1. in a way that relates to or uses the mind and reasoning rather than emotions or physical action
2. in a way that shows or requires intelligence, learning, or careful thought

Examples

• She found the novel intellectually challenging and rewarding.
• He approached the problem intellectually rather than relying on intuition.
• The debate was intellectually stimulating for all participants.
• Intellectually, I understand why she made that decision, even if I disagree emotionally.
• The course is designed to engage students intellectually and creatively.
• They were intellectually matched and enjoyed deep conversations together.