My own position is that prescinding from the existence of socalled dark matter and dark energy -- and I for one am certain that dark matter and dark energy do exist, the way people propounding their existence is not because they have empirical evidence.
And I want to know on what basis if not on empirical evidence these people say that there are dark matter and dark energy.
"Dark matter" and "dark energy" are essentially placeholders. We empirically observe (with telescopes, etc) for instance the amount of mass in a given galaxy, and the strength of gravity. It turns out that the amount of mass
that we are able to observe is insufficient to hold the galaxy together - therefore we
predict the existence of some other form of mass that we cannot directly observe. For simplicity's sake, we call it "dark matter." We have not empirically observed dark matter directly (if we had, we'd give it a better, more descriptive name and quantify exactly what it is), but we
have indirectly observed its effects.
Much like the discovery of the outer planets of the solar system - we empirically observe that there is a gravitational anomaly in the orbit of one planet, and predict that there must be an additional planetary mass causing the disruption, even before we observe the new planet directly. Another analogy would be thermometer - you don't directly measure the temperature. You directly observe the thermometer, and predict the temperature based on how high the mercury rises. The temperature measurement is empirical, but indirect.
The existence of dark matter et al is a prediction based upon empirical evidence.
For myself, how do I know that dark matter and dark energy exist?
I know that they exist from intelligent thinking.
"Intelligent thinking" is not an answer. You have not described your thought process or made a coherent statement. You may as well say "I know they exist because of phlogiston" - you would be giving the same level of explanation. Could you please elaborate?
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