Is there an empirical difference between thinking and knowing, perhaps one based in neuroscience?
For both terms to think and to know philosophical definitions exists:
To think means in according to a classical definition
- to form concepts
- to state propositions. i.e. sentences which are either true or false, and
- to draw conclusions from propositions.
To know a proposition means
- to believe in the truth of the proposition
- to be able to present arguments for this believe and as a basic condition
- that the proposition is true.
All three conditions are necessary: True belief without argumentation as well as false belief with argumentation are no knowledge.
Note. Apparently these are different mental activities. Do you ask whether one can detect different brain activities by imaging techniques relating to "I think employing modus ponens" versus "I know that snow is white"? I doubt that neuroscience has already reached that degree of selectivity. In addition, it seems difficult to prepare two groups of probands who focus themselves on the corresponding mental activity.
Added: I learned by the Gettier counter-example, that in certain cases the conjunction of the above named three conditions is not sufficient to assure the intended meaning of to know, see http://philosophyfaculty.ucsd.edu/faculty/rarneson/Courses/gettierphilreading.pdf The Gettier counter-example comprises a correct argumentation, the conclusion is also true, but the argumentation starts with a false premiss. The counter-example is designed cleverly so that it fullfills all three conditions. Nevertheless, one would not name the resulting statement knowledge.