Do the physical rewards and punishments in Bechukotai imply a lack of Olam Haba?

It would seem that the Tzedukkim did not believe in the existence of Olam Haba, based on the testimony of Josephus in Antiquities, Book 18, Chapter 1, Sections 3-4:

3. Now, for the Pharisees, they live meanly, and despise delicacies in diet; and they follow the conduct of reason; and what that prescribes to them as good for them they do; and they think they ought earnestly to strive to observe reason's dictates for practice. They also pay a respect to such as are in years; nor are they so bold as to contradict them in any thing which they have introduced; and when they determine that all things are done by fate, they do not take away the freedom from men of acting as they think fit; since their notion is, that it hath pleased God to make a temperament, whereby what he wills is done, but so that the will of man can act virtuously or viciously. They also believe that souls have an immortal rigor in them, and that under the earth there will be rewards or punishments, according as they have lived virtuously or viciously in this life; and the latter are to be detained in an everlasting prison, but that the former shall have power to revive and live again; on account of which doctrines they are able greatly to persuade the body of the people; and whatsoever they do about Divine worship, prayers, and sacrifices, they perform them according to their direction; insomuch that the cities give great attestations to them on account of their entire virtuous conduct, both in the actions of their lives and their discourses also.

4. But the doctrine of the Sadducees is this: That souls die with the bodies; nor do they regard the observation of any thing besides what the law enjoins them; for they think it an instance of virtue to dispute with those teachers of philosophy whom they frequent: but this doctrine is received but by a few, yet by those still of the greatest dignity. But they are able to do almost nothing of themselves; for when they become magistrates, as they are unwillingly and by force sometimes obliged to be, they addict themselves to the notions of the Pharisees, because the multitude would not otherwise bear them.

It makes some sense that they would deny Olam Haba, or reincarnation. It is not explicit in the peshat level of pesukim in Torah, and they would not hold of any derasha, being Sadducees. It is true that some other Biblical works refer to an afterlife, but Samaritans did not have any of Nach in their Biblical canon, and it is plausible that the Tzedukim did not have them either. If so, the discussions Chazal have about finding proof to techiyat hameisim in the Torah make sense, as well as their dismissal of those who do not maintain that such evidence can be found.

In parshat Bechukotai, the reward and punishment is purely physical. The obvious question is that if there is an Olam Haba, why does the Torah not mention it. Thus, the parsha begins:

ג אִם-בְּחֻקֹּתַי, תֵּלֵכוּ; וְאֶת-מִצְו‍ֹתַי תִּשְׁמְרוּ, וַעֲשִׂיתֶם אֹתָם.	3 If ye walk in My statutes, and keep My commandments, and do them;
ד וְנָתַתִּי גִשְׁמֵיכֶם, בְּעִתָּם; וְנָתְנָה הָאָרֶץ יְבוּלָהּ, וְעֵץ הַשָּׂדֶה יִתֵּן פִּרְיוֹ.	4 then I will give your rains in their season, and the land shall yield her produce, and the trees of the field shall yield their fruit.

All sorts of answers are possible, from an ain hachi nami, to hinting derashot, to hinting peshat, to perhaps explicit peshat in a pasuk.

Wouldn't we expect a Karaite to deny Olam Haba, and/or Techiyas Hameisim? Well, the Karaite who runs this website certainly doesn't. Karaites, recall, maintain Nach within their Biblical canon, and there are explicit references to these concepts there, e.g. in sefer Daniel.

Aharon ben Yosef the Karaite has an interesting answer to this question, pictured to the right. As a rough summary, not encompassing all his points:

He cites the pasuk about physical rewards, and notes that there is only mention of physical reward and punishment, with no mention of the world to come. He answers, in part, that this is due to the nature of the world to come, for it is not something murgash {sensed physically} but muskal {via intellect?}, and it is a doubt even to most intelligent people. But the words of Torah are targeted to people of all levels, intelligent and simple, young and old, men and women, most of whom desire peace of the body or the world.

Also, with temporary physical concerns (hunger, thirst, hardship) taken care of under chayei shaah, a maskil will be able to attain the eternal.

He also cites pesukim such as Vayikra 18: וּשְׁמַרְתֶּם אֶת-חֻקֹּתַי וְאֶת-מִשְׁפָּטַי, אֲשֶׁר יַעֲשֶׂה אֹתָם הָאָדָם וָחַי בָּהֶם, and calls these just remez, hints, rather than clear-cut statements.

So it is something which is true, but outside the Biblical text because of the nature of the Biblical text, and its target audience. Interesting idea, coming from a Karaite.

Another idea, somewhat related, though not found here, is that certain things are implicit. We see from certain idioms in Torah that they held of the existence of an afterlife. Perhaps of course there would be reward in the afterlife, such that it need not be stated. But these are extra promises about a good life in this world. See this post discussing one of Rabbi Broyde's points about conversion, and how the obvious needs not be said, but this lack of explicitness should not be taken as proof of its absence.

Thus,

Much has been made of the fact that there is very little explicit mention in the literature of the requirement that a convert accept the commandments as a sine qua non of conversion.
...
This lacuna is easily explained. It is a given in the History of Law (especially non-constituion-based law), that 'That which goes without saying, usually does,' The tacit assumptions of a legal system, though, are no less binding for their being tacit. Until the Emancipation, being Jewish and observing the commandments were absolutely identical. There was no need to state the obvious. That, indeed, is why references to Qabbalat ha-Mitzvot are all very much en passant. No one EVER questioned its centrality. The operative questions were what (if any) place it had in the actual conversion ceremony (e.g. Bes Din, Tevilla etc.)