Determination

Determination is a power that allows SOULs to persist after death. Beings with the highest determination also grants the ability to SAVE.

Overview
Determination is naturally possessed by humans. Should a monster acquire a high concentration of determination, its body will melt, usually into an amalgamate. The only known monster to naturally possess determination is Undyne. A being without a SOUL can gain the will to live if it acquires determination, the prime example being Flowey.

Main Story
SAVE Points can be found throughout the game. These SAVE points express the protagonist's determination and thoughts in regards to recent events.

True Pacifist Route
In the True Lab, it is revealed that Alphys started experimenting with determination extracted from human SOULs in an attempt to unleash the power of the SOUL. She built the DT Extraction Machine to obtain determination and begin injecting it into the bodies of monsters who had fallen down. The monsters injected with determination soon melted together.

Genocide Route
Undyne, fueled by her determination, challenges the protagonist as Undyne the Undying. When defeated, she melts in a similar fashion to amalgamates.

At the end of the route, the fallen human speaks to the player directly, explaining that they were brought back to life due to the player's determination.

Trivia

 * The SAVE point description in Temmie Village refers to determination as "detemmienation".
 * "Determination" might be a play on words, as the primary power it affords is the ability to reverse death, either the protagonist's or those they may have killed, hence de-termination.
 * It is unknown if the Amalgamates mimicking game elements such as Frisk's "!" dialogue box or SAVE points are actually happening and related to the Determination they've been injected with, or simply breaks of the fourth wall intended to catch players off-guard.
 * The DT Extraction Machine strangely resembles Photoshop Flowey.