No.

But then there is such a contradiction even in the title to your question that it would be hard to respond more positively. The coexistence of these paradigms, combined with philosophical disinterest and a number of competing ventures is more or less how I would describe how things are. I would say that empirical psychology is a mess scientifically, culturally, philosophically speaking. That said, those philosophical positions I consider more helpful have not attracted broad interest or support - so what kind of "should" are you considering?

What does it mean to proceed purely inductively? Or for that matter, purely deductively?

Thank you for your answers!

Bruce E Oddson, could you name those philosophcal positions you consider more helpful? With "should" I intend to ask, whether one procedure is superior to the other.

By proceeding inductively or deductively I refer to the distinction between Theory Application and Effect Application from a Paper by Calder, Phillips, and Tybout (Designing Research for Application, 1981, JCR). I understand Theory Application as proceeding deductively - thus trying to falsify a theory - and Effect Application as proceeding inductively - thus trying to expand an observed effect by replicating it in other settings.

So, what is being induced in the Effect Application?

Does an "inductive procedure" require a particular thing being induced? According to Calder et al. "The notion that observed effects will be repeated in the real world, given the use of correspondence procedures, is an inductive argument. The observation that something has happened is said to imply that it (or something similar) will happen again." With correspondence procedures they refer to an experimental setting that is close to the real world.

I understand Effect Application as proving generalizability and Theory Application as disproving generalizability. Proving works with induction and disproving with deduction.

Excuse my naïve comment as a reply to Lukas' comment: how to insert these static definitions in the never-ending loop linking deduction and induction? Having observed too often the perplexity of students facing unexpected results and disturbed by the temptation of changing the hypothesis...

Lukas, what constitutes an "inductive argument"? How would one determine if such an inductive argument is logically valid?

Inductive validity is a helpful but somewhat misleading term, given its differences from deductive validity.  In a deduction, validity requires that IF premises are true, the conclusion must follow.  In an induction, no such thing can be the case (for the usual skeptical reasons).  So, an inductively "valid" argument is just any argument in which the premises, if true, make the conclusion "likely" or "reasonable."  The skeptic will object (quite rightly) that "reasonable" is not an objective measure.  Thus, the inductivist will give some definition of "strong" induction or "good" induction, often by applying some set of probabilistic rules (Bayes, for example).  The skeptic will, quite rightly, say these rules don't really amount to anything at all leaving the inductivist with at least two choices: (1) accept some inductive framework for pragmatic reason or (2) abandon the project of predictive science entirely and be a falsificiationist.

In any case, as Françoise and Bruce helpfully point out, it's not clear at all how a psychologist could operate in a purely inductive or deductive framework. I would be surprised if a modern psychologist was willing to claim that there were any pure (i.e. non-empirical) truths about the human mind.  The latter case, pure induction, might be possible, but only perhaps for functionalists.  Still, avoiding deduction entirely in some scientific pursuit is going to be pretty difficult/impractical given the accepted place of falsification in scientific methodology.

Gorge, what is a falsificationist?

Lawrence, as I mean it here, a falsificationist is someone whose inquiry proceeds using a logic of deductive (usually) falsification.  The structure of falsification would work something like this:

Let's say I have a theory, T1, which entails some particular phenomena that I have not yet observed, P1.  I do a series of experiments and discover that P1 does not occur. Thus, I have good reason to reject T1.  Logically:

T1 -> P1

~P1

Therefore, ~T1

In this way of inquiring, experiments actually aim at falsifying.  Assuming that my theory is sufficiently precise and my experiments are sufficiently controlled, it seems possible to exclude certain theories.  There are some problems, of course.  Should I reject T1 or some other theory in my network of scientific beliefs?  How many contrary results are required for a theory to be discarded?  Etc.

In any case, the major concession that a falsificationist must give is that experiments cannot prove theories to be true, only not-yet-falsified.  This means that any non-falsified scientific theory is provisional and only capable of prediction in some (possibly) probabilistic way.  I say possibly because it is not possible to know the set of all possible theories, so we would need to have a long argument about the merits of Bayes theorem (or some other probability system) to explain what we mean by the statement "non-falsified theories are probably true."

When scientists say they want to "reject the null-hypothesis" they are engaging in a kind of falsification.

My question was not about what is falsification. That is easy. Any observation that a theory denies the possibility of if the theory is true, is a falsification. My question is about what is meant by falsificatIST. An experimental test is to see if the theory is false, of course. That is the sole purpose of a test. So, why do you refer to a falsificationist and not just someone who is testing a theory. Do natural scientists really see themselves as falsificaitonists?

Oh, I see.  I mean embracing the logic of falsification to the exclusion of anything else.  Some experimenters believe that they are not JUST falsifying.  That is, they are also verifying or doing something else.  In other words, some experimenters think that by way of induction and probability they can get at theories with predictive power or they can, in some measure, get to provably true generalizations or principles.  

I answered in that manner because because the original questioner was posing the problem as a case of mutual exclusion between induction and deduction in science.  It seems to me that one of the traditional methods of abandoning the shakiness of induction is something like embracing falsificationism as the key method in scientific inquiry.

Edited to add: I think some natural scientists do see theory testing as JUST a method for falsifying.  Whether this is the prevailing view or not, I cannot say.  But I must admit that I do meet many scientists who talk as if science does give us "provably true" theories.  I think, if pressed, most would admit that their theories are just tentative, but I do think that many scientists believe in scientific progress of a kind that falsificationism cannot really account for.

Well, apart from the simple fact of logic, one cannot verify or confirm an explanation since every explanation must included a premess in the form of a strictly universal statement (i.e, "all x are y"), induction in this manner is pointless. Again, why falsificationism instead of just critical testing a la Socrates?

I'm not sure I fully understand the meaning of your question, but I would provisionally say that what Socrates is up to in the dialogues is not scientific in the modern sense of the term.  Certainly he's employing logic and he often employs argumentative strategies that involve the rejection of a hypothesis, but Socrates more often rejects hypotheses for non-empirical reasons.  (Further, Socrates is really explicit about not being a natural philosophy.)

Maybe you are trying to appeal to some kind of view in which all forms of critical inquiry are continuous?  That's a promising view to take, though I think practitioners of the hard sciences think that they are doing something quite different from philosophy.

To be clear, I'm not advocating falsificationism.  I am only saying, in relation to the initial question, that some who are worried about saving some measure of special, truth-finding status for the sciences advocate something like falsificationism as the "real" cornerstone of scientific inquiry.  Certainly Karl Popper thought that non-falsifiable theories were interesting (and even useful), but they were not science.  If you want a deductive science, falsification is the way to go.  If you're not at all worried about that your theory-statements are deductively true, then certainly some broader view of scientific-inquiry-as-critical-testing is attractive.  

(My own view would be that what makes science different from other forms of inquiry has little to do with induction and deduction and more to do with practices, values, and institutions, but the original question is not about that.)

Sorry, I should have said the Socrates of Plato's early dialogues. I am not sure what you are saying about Popper. If you are talking about his view of metaphysics, that is partially true (all though it took his student Joseph Agassi to point that out to him). But this is also why he is incorrectly identified as a falsificationist by Imre Lakatos.

As to your own view, I probably agree. I would put it as matters of attitude (critical, of course) and that might include all that you identify.