is the capital of Italy, and this plane lands in Rome; so the plane lands in Italy.
2. Moscow is the capital of the USA; so you can’t go to Moscow without going to the USA.
(3)
As we see, each case above has a final clause ending with ‘so’. All the claims coming before the so are called premisses. They give reasons. The claims coming after ‘so’ are called conclusions, and they “are what the reasons are supposed to be reasons for” (3). Priest notes, “The first piece of reasoning is fine; but the second is pretty hopeless,” since “the premiss, that Moscow is the capital of the USA, is simply false” (3). However, had instead this premiss been true, if for example somehow the US capital indeed was moved to Moscow, then the conclusion would also be true.
It would have followed from the premisses; and that is what logic is concerned with. It is not concerned with whether the premisses of an inference are true or false. That’s somebody else’s business (in this case, the geographer’s). It is interested simply in whether the conclusion follows from the premisses.
(3)
An inference is called valid when “the conclusion really does follow from the premisses;” “so the central aim of logic is to understand validity” (3).
Although this task of determining validity might seem like a dull and pointless mental exercise, it is actually bound up with “a number of important (and sometimes profound) philosophical questions” (3). Although we will work through some of them throughout the book, we for now will look more at validity.
Often two sorts of validity are distinguished. We first consider the following three inferences [quoting Priest]:
1. If the burglar had broken through the kitchen window, there | would be footprints outside; but there are no footprints; so the burglar didn’t break in through the kitchen window.
2. Jones has nicotine-stained fingers; so Jones is a smoker.
3. Jones buys two packets of cigarettes a day; so someone left footprints outside the kitchen window.
(3-4)
W begin with the first one. Since there are no footprints outside, the burglar did not break in through the kitchen window.
The first inference is a very straightforward one. If the premisses are true, so must the conclusion be. Or, to put it another way, the premisses couldn’t be true without the conclusion also being true. Logicians call an inference of this kind deductively valid.
(4)
Now turn to the second inference: Jones is a smoker since his fingers are stained with nicotine. Although the premisses give us good reason to draw the conclusion, they are not completely conclusively in making the inference, since there are other reasons Jones’ fingers might be nicotine-stained. For example, he could have made the stains without smoking just to trick people into believing he is a smoker. When the inference is not deductively valid, but still gives good reason for drawing a conclusion, it is said to be inductively valid. Now finally consider the third inference, that someone left footprints outside the kitchen window, since Jones buys two packs of cigarettes a day. It “by contrast, appears pretty hopeless by any standard. The premiss seems to provide no kind of reason for the conclusion at all. It is invalid – both deductively and inductively.” (4) If someone were really to give this argument, other people would assume that really there is a missing premiss, for example, “that someone passes Jones his cigarettes through the kitchen window” (4).
We often reason inductively; “for example, in trying to solve problems such as why the car has broken down, why a person is ill, or who committed a crime” (4). Nonetheless, in the history of logic, much more attention has been given to deductive logic, “maybe because logicians have tended to be philosophers or mathematicians” (4). Although we look more at inductive logic later, we for now concern ourselves with deductive validity. In fact, it is probably better to start with deductive inference, since it is more “cut-and-dried” (4d). So until we later shift attention to induction, for now “valid” means simply “deductively valid” (5a).
As we noted, a valid inference is one “where the premisses can’t be true without the conclusion also being true” (5). We now ask, what does the “can’t” here mean? In our normal usages of the term, it can mean ‘lacking ability,’ like “Mary can play the piano, but Jon can’t” (5). Or it can mean something like ‘not permitted by some code of rules,’ as in, “You can’t go in here: you need a permit” (5).
But in our usage, “It is natural to understand the ‘can’t’ relevant to the present case in this way: to say that the premisses can’t be true without the conclusion being true is to say that in all situations in which all the premisses are true, so is the conclusion” (5). But then, we might ask, what do we mean here by “situation?” That is, “What sorts of things go into their makeup, and how do these things relate to each other?” Also we might wonder, “what is it to be true?” (5).
We will return to these questions later, but for now let us consider the fact that this definition of deductive validity still has some problems. And, “In philosophy, all interesting claims are contentious” (5). The first problem is that we cannot really know what holds in all situations, since among them are situations on distant planets in the cosmos, situations in fictional works, and situations “imagined by visionaries” (5). And since there would also be an infinite number of such situations, it would be impossible to take them all into account (5-6). “So if this account of validity is correct, and given that we can recognize inferences as valid or invalid (at least in many cases) we must have some insight into this, from some special source” (6).
This source need not be “some sort of mystic intuition” (6). Priest suggests the possibility, following Chomsky, that there are a finite set of rules out of which the infinity of possible sentences can be formed, and also that these rules are hard-wired into our brain, so we know which of the infinitely many are correct or not just by reading them. [Perhaps Priest is further suggesting that also we can judge whether or not any supposed situation is true also on the basis of a finite set of rules that are hard-wired into us.]
Main Ideas of the Chapter● A valid inference is one where the conclusion follows from the premiss(es).
● A deductively valid inference is one for which there is no situation in which all the premisses are true, but the conclusion is not.
(quoted from Priest, 6, boldface his)
From:
Priest, Graham. Logic: A Very Short Introduction. Oxford: Oxford University, 2000.
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