As you know, I think this forum has a dual purpose: discussion, and also, teaching. I think that participants should learn things, and that includes why they are wrong.
Yes, but could they use another thread for 101 logic questions to the professor? This thread is about something else. I am getting tired repeating this.
On topic. I've written about four pages on my essay on deductive and inductive arguments. I'll post it here, the current draft.The formatting is slightly off due to incompatibilities between forum software and Open Office.
---------- Post added 01-16-2010 at 04:14 PM ----------
Deductive and inductive arguments
In this essay I will discuss theories that attempt to explain/give an analysis of what a deductive argument is and what an inductive argument is.
Relevant to this discussion are some other thesis which may or may not be true.
[INDENT] DIS. An argument is either deductive or inductive and not both.
[/INDENT] (DIS) is commonly assumed to be true in logic textbooks.
A first simple formulation of the central theses is:
[INDENT] An argument is deductive iff it is intended by the arguer to be deductive.
An argument is inductive iff it is intended by the arguer to be inductive.
Lack of knowledge of the distinction
What about arguers that do not know about the deductive and inductive distinction? Think of arguers in the 5 century BC and people not training in logic.
The arguer need not know about the distinction. It is enough if the arguer intended the conclusion to follow necessarily from the premises or some similar vague idea which people often have, even when not training in logic.1
Similarly for inductive arguments. Refined explanations are then:
An argument is deductive iff it is intended by the arguer to be deductive (in a broad sense).
An argument is inductive iff it is intended by the arguer to be inductive (in a broad sense).
Validity is not a fact about psychology
An objection is that it seems that any correct theory of deductive and inductive arguments do not depend on facts about human psychology such as what the arguer intends the argument to be. The justification for this is an analogy like the following:
Similarly to validity and soundness, whether an argument is deductive or inductive is not dependent on facts about human psychology.
Whether this analogy is apt I don't know. Perhaps the deductive and inductive distinction is different from the other terms.
There may be some confusion between tokens and types, so let's distinguish between them clearly:
An argument type
is a number of propositions where one, the conclusion, follows from the other, the premises, in some sense.
An argument token
is what is literally in this essay. Argument tokens is a number of sentences that express an argument type. Tokens have a location and a time of writing.2
All argument types are sound/unsound and valid/invalid. Are (all/some?) argument tokens sound/unsound and valid/invalid? It seems to me that a proper evaluation of the issue of deductive and inductive arguments depend on this.3
Two different argument tokens may express the same argument type. Let's imagine that there are three identical tokens and that a single person has written them. In the first two cases the person intends the arguments tokens to be deductive and in the third case he intends it to be inductive.
The question is now: Do all the three argument tokens express the same argument type? It seems to me that the answer according to intention theory is "no". The first two express the same argument type, but the last expresses a different argument type. These tokens, recall, are identical and so all the premises expressed by them are identical. The only difference between the two first and the third is the arguer's intention.
Thus, someone accepting this and accepting intention theory and (DIS) has to (for consistency) agree that there are two different argument types too, one deductive and one inductive. So the intention theory is ontologically more complex. This seems unnecessary and Occam's Razor advises us not to multiply entities beyond necessity. Are there really two different argument types? What is this property "being deductive" and "being inductive"? They seem very mysterious.
One could also accept both intention theory and that there is only one argument type but then that type would be both inductive and deductive and so the distinction between them would be false, that is, (DIS) would be false.
One could also accept both intention theory and that there is only one type but believe that the deductive and inductive distinction is only about argument tokens and not types. To clarify:[INDENT] DIS. An argument (token or type) is either deductive or inductive and not both.
DIS-token. An argument token is either deductive or inductive and not both.
DIS-type. An argument type is either deductive or inductive and not both.4
[/INDENT]So that person would reject (DIS) and (DIS-type) but accept (DIS-token). In that case the deductive and inductive distinction between argument tokens is dependent on facts of human psychology, but facts about argument types such as validity and soundness are not dependent on facts about human psychology.
A first simple formulation of the central theses is:
[INDENT] An argument is deductive iff it is valid.
An argument is inductive iff it is invalid.
All deductive arguments are valid
It implies that all deductive arguments are valid. But that implies that one cannot fail at making a deductive valid argument (though one could fail at making a deductive argument), for there are no invalid deductive arguments. Consider an analogy with addition (mathematics):[INDENT] "Not distinguishing between deductive arguments, and valid deductive arguments, is just like not distinguishing between addition, and correct addition." (Kennethamy, source
"A deductive argument is one such that if it is correct, then it is impossible for the premises to be true, and the conclusion false. (Logically impossible). But surely, you see there is a difference between an addition, and a correct addition. Why then is it so difficult to see the difference between a deductive argument, and a correct (valid) deductive argument[?] Just as not all additions are correct, not all deductive arguments are valid.
Just as we use addition to get true answers to sums, so we use deduction to get true conclusions from true premises. And, just as we sometimes fail to get true answers to sums, so we sometime fail to get true conclusions from true premises. [Both] are due to mistakes on the part of the person who does the adding, in the first case; and due to mistakes on the part of the deducer, in the second case. The two are quite parallel." (Kennethamy, source
[/INDENT]The question is if this analogy is apt. I think it has at least a lot of initial plausibility.
First, lacking a 'formal machinery' to evaluate analogies in, the conclusions reached about such matters are lacking a great deal of certainty.
Second, I note that the analogy goes on the level of the act
of adding and the act
of deducing and not at the level of additive arguments and deductive arguments. The analogy uses the word "correct". What is that to be understood as? I suppose it refers to validity in both cases. But let's assume that it refers to just validity in the case of deductive arguments. Then, what is the analogous part of validity in deductive arguments, in additive arguments if not validity itself? It seems to me that the analogous part of validity in deductive arguments, in additive arguments is validity. The analogy is circular. For this reason I think that it is not convincing.
These vague ideas of "following necessarily" and "not following necessarily but giving reason to believe" may be products of evolution.
There are also verbal argument tokens, but they do not strictly speaking consist of sentences but consist of sound waves that express sentences, I suppose.
This case is very familiar to the case of whether sentences are true/false by proxy. See my previous discussions of pluralistic theories of truth bearers, here
(DIS) is thus logically equivalent with the conjunction of (DIS-token) and (DIS-type).