Back    All discussions

2011-03-23
Arguments and conditionals: difference in meaning?
Hi!

coming from a bioinformatics background (aiming to represent the argumentative structure of research publications) I seek advice to clarify the concepts "argument" and "conditional".

Can these concepts, along with premise/antecedent and conclusion/consequent, interchangeably be used or are there actual differences in definition, meaning and/or use of these terms?

I'd be grateful for any advice on this and direction to relevant sources.

Christian

2011-03-23
Arguments and conditionals: difference in meaning?
An argument is a series of statements, one of which is the conclusion, the rest of
which are premises, such that the premises allege to provide ground or reason to believe
the conclusion is true. Arguments have no truth value, they are neither true nor false (though
the statements that comprise them have a truth value). They are good or bad, persuasive
or unpersuasive, etc. Above all, they are not statements or propositions, neither atomic
nor compound. They are sets of propositions. Every argument contains an inference,
an act of drawing a conclusion from the premisses. It is marked formally by
words like 'therefore,' 'hence, 'so,' 'consequently.'  An argument asserts the premisses
and it asserts the conclusion (typically).

A conditional is a compound proposition, it is either true or false. It contains an antecedent
and a consequent. There is no inference. It  asserts neither antecedent nor consequent.
So 'If I am president, then I am commander and chief,' asserts neither that I am president
nor that I am commander and chief. It is NOT the argument 'I am president; so I am commander
and chief.' The semantics of conditionals is controversial, but, for the material (non-subjunctive)
conditional (like the above example), it is often said that it asserts that it is not the
case that the antecedent is true and the consequent is false.  So the above conditional
is equivalent to the disjunction 'Either I am not president or I am commander and chief.'

2011-03-28
Arguments and conditionals: difference in meaning?
Reply to Jim Stone
Hi Jim and Christian. I am not sure if I agree with Jim or don't. An argument is not a conditional, because the former is neither true nor false, meanwhile the conditional really is either true or false. But, I ask Why the acceptability conditions (I mean, conditions under which we accept the argument as good or a conditional as true) are the same? We say that an argument is good, if it is not possible to accept the premises and to reject the conclusion. And, at the same time, we can say that a conditional is true, if it is not possible at the same time that the antecedent is true and the consecuent is false.  

It seems to me that it is possible (and I tend to think it is the right way) to analize the acceptability conditions of an argument in terms of truth conditions of a conditional. Actually, I imagine, we can put an argument in a conditional form... where the premises were the antecedent (a complex one) and the conclusion would be the consecuent. I have heard some people rejecting this, but I still don't understand those arguments. 

So far, I consider that the arguments and condicionals are linked in a logic way: if something is an argument, will be a conditional.... but not the other way around... 


Anderson



 

2011-03-28
Arguments and conditionals: difference in meaning?
Hello Christian!

Every text in Elementary logic I'm aware of (Copi, Quine, etc.) defines 'argument' pretty much as Jim Stone does, with one important caveat.  As Stone defines the term in the first sentence of his reply almost any set of propositions could be an argument. Thus the set of propositions:

    I'm blue.
    The moon is blue as well.
    Green cheese isn't blue.
    Neither are you.

Might be an argument but for the fact that no relation between the members of this set is either stated or claimed.  That is an important caveat and cuts ice in a number of different and interesting ways.
I define 'argument' as a set of propositions one of which is claimed to follow from the remainder in the set. This one proposition is the conclusion of the argument; the remainder are the premises of the argument. 
Arguments do not exist in an abstract impersonal vacuum.  They are creatures of personal intellectual activity with several possible goals in view.  One might in propounding an argument want to demonstrate that certain everyday assumptions have a surprising consequence ... or one might want to extend human knowledge by the addition of one's conclusion.... etc.  For this reason I'd rather say N argues for p if and only if N asserts certain propositions P1, P2, ..., Pn and claims that these Pi taken together logically require the conclusion C.

The rest of Jim Stone's stuff about arguments is good.  Arguments are not statements, and so it is inappropriate to say of any argument that it is true (or false), although in arguing for p, N does make a number of assertions and these, of course, must be either true or false. 

That said, it's also the case that for every argument there is a corresponding conditional whose antecedent are the premises of the argument and whose consequent is the conclusion of the argument.  Various names have been suggested for this conditional.  It might be called the argument's "principle of inference" or something of the kind.  N's argument for p would have as its principle of inference:
If (P1&P2,&... & Pn) then C. 
The important concept here is this: if the argument in question is a deductive argument the claim made about the relationship of premises to conclusion is of the strongest sort possible: that it is logically impossible for the premises to be true and the conclusion false.  (NB: thus far I've said nothing at all about anyone's beliefs.  I suppose N at least believes the premises of his argument.  But in propounding his argument for p, he might be committing himself to a set of propositions which turn out upon close examination to be inconsistent.  IOW, 'valid' is an objective concept in the sense that whether or not an argument is valid has no implications that anyone has any sort of propositional attitude toward that argument.)    Alternatively stated, the inference principle of a valid deductive argument is a logically necessary truth. 

Arguments may be evaluated (as Jim Stone suggests) in a number of ways beyond the first consideration of validity/invalidity.  The argument A:
A1  The moon is blue
A2  The moon is not blue.
AC So, you're green.
is formally valid, but useless since it's premises are inconsistent.  Minimally, then, in order for an argument to be useful, not only must it be valid, but its premises must be consistent.  One can ask that its premises be all true as well.  Valid arguments with true premises are said to be sound.  If one wishes to prove something to someone, that is the least one needs to do.  But propounding a sound argument is not sufficient for proof, otherwise one could easily "prove" every true proposition.  For let P and Q be any two true propositions; then argument B:
B1  Not P or Q
B2  P
BC  So, Q
is deductively sound.  But this is not what we ordinarily mean (or should mean!) by 'proof'. 

For the remainder of what I'd wish to say, I'd rather refer you to George I. Mavrodes, Belief in God, for his development of the notion of N proves that p to M.

2011-03-28
Arguments and conditionals: difference in meaning?
A conditional is a type of proposition. An argument is an ordered series of propositions from premises to conclusion. Thus a conditional is not by itself an argument but rather it can be the premise or the conclusion of an argument. Consider the following argument:

1. Socrates is a man.
2. If something is a man then it is mortal.
Therefore,
3. Socrates is mortal.

The above is an argument from two premises (1, 2) to a conclusion (3). In the above, one of the premises (2) is a conditional.

Argument: 1, 2 therefore 3
Conditional: If... then...

It is very important not to confuse the "therefore" of the argument with the "if...then..." of conditionals. This confusion has famously lead to many paradoxes. E.g. Lewis Carroll's paradox ( http://www.ditext.com/carroll/tortoise.html ).

2011-03-28
Arguments and conditionals: difference in meaning?
There is a kind of correlation.  Suppose you have a deductive argument with premises P, Q, R, and conclusion S.  There will be a corresponding condition whose antecedent is the conjunction of the argument's premises and whose consequent is the conclusion [(P&Q & R) -> S].
If the argument is valid, the conditional will be a tautology.

2011-03-28
Arguments and conditionals: difference in meaning?
The thought just occurred to me.  Given Goedel's result for higher order quantification, does it not follow that there will be some arguments framed in such languages which are valid, but cannot be shown to be valid?!

2011-03-29
Arguments and conditionals: difference in meaning?
Just to continue.

Lots of arguments do not allege to be valid. The premisses are supposed to provide some
support for the conclusion, but not conclusive support. Deductive arguments are those
that allege to be valid. Proofs are a proper subset of deductive arguments.

What is required for a proof? It must be valid, it must be sound (valid with true premisses),
but this isn't enough. 'The sky is blue; so the sky is blue' is sound but no proof, because
it is circular. It couldn't be used to demonstrate the conclusion for someone who doubted
it.

So we might say that a proof is a sound, non-circular argument--but this is insufficient too.

I might give a sound non-circular argument that we don't know is sound, because
we don't know the premiss is true. That won't prove the conclusion, since
for all we know the premiss is false.

So, supposing the last presidential election was going to be close.
"Obama will win. He is a Dem; So a Dem will win.'

'McCain will win. He is a Rep; So a Rep will win.'

As one or the other will win, and the second premisses are both true, and both are valid,
one of these is sound but we don't know which, so neither is a proof.

So I suggest that a proof is a sound, non-circular argument where we are in a position
to know it is sound.

2011-03-29
Arguments and conditionals: difference in meaning?
Reply to Jim Stone
Hi Jim...

Check out the slim volume by Mavrodes I mentioned, Belief in God.  He develops the concept of proof in a similar way...

N proves that p to M iff
N formulates an argument A for p (with p as its conclusion),
A is valid
the premises of A are true
A is cogent for M - i.e., M knows that A is sound,
and A is convincing for M i.e., M's knowledge of the soundness of A does not rest on or depend upon M's prior independent knowledge that p is true.

On the basis of this notion of proof, it turns out that those who hold that "you can't prove that God exists" must either commit themselves as atheists (thus eliminating every argument with 'God exists' as its conclusion from the set of sound arguments), or must maintain that 'God exists' is somehow epistemically prior to every other proposition (thus, e.g., forbidding even Aquinas to get started).  Since it's difficult to see how one would have to know that God exists first (logically) before one could know that snow is white, the "you can't prove it" seems a non-starter.

I am aware there are those who believe that God's existence is ontologically prior to any and every truth whatever... but that's a very different bramble into which I have not dared to enter, having learned my Uncle Remus stories almost by heart!

Mack Harrell
West Orange, NJ

2011-03-29
Arguments and conditionals: difference in meaning?
Reply to Jim Stone
Jim writes:
a proof is a sound, non-circular argument where we are in a position to know it is sound.
"in a position to know it is sound" doesn't get it without further emendations.

Consider A:
A1. Either nothing exists or God exists.
A2. Something exists.
AC. So, God exists.
(From the aforementioned discussion by Mavrodes.)

A is an interesting argument for the following reasons:
  1. No one can claim A is unsound without declaring her atheism.
  2. AC, if true, suffices to establish the truth of both premises.
  3. No theist would ever say that A is unsound.
  4. If A is not sound, then no argument for God is sound.
Still, A won't help us to prove that God exists.  The reason?  Probably because anyone who requires a proof would need to know AC is true before she could know that A is sound. 

For this reason, even cogency of an argument is not sufficient for proof.  It's for this reason that Mavrodes added the notion of an argument's being convincing for a person:

N proves that p to M iff N formulates an argument for p for N such that A is convincing for M.
A is convincing for M iff
  1. A is cogent for M
  2. M's knowledge of the soundness of A does not depend upon a logically prior independent knowledge of p.
I think this is the sort of thing you may have been striving toward.

Mack


2011-03-29
Arguments and conditionals: difference in meaning?
Reply to Mack Harrell

Thanks. This makes sense.


2011-04-04
Arguments and conditionals: difference in meaning?
While this relationship between a valid argument and its "corresponding" conditional holds in standard first-order logic (and in a number of other systems) it does not hold generally for arbitrary systems of deductive logic.  That it does hold in fact is an interesting result for a deductive system, and it is called "the deduction theorem" (see Wikipedia and any number of other places, including virtually any text book on advanced logic or formal semantics).

There are a number of perfectly respectable systems in which the deduction theorem fails -- that is, in which an argument from the premise P to the conclusion S is valid but in which the conditional 'P->S' is not a theorem. Indeed, systems which attempt to capture a sense of 'if ... then' not represented by the material conditional (e.g., subjunctive conditionals) will often be ones in which the deduction theorem does not hold.  Some philosophical reflection may then be needed to justify such a system -- or alternatively, to justify a proposed requirement that the deduction theorem hold in order for a system to genuinely capture a sense of 'if ... then'.

One thing that this failure of the universal correspondence between a valid argument and a "corresponding" conditional illustrates is that the question of the difference between an argument and a conditional is (semantically or pragmatically) a bit deeper than it may first appear.

2011-04-04
Arguments and conditionals: difference in meaning?
Reply to Gary Merrill
Thanks, Gary...

Mack

2011-04-05
Arguments and conditionals: difference in meaning?
By "conditional" we can for the moment mean "material conditional," symbolized with the arrow or horseshoe. A material conditional "P --> Q" has an antecedent "P" and a consequent "Q"; the arrow is defined in a truth-table as having the value true except when when the consequent is false and the antecedent is true.

An argument is what is called a derivation, whereby a sentence is shown to be a deductive consequence from other sentences by means of rules of logic. In mathematics, they are called "proofs," though virtually all proofs in mathematics are sketches because (i) the rules are never stated explicitly and (ii) many intermediate steps are skipped, otherwise things would get cumbersome.

There isn't any symbolism for "argument" as such, which tells you something right off the bat. The closest thing are those three dots in triangular form separating premises from conclusion, and the turnstile, but those are really promisory notes to the effect that a derivation is sought or may exist.

Also, arguments are valid or invalid, whereas conditionals are true or false. In all my years of teaching logic I managed to get very few students to internalize this distinction, alas.

So, as you can see, "conditional" and "argument" cannot be used interchangeably. This is all intuitive but can be made precise. Have a look at a book on metatheory, e.g., Hunter.
 
You may well ask whether there is any connection between the two concepts. There is, of sorts. If an argument is valid, then a truth-table will have only Ts under the material conditional linking premises (a long conjunction in some cases) to conclusion. In other words, a valid argument is a tautology. 

2011-04-05
Arguments and conditionals: difference in meaning?
As an illustration of some of the subtleties here, and the need for constant vigilance in terms of precision ...

Arnold Cusmariu writes:
(1) "Also, arguments are valid or invalid, whereas conditionals are true or false"
This is an important distinction, and then,
(2)  "In all my years of teaching logic I managed to get very few students to internalize this distinction, alas."

and then,
(3) "In other words, a valid argument is a tautology."

But (3) is not true.  A valid argument is NOT a tautology.  Rather it is RELATED to a tautology provided that the deduction theorem holds in the system under consideration.  An argument is (as AC has noted) a sequence of sentences (or if your prefer, statements, propositions, etc.) in which certain conditions hold for each member of the sequence and with respect to inference rules and methods of proof.  But a tautology is a sentence (not a sequence).  The relation between a valid argument and a tautology is (again) an important one that in fact does not hold in all deductive systems; but moreover, arguments and tautologies (whatever the relations between them) are quite different kinds of things.  Soundness and completeness results for logical systems are  not trivial, and in fact they expose important fundamental relations among the logical concepts formalized in such a system.

For reasons of this sort it is quite difficult to achieve a full understanding of (1) if -- even for the sake of attempting to aid the intuitions -- you at the same time make assertions such as (3).  Alas, in such circumstances, students must be pardoned for not grasping the details of such distinctions.


2011-04-05
Arguments and conditionals: difference in meaning?
Reply to Gary Merrill
To which we add another wrinkle: many arguments, asserting the premises and the conclusion,
do not maintain that the premises' truth NECESSITATES the conclusion's, but only
that the premiss supports the conclusion, provides ground or reason to believe it's true.
Such arguments aren't valid, but it's inapt to call them invalid, as they aren't
meant to be deductive.

So many arguments given these days for God's existence do not claim to prove it,
but only to make it more plausible and perhaps to have cumulative force.
Same goes for arguments for implausibility--they don't claim to disprove
anything but only to  show that a certain thesis is unlikely.

Of course the whole field of inductive argument, probability theory, is found here.

2011-04-05
Arguments and conditionals: difference in meaning?
Reply to Gary Merrill
Hey Gary,

I was trying to explain intuitively to someone who doesn't have the background. I doubt he knows what the deduction theorem is, i.e., when and only when the turnstile can be replaced with the arrow. I noted that the issues are complex and referred him to Hunter for more on conditionals and proofs.

Cheers,

Arnold

2011-04-05
Arguments and conditionals: difference in meaning?
Reply to Jim Stone
This is a more informal, or perhaps epistemological, notion of "argument".  I suggest, however, that it is not "inapt" to call them invalid.  It is perfectly accurate.  They are not valid (hence they are invalid), given the precise notion of validity in question.  This is not so say that they lack epistemic force.  But let's not confuse (too much) logic with epistemology.

In addition, this is not some relatively recent phenomenon in argumentation or in the theory of argument.  It goes back at least to the Middle Ages (and likely further to Aristotle's distinction between logic and rhetoric).  The "five ways" of Aquinas are, for example, often interpreted more as "plausibility arguments" than attempts at constructing valid deductive arguments.  Aquinas himself, you must recall, was most concerned with enforcing his view that faith was CONSISTENT with reason, rather than that the existence of God FOLLOWED by means of reason alone.

Similar threads, pertaining to the use and evaluation of argument, may be found in the 14-th century nominalists, such as in Buridan's "Sophisms on Meaning and Truth".  All of these, from my perspective, speak to the issue of the role of logic (in particular, in the context as originally introduced here) deductive logic in determining "what it is most reasonable to believe".  Certainly one of Aristotle's primary goals in distinguishing logic from rhetoric was to provide a FORMAL system in which arguments could be judged as "good" or "bad" on clearly objective grounds -- and this, I think, introduced the distinction between the "valid" and the "invalid" in a purely formal sense.





2011-04-05
Arguments and conditionals: difference in meaning?
Reply to Gary Merrill

Well, these are arguments fair and square by the definition I offered earlier:
'A set of statements or propositions, one of which is the conclusion, the rest of which
are premisses, such that the premisses allege to provide ground or reason to believe
the conclusion is true.' This allows arguments that purport only to provide some support
for their conclusion, that is, arguments that do not purport to be deductive.

'Apt' means 'entirely suitable,' by some definitions. Calling such arguments 'invalid' is certainly accurate,
as is calling successful reductios 'unsound,' but not entirely suitable (at least not in debate, discussion, contexts where it can be taken as a criticism) because it can be misleading.

Lately philosophers (especially Richard Swinburne) have moved away from efforts to
prove God's existence and offered arguments that are more like a prosecuter trying
to prove OJ did it. No one argument is meant to prove guilt, but cumulatively the combination
of motive, shoe size, prints, proximity, etc makes guilt highly likely, perhaps even amounts
to knowledge. You can see William Lane Craig using this strategy in debates
on Youtube.

This is quite different from the way these arguments were treated when I began my studies.
Also intelligent atheists (unlike New Atheists) now tend to argue for God's implausibility.

I didn't mean to suggest that this is the first and only such effort in the history of
philosophy. However things have certainly changed since the 50s, and become
a lot more interesting too. Discussions about the problem of evil now draw a great
deal on the Probability Calculus and Bayes's Theorem.

Studying philosophy of religion has lately become one of the ways to engage
philosophy of science.




2011-04-06
Arguments and conditionals: difference in meaning?
Reply to Jim Stone
If we return for a moment to the context of the original question, which was bioinformatics literature (and with which I have a rather high degree of familiarity), the answers to the original questions are:

  1. The terms "argument" and "conditional" cannot be used interchangeably.
  2. Similarly for "premise" and "antecedent" and "conclusion" and "consequent".
  3. There are actual (and important) differences in the meanings and use of these terms.
  4. Relevant sources include most introductory books on logic (either informal or formal), or broader sources such as Wikipedia or the Stanford Encyclopedia of Philosophy.
  5. The very best approach to understanding this cluster of concepts and their significance would be to take one or two courses in logic (preferably with some formal semantics).
Any other routes that we have wandered down in this discussion -- however interesting they may be to philosophers -- are of little (if any) immediate concern to those in biomedical informatics (more's the pity).

This is rather a continuing sore point with me since (as I have remarked in publications) much of the confusion and incoherence in the literature of biomedical informatics stems from a lack of understanding of these fundamental concepts in logic and semantics.  Note that even the phrasing of the original questions exhibits a failure to grasp the use/mention distinction and such distinctions as those between word and object, and term and concept.  Such distinctions are absolutely critical to the work of biomedical (and other) informaticians (or informaticists, if you prefer).  But still the required subject matter is not typically included in their training.

As always, my recommendations in such cases (largely unheeded) are:

  • Take a good course in informal logic.
  • Take a good course in standard first-order logic
  • Take a course in formal semantics, if you can find one
  • Take a course in the philosophy of language
  • Treat these recommendations as at least as important as ones concerning courses in programming, databases, algorithms, and statistics.
If not, then good luck.


2011-04-06
Arguments and conditionals: difference in meaning?
Reply to Gary Merrill
Amen!  And again I say, Amen!

2011-04-06
Arguments and conditionals: difference in meaning?
Well, consider this argument:

We've seen millions of crows and they've all been black.
Here comes a crow:
Therefore
It will be black.

Now we could view it as a bad deductive argument, bad because the premisses
do not necessitate the conclusion. But generally it is viewed as inductive,
which is a sort of argument less ambitious in its intentions. In giving the argument
we allege that the premisses provide ground or reason to believe the
conclusion is true, NOT that their truth necessitates the conclusion's truth.

Another distinguishing feature of such arguments is this:

If an argument is valid, it's premisses (suppose true) support the conclusion as much
as premisses possibly can. Necessitation isn't a matter of degree. No valid argument
can be more valid than another.

Compare:

We've seen billions of crows and they've all been black.
Here comes a crow.
Therefore
It will be back.

This is a stronger argument than the first. Both are good, they warrant
their conclusion, but the second supports its conclusion MORE.

This sort of argument is common in science, but there are other
non-deductive arguments too, e.g. abductive arguments, Bayesian arguments,
arguments from the probability calculus.

And there are all sorts of anomalies.

so

p
q
r
l
a
b
c
may all be true, but given the probability calculus,

p&q&r&l&a&b&c  false.

Maybe bioinformatics just needs deductive arguments, but I should hate to do science
and know nothing about non-deductive arguments, which generally play a crucial role.

2011-04-06
Arguments and conditionals: difference in meaning?
Reply to Jim Stone
Not to dismiss the importance of abductive, bayesian, probabilistic, et al. arguments, but ...

"This sort of argument is common in science, but there are other
non-deductive arguments too, e.g. abductive arguments, Bayesian arguments,
arguments from the probability calculus."

Actually, it is more accurate to say that this sort of argument is common in philosophical writings about science.  In actual science, such arguments are pretty infrequent.  Most arguments IN science are straightforwardly deductive (conforming to the hypothetico-deductive model) or are statistical in nature (with statistically phrased consequences and based on standard well-known statistical techniques and models).  Where probabilistic reasoning takes place, in general this is done in deductive arguments in which the probability is buried in transformations in the premises -- rather than being exhibited as a kind of non-deductive inference.  More recently, Bayesian methods of various sorts have been employed in a variety of disciplines; but even there you would be hard pressed to extract a peculiarly Bayesian "form of argument".  Vide the actual (scientific) literature.

One never -- so far as I am aware -- sees arguments in scientific journals that resemble the classic philosophical one concerning black crows.  For one thing, this is not the sort of conclusion or premises with which contemporary scientists are concerned.

It is true that certain automated inferencing systems use a variety of non-deductive techniques (ranging from artificial neural networks to different sorts of machine learning algorithms and heuristics -- e.g., association rule inducers), but these do not appear "in science" in the sense of being directly employed or described in scientific (empirical) research papers.  I'm just always a bit amused when philosophers make reference to the sort of argumentation that occurs in science.  It is best to read the actual literature.  One thing you will discover is that often the arguments are frighteningly dreadful (especially in the social sciences, but in other more "scientific" areas as well).  A couple of papers written by statisticians and published in the past few years, for example, demonstrated that in peer-reviewed epidemiological publications, the error rate in terms of incorrect or incorrectly applied or incorrectly interpreted methodology was -- as I recall -- on the order of 80%.  That is, roughly 80% of the random sample of such papers reviewed contained fundamental errors of that sort.  I don't have the references at my fingertips any longer, but one of the authors on at least one of those was Stan Young -- who has rather an ongoing campaign concerning the sloppiness of inference and the interpretation of data in epidemiology.  A lesson to be drawn here is that one needs to take a bit of care in choosing one's paradigms.

 


2011-04-11
Arguments and conditionals: difference in meaning?
Reply to Gary Merrill
Minor qualification of Gary's assertion: There are standard first-order systems where the deduction theorem does not hold unconditionally (e.g., the system in Mendelson's Introduction to Mathematical Logic or Ted Sider's Logic for Philosophy). Specifically, in such systems, premises can contain free variables and the rule of Generalization is unrestricted.  Hence, e.g., (x)Fx is provable from the premise Fx but the corresponding conditional Fx -> (x)Fx is not a theorem (rightly so, of course, as it is not valid in standard first-order model theory). Thus, in such systems, the corresponding conditional for a deductively valid argument is provable only in those cases where the conclusion of the argument can be derived in such a way that no application of Generalization results in the quantification of a variable that occurs free in one of the premises. (This is actually not quite true, but close enough to get at the idea; see Mendelson for a precise statement of the conditions.) Systems in which the deduction theorem does hold without qualification instead (in effect) simply disallow such applications of Generalization in the first place.





2011-04-11
Arguments and conditionals: difference in meaning?
Right.  My use of "first-order" was unthinkingly sloppy since what I really had in mind were systems of sentential logic.  In first-order systems of this sort the deduction theorem breaks as a result of "uantificational" features.  And, as Chris points out, in a perfectly understandable manner.

2011-04-18
Arguments and conditionals: difference in meaning?
Reply to Jim Stone
As a biologist, that's not at all how I think. How I think is closer to this:

Here comes a thing.
It looks like a bird.
It's black.
It has a black bill and feet.
It caws.
Therefore, it is a crow.

In other words, it's almost the opposite order of what is presented above. My definition of "crow" includes the observation that all crows observed so far are black, but I do not think "this bird must be black because it is a a crow". I think "this bird must be a crow, in part, because it is black".

Categories, definitions, etc. are all provisional for me. I'm not really interested in whether or not something is "true". I am interested in whether or not a model works. I may say "true", but that's a short-hand for "This model manages to be a better fit to whatever data are available than the other models I've come across."

When I write papers, I need to show that my conclusions follow from my data and that my data is obtained through replicable methods that are not overshadowed by artifacts.  Does that make it "real"? Is it actually the machinations of a maniacal marmoset who has all scientists chained in Plato's cave? From the point of view of a biologist, it doesn't matter, so long as we're all in the same cave. If somebody figures out a way for us to get into a "better" cave, most of us will eventually come along, but most of us are already aware that we still just trade one cave for another. However, we're a lunatic lot, and we just can't get depressed over that prospect. "You might never know the TRUTH!" is met with a shrug and a mental pat on the head. "Yes, that's nice dear. You did a very entertaining bit of word play, but big people have work to do."

As far as we can tell, our current models take into account more of the messy data than older models did. Doesn't necessarily make them any more true, but it doesn't matter. Do diabetes and atherosclerosis exist? Well, one can make all kinds of pretty epistemological arguments, but I doubt that any uncertainty over the metaphysical bases of the life sciences is going to make most professionals in the field of Philosophy refuse to seek medical assistance.

"I believe I heard you knock, David, but you have already shown that, even if the solidity of my door has prevented you from simply walking through it yesterday, it in no way proves that it shall do so today. So I don't need to open it for you to come in." --allegedly said by Swift to Hume.

2011-04-18
Arguments and conditionals: difference in meaning?
Reply to Bryan Maloney
I think you and I are saying about the same thing in different words.
The point is that there are non-deductive good arguments, traditionally called
'inductive.' You've just given one. The concern is truth, premisses that provide a
reason to believe the conclusion is true (both deductive and inductive arguments
share this), but no particular theory of truth is presupposed. If what's true is what
works, suppose, that's no problem.

One can always change an inductive argument to a deductive one by adding
more premisses (the right ones, of course)..

The sun has always risen.
The future will resemble the past as far as the sun is concerned, anyhow.
Therefore the sun will rise tomorrow.

that's deductive, but it's really no stronger than the argument sans second premiss.
It's that argument (or more arguments like it) that grounds the second premiss, in fact.
So we really are dealing with another mode of reasoning.

By the way, I didn't mean that scientific publications contain lots of non-deductive
arguments, but that scientific reasoning, the sort that people use to arrive at
theories, is often non-deductive--however it's finally presented.

We see a shift in the orbit of a planet at a certain point, and we infer that there is
a large body in the vicinity that we cannot yet see. It's an invalid inference
but a pretty good non-deductive argument. We infer that a disease is caused by
a deficiency of vitamin X by noting that large numbers of people with the disease
don't get enough X while those who don't have the disease get X.
Another invalid inference but a pretty good non-deductive argument--though it
may lead us down the wrong path. Again, we
can always make these cosmetically deductive.

2011-04-18
Arguments and conditionals: difference in meaning?
Reply to Jim Stone
A couple of points here.

First, consider please that it is NOT the case that "the concern is truth".  Consider that the concern is rather "what it is reasonable to believe".  Bryan's statements represent -- so far as I can see -- a position that is quite strongly empiricist and anti-realist.  The role of truth in such a position is not nearly as central (and does not appear in the same manner) as in other positions.  But I won't go on any more about that now.  To say, in a circumstance such as this, "Well, you just have a different theory of truth" is not quite correct (and in fact may be seriously misleading).  So far as I can see (and perhaps I am projecting my own views here), the underlying theory of knowledge is not compatible with the "classic" one according to which knowledge is "justified TRUE belief".  Justification and belief (and inference) are central.  Truth, not so much, and certainly not in such a direct manner when it comes to general or abstract assertions.  Recall van Frassen, for example:  Theories in science are to be literally construed, "but its theories need not be true to be good" (in "To Save the Phenomena").  And there are a number of related or positions (e.g., see Arthur Fine's "The Shaky Game ...").

You offer as an illustration

"We see a shift in the orbit of a planet at a certain point, and we infer that there is
a large body in the vicinity that we cannot yet see. It's an invalid inference
but a pretty good non-deductive argument."

But I would say that this not an argument at all.  It is a very brief and stripped down account of a step or two that take place in theory construction.  To say that we "infer" that "there is a large body ..." would be regarded by many as a serious distortion.  Rather, they would hold, we offer a hypothesis that "there is a large body ..."  (again, as part of our construction of a broad theory), and then (using various arguments, to be sure) set about confirming that hypothesis.  It is, in fact, an illustration of the hypothetico-deductive method -- in which deductive reasoning plays a critical role.  But to suggest that there is a rather simple and non-deductive argument and inference here is, I think, to miss the mark.  There is no invalid inference in this case -- or certainly there does not need to be one -- because there is not what most of us would regard as an inference, and most scientists would not think that that is what they are doing.  They really are more sophisticated than that.  Of course, if you broaden you notion of "inference" enough, than almost anything can be seen as an inference.


2011-04-18
Arguments and conditionals: difference in meaning?
Reply to Gary Merrill
Well, I think we are making heavy weather of Baby Logic. Arguments consist of premisses which allege to support conclusions. 'Support' traditionally amounts to 'provide reason to believe
the conclusion is true.' Reasonable belief is reasonable because the belief is thereby more likely to be true. Something is ultimately playing that role, or one can't make sense of support or
reasonable.  That's all I meant. Bryan wrote: 'I'm not really interested in whether or not something is "true". I am interested in whether or not a model works. I may say "true", but that's a short-hand for "This model manages to be a better fit to whatever data are available than the other models I've come across." Fine with me.

No, it's an argument all right. My very point. Non-deductive arguments are part of theory construction. I say to you: 'The planet wobbles at this point in its orbit. I infer that there is a large object affecting it, one we can't yet see. That's my theory.'  There is a premiss, a conclusion and an inference, the act of drawing the conclusion from the premiss, which in fact supports the conclusion--though it hardly proves it. I offer the hypothesis on the basis of the argument, I might say: 'Here is an argument that helps motivate my hypothesis that there is an unseen planet,' and then give the above argument.  This is not an overly expansive notion of 'argument,' it satisfies the definition, and, necessarily, every argument contains an inference. It just isn't a deductive argument (or inference), and to deny it's an argument on this ground, in a discussion about whether there are non-deductive arguments playing this role in science, is question begging. This is how the hypothetico-deductive model sometimes begins.