Armchair theorizing (armchair theory or armchair philosophizing) is an unofficial term for the approach which economists are perceived to mostly use for coming up with a new economic theory.
"Economists can discover basic facts by observation of their own and other people's decision making. They even have the advantage of being able to observe the basic elements of their theoretical generalizations (human individuals and their strivings) directly, while the natural scientists must postulate or infer their basic but not directly observable elements from whatever phenomena they can observe directly. Much as geometers deduce many theorems from a few axioms, so economists deduce a powerful body of theory from a relatively few empirical generalizations, ones so crushingly obvious that their failure to hold true is almost inconceivable in the world as we know it. [...] Armchair theorizing need not be the mere sterile juggling of arbitrary assumptions; it can have a sound empirical basis." [1]
Armchair philosophy is a term used to highlight the difference between passively guessing the nature of the universe and actively investigating the nature of the universe using the scientific method; which consists of collecting data and physical measurements, formulating theories which explain observations, and then testing these theories with further measurements using various specially constructed apparatus. A philosopher seated in an armchair passively contemplating the nature of the universe is never going to produce the results of a scientist who actively investigates the unknown.
It should be noted that scientific inquiry has long been considered part of philosophy, as the scientific method was first formulated by philosophers such as Francis Bacon and successfully applied by foremost philosophers such as René Descartes, Blaise Pascal or Gottfried Leibniz. Only by the late 18th century did scientific enquiry and philosophy become two distinct disciplines, philosophy now focusing mainly on ethics, epistemology and metaphysics while science is left with the empirical realm.