"Is it today?"

"Is what today?"

"Today."

"Is today today?"

"Yeah."

"...Yes. Yes it is."

20 minutes later

"Is it still today?"

"Yes. The answer to 'is today today?' will always be yes."

"Is it today, or Tuesday?"

"It's today. Though if you ask me that question on Tuesday, it will be both today and Tuesday."

Later that evening

"Is it still today?"

"It'll be today until you go to bed. Then when you wake up, it will be tomorrow."

Next morning

"Is it tomorrow?"

--
* Except for the two Tuesdays, where the conversation varied slightly.