logicandlanguage.net

Each overstates the responsibilities of logic, which is the study of what follows from what - implication relations between interpreted sentences; one can know the implication relations between sentences without knowing how to update one's beliefs.

Suppose, for example, that S believes the content of the sentences A and B, and comes to realise that they logically imply C. Does it follow that she should believe the content of C? No. Here are two counterexamples:

1. Suppose C is a contradiction. Then she should not accept it. What should she do instead? Perhaps give up belief in one of the premises, but which one? Logic does not answer the question - as we know from prolonged study of paradoxes - because logic only speaks of implication relations, not about belief revision.

2. Suppose she already believes not-C. Then she might make her beliefs consistent by giving up one of the premises, or by giving up not-C. Or she might suspend belief in all of the propositions and resolve to investigate the matter further at a later date.

Hence these questions about inference and belief revision - about what she should believe given i) what she already believes and ii) facts about implication - go beyond what logic will decide. That's not to say that logic is never relevant to reasoning or belief revision, but it isn't the science of reasoning and belief revision. It's the science of implication relations.

Convinced? Gil has a short and very clear discussion of this, and the pernicious consequences of ignoring it, in the second section of his new paper (co-authored with Sanjeev Kulkarni) for the Rutger's Epistemology conference.

Hi Gillian-

Conversely, your post brings to mind the following passage from Paul Grice:

"I have two hands (here is one hand and here is another). If I had three more hands, I would have five. If I were to have double that number I would have ten, and if four of them were removed six would remain. So I would have four more hands than I have now." Is one happy to describe this performance as reasoning? There is, however, little doubt that I have produced a connonically acceptable chain of statements. (Aspects of Reason, p. 15).

This discussion is quite eye-opening and interesting to me, as someone working in computational (but not philosophical!) logic. Is the following another possible way she could respond in case (2) which you listed, where she already believes not-C:

-- she might continue to believe A, B, and not-C, but suspend belief in the claim, which (presumably) seems to her to be a logical truth, that A, B, and not-C are inconsistent. She might await some further insight that would show her that A, B, and not-C really are not inconsistent.

I say "presumably," because the claim she believes in the situation here is that A and B imply C. It is conceivable but perhaps psychologically impossible or very unlikely that while that seems to her to be a logical truth, its obvious consequence ("A, B, and not-C are inconsistent") does not.

Gillian,

Firstly, congratulations for your posting. It is one among the best posts I've ever read through the internet. Secondly, the link you have included is one the funniest, a true form of clever humour.

But, just commenting on Gilbert Harman's question patterns, it seems to me that your colleague had mastered a technique of conversation. Actually, that is something difficult to do: he found three general templates that he could use everywhere and probably direct conversation accordingly to his own academic interests. Of course, you and others have been able to detect and analyse his technique, whereby he would not always succeed in controlling the debate with you. But I think most of us humans have certain illusions about intellectual performance and, because of that, seek some sort of magical formulae for argumentation like the ones Harman found.

Surely no one, with the possible exception of formal logicians (and then, only at their desks during office hours) believes either of the two claims you give as ubiquitous and false. Surely everyone (again, with the possible exception of formal logicians at work) uses some form of argumentation to reason, and to update their beliefs.

Logic is an *abstraction* from real human reasoning, not a representation of it. It astonishes me that anyone ever thinks otherwise.

Hi Peter,

Welcome to the blog; it's nice to have so many computer scientists around!

There are a couple of things that I wanted to say in response to your comment.

First, to the point about whether anyone believes the claims I am criticising, I think they really do. I think many people think of the claim that logic is the study of the principles of reasoning, for example, as a harmless plattidue. Here's what you get as the first five hits if you search for "logic is the study of" on google:

1. Logic is the study of methods of reasoning and argumentation, both proper and improper.

2. Logic is the study of reasoning---the nature of good (correct) reasoning and of bad (incorrect) reasoning.

3. Link 3 is Wikipedia, which does a much more nuanced job, claiming that "logic is the study of of arguments. Its primary task is to set up systems and criteria for distinguishing good from bad arguments" and adding latter: "As a byproduct, logic provides prescriptions for reasoning, that is, how people – as well as other intelligent beings, machines, and systems – ought to reason. Such prescriptions are not essential to logic itself, however; rather, they are an application. How people actually reason is usually studied in other fields, including cognitive psychology." That doesn't seem to be conflating inference/implication like the previous two posts.

4. Link 4 is by Peter Suber, (author of the very sensible Clinical Attitude, which I linked to previously). Here we start out well: "Logic is the study of argument" but goes on to say: " an argument is [...] an example of reasoning."

5. is devoted to mathematical logic in particular, (and so doesn't really contain a sentence that begins "logic is the study of.")

But 6. is a discussion of a number of definitions of logic, and quotes a textbook author (Daniel Bonevac): "Logic is the study of correct reasoning."

In addition, here's the first sentence of Warren Goldfarb's new textbook, Deductive Logic: "Logic is the study of the principles of reasoning." Goldfarb is a brilliant man, and Deductive Logic is an excellent introductory textbook, but many, many people just aren't in the habit of distinguishing logic (the study of implication) from inference (the study of belief-revision.)

That said, it seemed to me that you were making a different point when you said that logic is not a representation of human reasoning. One natural way to understand you here is as saying that logic does not describe the way people actually think. That seems right; if only because we make all kinds of mistakes. And - if this is what you mean - I think you're right that lots of sensible people recognise this. But the inference/implication point I was making is a different point; logic doesn't even tell us how we ought to think. (This is what the examples are designed to show.)

Just to be absolutely clear: this is not intended as a criticism of logic. I think it more akin to pointing out that statistical analysis won't tell us how to make public policy decisions. That's not to say, of course, that its results won't prove to be important in making those decisions.

Hi Gillian --

Thanks for your reply. I didn't say that people don't claim (or don't write websites or textbooks claiming) that logic represents real human reasoning. I said that people don't *believe* this, which is subtly different from them claiming it. I've not met anyone, not even a logician, not even famous ones, who does not use logically-invalid (so-called fallacious) forms of reasoning in their everday life - eg, accepting arguments from authority when receiving medical advice; reasoning inductively about everyday phemonena; etc.

Perhaps my second claim was also unclear.
When I said that logic is not a representation of human reasoning, I meant the following: Human reasoning is too complex, too subtle and too sophisticated to be captured by any formal system which uses only deductive inference. This is most definitely (sorry for shouting on your site, Gillian) not to claim that people make mistakes when reasoning. People may or may not mistakes in their reasoning. Rather, it is because deductive logic is inadequate to the task of representing the full subtlety of everyday human reasoning.

Both this post and my previous post are intended as criticisms of formal deductive logic, not of human thinking, which I think is a wonder to behold.

We have seen the same phenomenon now in several disciplines -- in formal logic, in modeling of uncertainty, and in economic decision theory: An abstraction is made from a real human phenomenon, and then the abstraction is taken as being the reality, instead of just an abstraction from it.

• Deductive logic is taken to be correct reasoning.
  
• Probability theory is taken to be the only (and correct) way to represent uncertainty.
  
• Economic decision theory is taken to be the only (and correct) way to make decisions.
  

In each case, the map is mistaken for the territory. Even worse, the map is used as a guide to how the territory should be landscaped, so that (for example), human decision-makers are criticized because they do not conform to some ideal notion of expected utility maximizers. In all three cases, the problem lies with the academic abstractors (logicians, statisticians, economists, respectively), not the humans under study.

I suggest you read a nice book by Stephen Toulmin, called Cosmopolis: The Hidden Agenda of Modernity, which explores the origins and pernicious effects of this late western cultural tendency to abstract from messy reality.

-- Peter