User talk:Peter Damian/logic

A note for the confused: this article proposes new structure and content for the logic article, and came up during Peer review/Logic/archive1 --- Charles Stewart 00:42, 9 December 2005 (UTC)

Issues
I'm dividing my comments into issues, which I think potentially stand in the way of this replacing part of the article as it stands, and quibbles, which don't.
 * 1. The Division of logic section strikes me as awkward and not based on clear principles, particarly the last point.
 * 2. This is a narrower conception of when logic is formal than what exists in the existing article. The treatment of schema persuades me that Aristotle fits this narrower conception (I spent quite some time with the Prior Analytics and it never stuck in my mind that he used variables until I read this: very good point...), but I still think there is plenty of formal work on logic that does not fit this narrower schema.  I'm away from most of my books until May, and I'm, not sure I can furnish good references without this, but this remains an issue for me. --- Charles Stewart 19:34, 8 December 2005 (UTC)

Quibbles

 * 1. My tortured presentation of the definition of what formal argument constitutes, that you accused of not being a definition, did have one virtue that yours does not: it does not presume that we have already identified what the logical constants are. If we are going to use this notion of logical form to define logic, then we are going to be accused of circularity or arbitrariness.
 * 2. I'd say that a more fundamental difference between ancient logic and modern logic is that the former uses fixed schemes for judgements, where the latter uses recursive schemes. This difference cuts to the heard of the problem of multiple generality, and why modern logic is more powerful than what it replaced. --- Charles Stewart 19:34, 8 December 2005 (UTC)


 * 3. Critical thinking isn't really a subdiscipline of logic, since it includes all sorts of non-subject-neutral content. There is a major component of this topic that is an important part of logic, though.  But I've never been able to find a good name for it: the logic article currently labels it logic and reasoning, which used to be called college logic and dialectical logic, both of which have serious problems (I've also seen this topic called informal logic, which is even worse). I'd really like to see a better name for this. --- Charles Stewart 00:34, 9 December 2005 (UTC)

Comments
> The Division of logic section strikes me as awkward and not based on clear > principles, particarly the last point.

Quite true. I scribbled this down in about 5 minutes. The main thing is that there needs to be a division of the subject. How it is divided is another thing.

Inductive logic is usually defined as reasoning that leads to probable conclusions. I'll look up some more definitions, and see if I can't come up with something clearer. Could you do the same? Why not just edit the draft as you see fit.

Not that there is a reasonable definition of 'inductive' lower down in the existing article anyway!

> This is a narrower conception of when logic is formal than what exists in > the existing article.

Can you give an example of some treatment of logic which would not be formal in the sense I defined it?

I took the notion of 'formal' from Lukasiewicz. (Authority enough?)

He says:

'It is usual to say that logic is formal, insofar as it is concerned merely with the form of thought, that is with our manner of thinking irrespective of the particular objects about which we are thinking [he quotes Copleston with apparent disapproval]'.

Note that logicians called logic 'formal' long before modern logic was around. The terminology (as I mention) comes from the ancient distinction between the 'matter' and the 'form' of the proposition.

Then he says that logic is not the science of the laws of thought 'logic has no more to do with thinking than mathematics has'. Then he makes the observation about Aristotle's use of variables.

He also says (which connects with your point about logical constants) that 'To the form of the syllogism belong, besides the number and the disposition of the variables, the so-called logical constants. Two of them, the conjunction 'and' and 'if', are auxiliary expressions and form part, as we shall see later, of a logical system which is more fundamental than that of Aristotle. The remaining four constants, viz 'belong to all', 'belong to none', 'belong to some' and 'to not-belong to some' are characteristic of Aristotelian logic. The medieval logicians denoted them by A E I and O respectively. The whole Aristotelian theory of the syllogism is built up on these four expressions with the help of the conjunctions 'and' and 'if'. We may say therefore: The logic of Aristotle is a theory of the relations A,E,I and O in the field of universal terms' (Aristotle's Logic, p14.)

>> I'd say that a more fundamental difference between ancient logic and modern logic is that the former uses fixed schemes for judgements, where the latter uses recursive schemes. This difference cuts to the heard of the problem of multiple generality, and why modern logic is more powerful than what it replaced. <<

This is true. Do you want to edit the draft accordingly?
 * Will do. --- Charles Stewart 16:18, 10 December 2005 (UTC)


 * Your edit looks OK, except do you need an explanation, or a link to recursive schema? Any more thoughts about the 'division' section?  I looked up the definition of 'inductive argument' and got a bewildering variety of different definitions (excluding those of mathematical induction, obviously)  Dean

Comments on current article
On the other parts of the current article ' Rival conceptions of logic' is messy, and is misleading about Kant's influence on Frege. Beaney argues that Frege only mentions Kant in order to make his work more accessible. In any case, the statement 'logic should be conceived as the science of judgement' is so sparse as to be unintelligible, particularly in an encyclopedia article. What is 'judgment'?

Note also that the idea of 'intended interpretation' (and hence of 'interpretation') is introduced without any explanation.

'Relation to other sciences' is too cursory to make any sense to the 'intended readership'.

>>> Aristotle's work was regarded in classical times and from medieval times in Europe and the Middle East as the very picture of a fully worked out system. It was not alone: the Stoics proposed a system of propositional logic that was studied by medieval logicians; nor was the perfection of Aristotle's system undisputed; for example the problem of multiple generality was recognised in medieval times. Nonetheless, problems with syllogistic were not seen as being in need of revolutionary solutions. <<<

This is another of those sentences where the internal logic is bizarre. Here are the thoughts

1. Aristotle's logic was regarded as the very picture of a fully worked out system. 2. [But] there was another system of logic. 3. It was studied by medieval logicians. [But did they not notice that Aristotle's logic was not therefore the very picture of a fully worked out system?] 4. The perfection of Aristotle's system was not indisputed. [Does this not contradict the earlier claim that it 'was regarded as the very picture of a fully worked out system'?] 5. The problem of multiple generality was recognised in medieval times [so why did they continue to regard Aristotle's logic as the very picture of a fully worked out system?] 6. 'Nonetheless' - concession - they continued to regard Aristotle's logic as the very picture of a fully worked out system

Dean

Dean's new section
This should combine well with what we have in the current article: I'm very pleased to see you tackle these topics. I should respond to what you said above: the phrasing is mine, as is the bizarre internal logic. To follow, sorry I missed the remark earlier. --- Charles Stewart 22:03, 31 December 2005 (UTC)

Hypothetical syllogism
We have an article on this, which is a fairly shallow explanation of the inference rule of propositional logic. I'm hesitant to expand this beyond what I have done already, since I do not know the history you talk about. --- Charles Stewart 16:37, 1 January 2006 (UTC)

Modern logic
I guess the figures you are thinking of are Hilbert & Tarski. It might be nice also to introduce natural deduction here. I'll put something together, but I'm not sure yet what to say. --- Charles Stewart 16:37, 1 January 2006 (UTC)

More time
I've got a bit more time for this now. I'll probably get stuck into the revisions on Monday. Logic is the Philosophy wikiproject's featured article. --- Charles Stewart(talk) 20:23, 3 February 2006 (UTC)

the big picture
Since the subject of this discussion is the overarching structure of the article, rather than the details, I would like to sketch out what I see as the overarching structure of logic. Whether the article should mimic this or not is another question.

The human mind evolved with the ability to think rationally. Aristotle set down rules for manipulating language in such a way as to mimic rational thought. The value of these rules is not that they are used to construct rational arguments, but that they can be used to check arguments offered as rational. Aristotle’s various works on logic were gathered together in the Organon.

Euclid used logic to prove theorems, most notably in his book Elements. His logic is not rigorous by modern standards, but it was good enough that every proposition he proved is still considered true today, a record that few ancient books can match. Throughout the Western world, Euclid's Elements has been used everywhere to teach logic, until it was abandoned by the American school system in 1960.

Independent of Aristotle, there were similar attempts to formalize logic in China and India. (I would love to read an article comparing and contrasting these systems of logic.)

Aristotelian logic, reintroduced into Europe by Averroes, gave rise to scholasticism. The most famous attempt to apply Aristotelian logic to the Bible is the Summa Theologica of Thomas Aquinas.

Flaws were discovered in Aristotle, and there was a reaction against scholasticism. One movement, advocated by Francis Bacon in The New Atlantis, was to check the excessive abstraction of Aristotelian logic by observation and experiment.

Beginning with Fibonacci (c. 1200), European mathematicians began once again to use logical arguments to prove new theorems. This use of logic produced a body of work much more internally consistent than that of the scholastics. Over the centuries, this mathematical logic became increasingly rigorous, departing from the rational argument of the philosophers. The combination of the deductive method of mathematics and the inductive method of observation and experiment proved spectacularly successful, leading eventually to the industrial revolution, which brought about major changes in the way people lived.

Some philosophers, notably Kant in Critique of Pure Reason, attempted to apply mathematical rigor to philosophical questions, with mixed success. (For example, Kant "proved" that the mind of man could conceive of no geometry other than that of Euclid shortly before Lobachevsky discovered of non-Euclidean geometry.)

Today, thanks to Frege, Russell, and others, rigorous mathematical logic has become a separate field from Aristotelian logic. (I believe that all of Aristotle’s patterns, summarized in diagram form by the scholastics, are elementary consequences of mathematical logic, but I would have to do some research to be sure.)

Mathematical logic now includes propositional logic and predicate logic. Reference: Logic for Mathematicians by Hamilton.

end of rough outline Rick Norwood 21:31, 23 February 2006 (UTC)

Inference revisited
Welcome back folks!

Now, to finish the darft of the Inference section. I've figured out what to say here, but not best how to say it. The key points will be: I think the above points capture the spirit of the change in the nature of logic without, I hope, taking too much space to make. I think I should avoid getting into the following: Will probably get started tomorrow or Friday. --- Charles Stewart (talk) 10:13, 24 April 2007 (UTC)
 * Boole's invention of algebraic logic, capturing inference through algebraic equalities and inequalities, Boole's partially successful attempt to express syllogistic figures algebraically; Schroeder & Peirce's reformulation of Boole's system;
 * Frege's account in the Begriffschrift of formal inference & argument for superiority of formal over natural inference.
 * Road to FOL: metamathematics & inference, Hilber&Ackermann's work. Thesis of completeness of FOL for explicit reasoning.
 * Frege's theory of assertions & thoughts, which is no doubt very important for understanding Frege's later theory of inference, but which is less universal;
 * Peirce's ideas about expressing inferences using diagrammatic notations, which are very nice, but not hudegly influential;
 * Later developments in the theory of inference, eg. constructivism, Wittgenstein's skepticism about formalisation, which are probably best dealt with in other sections or even other articles.

Hello - just realised you were hanging out here after following your contributions trail. Do we need to revisit this draft? The official article has changed since we last worked here. Plus, is the draft so far OK? I was just looking at the opening section on 'validity' and wondering if that is all correct. edward (buckner) 15:23, 24 April 2007 (UTC)


 * PS the plan looks good, by the way. Is there any existing Wiki article on completeness of FOL by the way?  edward (buckner) 15:29, 24 April 2007 (UTC)

The changes to the main logic article have not addressed the complaints made in the peer review. I think that it's nopt obvious how best to incorporate the material here into the logic article, but this material does show how the article can be changed from one that simply talks about logic to one that explains it. My plan is to finish this draft, then talk about what to do with the main logic article in that talk page. One way or another, this material should get used.

Gödel's completeness theorem says most about completenss of FOL, there's a bit in proof theory as well. (none there -- my misrecollection) --- Charles Stewart (talk) 09:40, 25 April 2007 (UTC)