When expressing an idea that is not based on any consideration, one can use a variety of phrases to replace "without considering". These include "irrespective of", "regardless of", "disregarding", "overlooking," "neglecting", "ignoring", "omitting", "neglecting", "unmindful of", "indifferent to", "impartial to", "blind to", and "unaware of". Each of these phrases conveys the notion that the speaker or writer is disregarding certain factors and not taking them into account when making a statement. It is important to use these phrases appropriately to ensure that the message is clear and effective.