There are four basic forms of logic: deductive, inductive, abductive and metaphoric inference. In deduction inference leads fro true propositions to true propositions. In induction we can infer from cases to generalizations, which get conformation from premisses. In abduction one can infer causes from effect, thus going backward from "conclusions to premisses". Abduction is also called diagnosis. In metaphoric inference  we transfer knowledge from  one area to another area, say we study economy in terms of evolution theory. 

The abstraction of reasoning is mathematical logic. There we do not have different cause and different reasonings. There is just one reasoning. However we should make a distinction of "theoretical reasoning", "approximate reasoning" "algebraic reasoning" and "computational reasoning"and "applied reasoning". These kinds of reasoning correspond to "general theoretic" framework, analysis and topological framework, "algebraic framework" "applied framework" and "computational framework. 

Taking mathematics as the main activity and regarding "logic" as "mathematical logic" a part of mathematics and not the other way around, we may consider the Bourbaki's mother structures (partially ordered sets, topological spaces, and algebraic structures) we add up to three types of reasoning.

one I know about is "case-based" reasoning. how about inductive and deductive reasoning? does it counts in too?

Dear Wira, 

Yeas, "deductive inference" essentially means "mathematics" and "inductive inference means science". And of course these are methods of reasoning.

Dear all,

In my opinion, "reasoning" is more a tool than a cause. If all of our actions should come out of formal reasoning, this would imply that all possible actions should somehow be available to us as premises, and reasoning should point out which should be the action to take.

I think that action is a combination of spontaneous biological activity combined with mental pondering and evaluation, yes, reasoning. Do you ever reason like "well, it must be the case that I am hungry"? I guess you don't, you happen to be hungry as the result of your biochemical processes, and this fact is highlighted to your consciousness. From there you may apply reason, access your memory for known solutions, consider if you should by some food or kick your friend and steal his sandwich, but the trigger, the fact that you are hungry, comes from somewhere beyond reason. In this sense I think that reason is a tool.

Then, what about artistic expression? Dancing, singing, laughing. I believe they do not follow from reasoning. I think that "reasons" is a broader thing than "reasoning", that there are reasons beyond our reasoning.

Cheers,

Fernando

Costas, and to add to Bruce (or maybe go to far for his liking) Gödel, I think, shows that human beings, if I can be so vein, do more than computation. I mean, he liberated himself to show Gödel's theorem, something an artificial intelligence cannot do. He was able to step outside the water, like a fish, and see that one can't prove an axiom in a system. A computer can't do this to my knowledge. I should put a semicolon after this statement because the big debate goes on.

Is everything computable? Well what was Gödel doing that was different from computation? Also, look at Searle's Chinese Room. He shows we have an intentionality side that shows we have a capacity for "meaning". Finally, with Wittgenstein we can see that language is a social phenomenon that we share in a cultural context, something that computers don't do. He uses the Beetle in the Box example.to express this.

All this aside, I don't want to say that we just compute. However, Costas, you may damn well be right. However, if we look at a computer, for example, playing chess, is it really "playing" chess or is it dark inside? I mean, does it enjoy it so much that it doesn't want the activity to end like how we don't want our own journey of life to end. There seems to me to be more to reasoning than just computation.

If we take a court case, for example, where a man shot another man, there may be more than just one reason why he did it. One reason why he did it might be out of computational reasoning. But was there something driving that computational reasoning, like what Bruce was mentioning ( I think, I hope I'm not misinterpreting you, I do that sometimes! Could emotion be more than just a cause, but also a reason???) with the addition of emotions. Emotions and computational reasoning go hand in hand, they can't be separated, and I think in a court of law one will notice that it was emotion (or passions) that was part of the reason why he did it. For example, if he killed the man then he would attain that man's estate. So there is a cold calculating side, but also a desire in his chest that impelled it. I'd think both are reasons, however, one "caused" the other, like a billiard ball (reason 1) hitting billiard ball 2 (reason 2). Do you guys think this is incorrect, that passions, desires, emotions cant be reasons?

Fernando, I don't even know where to begin with artistic genius. That is an excellent point that I didn't even think about, nor wrap my head around. What type of reasoning would one use to compose a symphony or something comparable to Shakespeare's genius?

That's a though question! In AI, where it's studied as a basic tool, there're whole conferences dedicated to it. Basically, there is formal logic and there's common sense reasoning. The first one --deductive, abductive, and inductive logic-- has been studied for more than 2000 years with an acceleration during the last 150 years or so. The other one, common sense reasoning, encompass formal logic but is less formalized given the difficulty involved in understanding it.  Defeasible reasoning, informal logic, etc, are areas you can look up. Wikipedia can help.

There are four basic forms of logic: deductive, inductive, abductive and metaphoric inference. In deduction inference leads fro true propositions to true propositions. In induction we can infer from cases to generalizations, which get conformation from premisses. In abduction one can infer causes from effect, thus going backward from "conclusions to premisses". Abduction is also called diagnosis. In metaphoric inference  we transfer knowledge from  one area to another area, say we study economy in terms of evolution theory. 

Dear Ariti:

I like this.  Simple and direct.  

Mike

Dear Antti,

Based on logic this taxonomy is OK. But since you based your opinion on logic, why you did not include e.g. Many-valued logic, fuzzy logic, etc. Even the Theory of reasoning, it is not included in your taxonomy.   

Dear Costas:

If you were to write a book called Applied Logic made Simple, ---by applied I mean for university students to help them think across disciplines to get better grades and pass standardized tests such as the graduate record exam, etc.--- what basic logical rules would you recommend?  The larger picture is to reverse the Reverse Flynn affect where the kids are getting dumber and dumber as measured by IQ tests because, I think, of Sesame Street, YouTube, and the decline of the book,  How can the kinds understand fuzzy logic when they don't know the difference between induction and deduction?

Mike

I agree with you Mike!

You might like to consider Aristotle's three appeals in the Rhetoric as a guide. In the context of ancient Greek society, he lists the rhetorical appeals pathos, ethos and logos. Sometimes we think of "logos" as reasoning, though the Greeks associated logos with using language to think (as in Plato's Phaedrus). So it could be a "reason" for an appeal to one's audience. Then there was the emotional appeal or "reason" and the appeal to authority as a "reason." This suggests that there is reasoning based on an emotional need, a need based on a common authoritative text or source (sometimes an authoritative set of rules, right/wrong),  and a need based on thinking alone. In some ways this dovetails with Habermas's notion of discourse or communicative action. Habermas considers the need to deceive as a reason in his concept of  "strategic communication" (sincere communication attempts to expose its reasoning or rational thinking to the listener).

Playfully, one might then propose the idea of sincere and insincere reasons. That would begin a great discussion of our recent demand for "transparency." Under each label (sincere and insincere) one could then begin to list the usual human reasons for a discursive action. Godel wanted to liberate himself from developed computational devices: was he limited by them? (He was the only barber in town who shaved himself, the only mathematician free of the fallibility of computational devices.)  His "Godel numbers" assigned arbitrary values to mathematical operations (as I understand it) in order to determine if these could result in contradictions or paradoxes, which would disqualify math as a logical positivist approach to language. However, Wittgenstein made a similar move, perhaps with different reasoning, to arrive at ordinary language philosophy that could accept logically meaningless statements (metaphysical statements) as meaningful.

One might say that "reasons" and "reasoning" diverge dangerously in meaning.

Dear Stephen,

Sorry about this late answer. I always consider that computational approaches are very limited in approximate human intelligence. After a looked in the book: Ray_Kurzweil_The_Age_of_Spiritual_Machines, I think that giving to concept "computable" various extended senses, we might approximate human intelligence from above and from down!

In our discussion we do not mention "dialectical thinking". According to Lawvere, this can be expressed using  adjoint functors. This give am unexpected future to such a reasoning.

Examining our brain, I can see three types of reasoning: Analytic and element-wise (left hemisphere), Structural-holistic (right hemisphere) and a third one which is a dialectical synthetic way of the two. For example, "algebraic topology" is a kind of synthetic reasoning, since algebra is located at the left hemisphere, whereas topology is on the riight hemispher. Thus   "algebraic topology" is a synthetic one!

No one has yet mentioned induction and deduction: what's up with that?

Dear scott,

Yes, induction and deduction have been discussed. Just Check the thread. Furthermore we may also consider: analogical and intuitive thinking.

I think that there is just one type of reasoning: looking for patterns that can be useful in the given situation, and applying them. Dependent of the result, the pattern search continues in a more narrow or more wide domain, untill a solution is found.  Inductive and deductive reasoning reduce to that. Intuitive reasoning does it also. Rhetoric reasoning, where you are ready to tell doesn't matter what, in order to argue in your purpose, is finally the same thing. I am quite confident that there is only one type of reasoning - it companions us along our whole life, cannot avoid mistakes, but sometimes, not too often, is able to accomplish great achievements. Persons might be more analogical, more deductive, more intuitive - and this is about where and how and in which order they are looking for the patterns to apply. But reasoning is of only one type.

@Mihai Prunescu

I tend to disagree. You're using the word "pattern" instead of the word "reasoning", but everything remains the same.  I'm sure you'd agree that there are different patterns, wouldn't you? Thus, coming back to the use of the word reasoning, there exist a number of different forms of reasoning, or more correctly put, there exist a number of different patterns of reasoning. Research on these different patterns of reasoning allows us to understand what we do when we use deductive, inductive, abductive, or defeasible; that is, analytical or ampliative reasoning, and so on.