If a Jew observes Torah Law, yet does not believe that there is a God or that the Torah is true, do his mitzvot have any value? For example, one born into an observant home who stays observant, but in his heart doesn't accept the Torah as valid.
This is an extreme example, obviously, but your answer may help me understand what my own mitzvot accomplish if I perform them without 100% faith in their necessity. Basically, is "going through the motions" without the inherent belief worth anything? Thank you.
In principle, the fulfillment of a mitzvah requires the belief in God, and that He wants us to do the action. The word "mitzvah," commandment, implies a Commander. The real spiritual value of a mitzvah is when it is performed with this understanding. Still there are many reasons to "go through the motions" even though there may be less than 100% belief, and I will try to elaborate briefly as best as I can.
First of all, there are many, many levels of belief, and often even a very low level can produce a lot of benefit, and make mitzvah observance worth something.
Secondly, in terms of negative commandments, the "Thou shalt nots," if he refrains even for the wrong reasons, still he is refraining and not bringing all kinds of negative consequences onto himself.
If there is a basic belief in God, just a lack of understanding of the necessity of the mitzvah, then performance with trust in God that it is the right thing is really performance on a high level. The very acceptance of mitzvot by the Jewish people at Sinai was with the condition "na'aseh v'nishma," "we will do and we will understand," meaning that we will do even before we understand.
True, a person should try to understand, and certainly an understanding of the background and fullness of the mitzvah will create a deepened satisfaction in mitzvah performance. This usually comes with increased Torah study. Lack of this understanding, however, does not take away from the fulfillment of the mitzvot.
A person in the state that you describe will either go one way or the other. Hopefully, the continued performance of the mitzvot will keep him in tune, like the parable of a watch which isn't keeping time: If the person keeps winding it then ultimately when he brings it to a watchmaker there will be something to fix. But if he just lets it sit, it'll get rusty beyond repair.
