Bring a large pot of salted water to a boil. Add the potatoes and cook until tender, about 20 minutes. Drain and let cool slightly. Slice the potatoes 1/2 inch thick.
Meanwhile, in a large bowl, whisk the olive oil with the vinegar and season with salt and pepper. Gently fold in the potatoes and celery. Let stand at room temperature until cool, about 30 minutes. Just before serving, fold in the radishes and scallions and season with salt and pepper.