No, the scientific method is still the major way of assessing truth. It may not be as rigorously applied in the social sciences (the "soft" sciences, like philosophy, sociology, history, etc.) as it is in the natural sciences ("hard" sciences, like mathematics, physics, chemistry, etc.), but the underlying methodologies and motivations are all still there and all still intact.
Perhaps you're wondering about logical proofs? Philosophical arguments are commonly made in this format, with the most common example being a syllogism. A syllogism presents two premises (or claims), and argues that the proposition (conclusion) must be logically inferred from those two premises. In other words, if you accept the premises, the conclusion must logically follow. For example:
Premise One: Tom Jones asked a question on Philosophy—Stack Exchange.
Premise Two: People who ask questions on Philosophy—Stack Exchange are smart and well-informed.
Conclusion: [Thus,] Tom Jones is smart and well-informed.
There are lots of other ways in which to frame a logical argument, ranging from the very simple to the very complex. At their highest level, logical proofs can look a lot like formal mathematical proofs because, well, they are the same. When reading standard philosophical treatises, you'll often find these arguments presented in words rather than in the more complex symbolic notation you might see in a formal logic textbook, but the methods and the process are all still the same.
The above example is actually an application of deductive reasoning, which can be more generally defined as reasoning from the general to the specific. Using such a logical framework, you make two (or more) claims about the world, and then attempt to show that a conclusion necessarily follows (or is logically implied) from those two premises. However, it's worth noting that deductive arguments are classified as either valid or invalid, not true or false.
The scientific method, by contrast, tends to follow the other prevailing method of reasoning, called inductive reasoning. Inductive reasoning can be somewhat loosely defined as the reverse of deductive reasoning: reasoning from the specific to the general. Using the scientific method, one makes certain, specific observations about phenomena in the surrounding world, and then attempts to draw a more general conclusion based on those data. In this way, unlike deductive reasoning, it does work in search of truth, and an argument framed in this way can be dismissed as false (or untrue) given sufficient contradictory data.
Finally, you should note that not all schools of philosophical thought have the pursuit of "truth" as their ultimate goal; in fact, such a goal lies in direct contradiction with many significant branches that would contest the very notion of "truth". They might argue that "truth" is simply unknowable, or they might argue that it is socially determined and therefore impossible to discuss objectively.