Chizuk Emunah Under the Microscope: Chapter 18

In Chapter 18, Troki responds to a Christian objection that the Mosaic code does not address life after death, but delivers earthly rewards and punishments. Troki notes that humanity is not material, but composed of matter and spirit. He also argues that the bodies of the righteous will be free of disease, indicating life after death. He quotes Leviticus 18:5, 26:11-12, Genesis 17:7-8, and Genesis 28:21.

     You shall therefore keep my statutes and my rules; if a person does them, he shall live by them: I am the LORD.
(Leviticus 18:5 ESV)

     I will make my dwelling among you, and my soul shall not abhor you. And I will walk among you and will be your God, and you shall be my people.
(Leviticus 26:11-12 ESV)

    And I will establish my covenant between me and you and your offspring after you throughout their generations for an everlasting covenant, to be God to you and to your offspring after you. And I will give to you and to your offspring after you the land of your sojournings, all the land of Canaan, for an everlasting possession, and I will be their God.”
(Genesis 17:7-8 ESV)

     so that I come again to my father's house in peace, then the LORD shall be my God,
(Genesis 28:21 ESV)

The excision of the soul to which Troki refers may refer to spiritual death under Karaite tradition. I will admit that I do not know Karaism well enough to say one way or the other. The Rabbis have a technical term for this excision of the soul called karet. Rabbinical Jewish law explains karet as premature death (Sifra, Emor, 14:4).  There are traditions that include post-mortem punishment as part of karet, but this is controversial, even within Rabbinical Judaism.

Troki also argues that Christians believe that the threat that God gave to Adam "you will surely die" meant spiritual death. Troki takes issue with this, as do I. The same term is used in 1 Kings 2.

    Then the king sent and summoned Shimei and said to him, “Build yourself a house in Jerusalem and dwell there, and do not go out from there to any place whatever. For on the day you go out and cross the brook Kidron, know for certain that you shall die. Your blood shall be on your own head.”
(1 Kings 2:36-37 ESV)

Shimei did not die that day. As Nachmanides writes, that term is generally used to indicate when someone will incur the death penalty, not when they will actually die.

Paul affirms this in Romans and 1 Corinthians.

Just as through one man sin entered into the world, and through sin, death. So death spread to all men, because of which all sinned.
(Romans 5:12, my translation)

Some may think this is spiritual death, but it ignores Paul's use of the term in his earlier letter to the Corinthians.

    But in fact Christ has been raised from the dead, the firstfruits of those who have fallen asleep. For as by a man came death, by a man has come also the resurrection of the dead. For as in Adam all die, so also in Christ shall all be made alive.
(1 Corinthians 15:20-22 ESV)

Here, the context is resurrection of the body, which parallels the death of the body. Spiritual death and spiritual life are not part of the context of 1 Corinthians 15.

Troki also argues that the law will be in force forever. Immanuel Schochet  takes issue with this:
Also, when I was with the Orthodox, one Modern Orthodox Rabbi with a Harvard PhD in Jewish history complained quite a bit about this "reward in the hereafter" business.  Artscroll Judaism heavily emphasizes life after death as authentically Jewish. Generally, the Modern Orthodox, and especially the followers of Maimonedes, heavily de-emphasize or eliminate this aspect. Following the mitzvot is supposed to give reward and punishment in this life. To emphasize reward and punishment in the afterlife is to Christianize Judaism.