Is the debt that the son promised to pay after the death of the loan written by the father a debt?

This is inheritance, not a new debtor in the form of guarantee, nor does it belong to debt joining.

Debt joining is essentially adding a new debtor to ensure the realization of creditor's rights, which belongs to the interests of creditors and does not require creditors' consent. If a third party and the debtor agree to join the debt, it shall notify the creditor. Or the third party directly expresses its willingness to join the debt to the creditor. The constitutive requirements of debt joining mainly include: First, the original creditor-debtor relationship exists effectively. Second, the debtor is not divorced from the debt relationship. After the third party joins the debt, the original debtor shall still undertake to perform its obligations within the scope of the original debt. It does not exempt the third party from performing its obligations because it joins the debt, that is, the third party only adds a new debtor on the basis of the original debtor, which has the function of ensuring the realization of creditor's rights in essence. Third, creditors should be notified.