Likewise, speaking deductively we may permissibly say. In propositional logic, the set of all true propositions is deductively closed. Thus induction cannot be justified deductively. Follows deductively from the other premises. Thus, what follows deductively does not follow historically. The objects of thought are geometric properties, which the student has learned to connect deductively. Consider the set "W" of all deductively closed sets of formulas, ordered by inclusion. Such spreadsheets can be used to reason deductively about their cell values. Legitimate ends are felt deductively in hearts or guts or souls.