I ran into my favorite former student today, and the meeting reminded me of a topic I've been thinking about for some time. I have posted numerous pro-Carnap views on this blog, but while one might thus have correctly guessed that I take Carnap's side against Heidegger, I don't think I've explained satisfactorily where I think Heidegger is wrong. Indeed, as with most philosophers, I've come to respect Heidegger more as I've studied this issue; I am increasingly of the opinion that Heidegger really did understand Carnap's position fairly well, and that he understood the problems with his own position (though obviously he didn't consider those problems fatal, and that's where we disagree).
The basic disagreement between Carnap and Heidegger is that Carnap rejects all authority, and Heidegger considers the rejection of all authority to amount to the unacceptable rejection of all value. It certainly is the rejection of objective value as that is usually understood; an objective value would be something that would have authority over us. So Heidegger is allied with many other defenders of objective value.
Still, Heidegger correctly recognizes that he has opposition; the scientific world-view excludes all authority. Science merely discusses "the truth about what-is," it doesn't make decisions for us. In a puzzling but revealing clause, Heidegger says that the scientific method of objectivising what-is "provides itself with the possibility of future advance;" it is in this sense that Heidegger sees the scientific world-view as manifesting the will to will, the will to power (quotes from the postscript to "What is Metaphysics?")
Science "provides itself with the possibility of future advance" because it treats everything as questionable. This is unacceptable to Heidegger; a value which could be questioned, which could be rejected, is no real value at all. If there isn't some authority, something beyond the questions and theories of the scientific, then life is meaningless. And because of Heidegger's belief in the authority of authority, he thinks he has a powerful criticism of science; in denying that there is any such thing as authority, science is admitting that science itself has no authority (a point he probably got from Nietzsche, though Nietzsche of course didn't draw the conclusions from this that Heidegger did). If science has no authority, then how can it tell us not to look for authority elsewhere?
Still, the whole idea of Heideggerian authority is a puzzling one, and Heidegger's method illustrates well why. After all, he investigates and theorizes and raises questions about metaphysics, about his authenticity and about nothing. How can it make sense to raise questions about what can't be questioned? How can he theorize about what is beyond our capacity to theorize, what he himself describes as beyond logic? Heidegger himself says that it's very hard and one is constantly in danger of slipping into nonsense; Carnap's view, that in fact it's impossible and Heidegger is not merely in danger of slipping into nonsense but spends most of his time there, is only a slight step beyond what Heidegger himself confesses.
For my part, I think that whatever we can think about, we can think about. Whatever we can talk about, we can talk about. Whatever we can question, we can question. Note that this is very different from saying that what we can think about now is all we can ever think about. People are forever finding new things to think about, to talk about, to question; science "provides itself with the possibility of future advance," as Heidegger says, or "overcomes itself" as Nietzsche might say, but no worthwhile scientist says otherwise. There are certainly those who misinterpret science as giving final answers and try to use it as an authority, but even Heidegger recognizes that those people don't understand science; Heidegger shows by the nature of his criticism of science that he recognizes what the scientific world-view really involves. But there is only one final answer, and if Nietzsche was right that most philosophers have really been seeking that final answer (death, of course), I also think he was right that it's time to give up on this immature desire for final answers.
Still, people find the absence of authority very hard to cope with, or even to make sense of. Positivists like Carnap are often interpreted as having made sense data and/or logic into authorities, and then condemned because by their own principles they shouldn't have such authorities. The criticism is right that they shouldn't, but I think wrong that they did. Observation is important to the positivists because if a claim is based on observation, people can look for themselves; they don't need to rely on authority. But looking isn't another kind of authority; it makes perfect sense to question what we see, and we do so on many occasions. Observation is the start of questioning, not the end. As for logic, they of course struggled with how to understand that, but the mature Carnap, with his principle of tolerance, was obviously not treating that as beyond question either. "In logic there are no morals!"