I'm not really clear on what the implications are for inductive vs deductive research methodology and analysis. Any examples or input would be great!
As far as my knowledge goes, I don't think these two types of reasoning in cogsci are any different to other forms of inductive or deductive reasoning: one is a bottom-up approach and the other a top-down process.
Deductive reasoning starts at the general and moves towards the specific, going from theory to hypothesis, observation to a confirmation. This is good science: a priori we form specific predictions and test them in very restrictive lab settings. An example could be examining modular and embodied approaches to cognition, forming a specific hypothesis about a specific circumstance, and then testing it.
Inductive reasoning on the other hand works visa-versa, going from an observation to a pattern, a tentative hypothesis to a theory. This is not always a good way to work, especially for quantitative methods, as it relies upon post hoc interpretations of observed effects. Work of this form could be interested in understanding stress in the workplace, may interview people about it and then finally form a conclusion based upon these conversations.
The latter is more useful to qualitative research, the former is practically necessary for quantitative work.