September 29, 2015 09:20 PM

Now that he’s been a dad for six weeks, Joseph Gordon-Levitt‘s fatherly instincts are in full swing.

“Being in the public eye is a great thing. It allows me to do what I love to do, which is act in movies, but it’s a choice that I made. I decided to have a career in show business, and so people know my name and know my face. And that has its upsides and honestly, some downsides,” the actor said Tuesday during an appearance on Live with Kelly and Michael.

“My son, he’s just a baby, you know? He hasn’t made the choice to be in the public eye, and that’s a choice that I would like him to be able to make when he’s older, when he can think about these kinds of things and make that decision for himself. And so, for now, I’m just a protective dad, and I want to protect his privacy.”

Pawel Kaminski-Disney/ABC Home Entertainment and TV Distribution

The Walk star, 34, welcomed his first child with his wife, Fellow Robots co-founder and CEO Tasha McCauley, in mid-August. Though the couple won’t be releasing the baby’s name, “the family is all happy and healthy,” a source previously told PEOPLE.

Growing up in the spotlight, the Snowden actor admits he was fortunate enough to have a supportive mother who fostered his interests but didn’t push him unnecessarily.

“And throughout working as a kid, I always just really loved doing it,” Gordon-Levitt, who starred in Angels in the Outfield as a child, said. “But of course there are days when you don’t feel like doing it. And any time I would be like, ‘Ahh, I don’t want to go on this audition today,’ [my mom] would always say, ‘You don’t have to. You can stop this any time you want to.’ “

He adds, “She was a great stage mother. She encouraged me and supported me because she knew it was something I loved to do, but she never pressured me into doing it and always gave me that decision.”

— Christina Dugan

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