How is resistance defined when there is no current? By definition, a component has a resistance of $1\Omega$ if a potential difference of $1$V makes a current of $1$A flow through it. So I was a bit confused when I saw somewhere "a filament lamp has a resistance of $4\Omega$ when it carries no current."
How is it possible to define resistance if there is no current (and hence no potential difference, since $V=IR$)?
 A: The resistance of a lamp filament is not constant. As the current increases and the filament heats up the resistance increases. That's why the statement you quote is phrased that way. It means that the resistance is 4 Ohms when the current is low enough that the heating and resistance change are negligable.
More verbosely it could be phrased:

The limit of the ratio $V/I \rightarrow 4\,\Omega$ as $I \rightarrow 0$.

A: Most resistive materials have a nonzero temperature coefficient: the resistance changes with the temperature of the device.  An incandescent lamp filament, which glows because it is hot, might have an temperature of several thousand kelvin.  On the other hand, if you probe the lamp with an ohmmeter while it is off, you'll typically use a current of a few microamperes, maybe as much as a milliamp, and the filament temperature won't change from the ambient temperature of 300 K.  So the resistance you read by sticking an ohmmeter against a light bulb doesn't predict the current that bulb will draw when you turn it on.
