Does a level 1 Wizard casting the Ray of Frost cantrip deal damage equal to 1d4 + spellcasting modifier?

Question

I am GMing for a Pathfinder 2e group. A player noticed that cantrips are automatically heightened to half the PC's level rounded up. They therefore believe that a level 1 wizard casting Ray of Frost should count the spell as "heightened" and therefore deal damage equal to 2d4 + spellcasting modifier.

I believe that cantrips are level 1 spells that have the cantrip trait. Therefore, a level 1 wizard cannot "heighten" the cantrip to gain the extra 1d4 damage.

Ray of Frost: https://2e.aonprd.com/Spells.aspx?ID=245 (CRB 362)

Cantrips: https://2e.aonprd.com/Rules.aspx?ID=275 (CRB 300)

Trait: https://2e.aonprd.com/Traits.aspx (CRB 13)

Answer 1

Spellcasting Classes

A level 1 wizard casting ray of frost deals 1d4 + their spellcasting modifier in damage.

As you noted, a cantrip is automatically heightened to 1/2 of the wizard's level, rounded up. A level 1 wizard can therefore heighten something to 0.5*1, rounded up. 0.5 * 1 = 1. Therefore, the cantrip can only be cast as a level 1 spell (it's minimum level). As a level 1 spell, ray of frost deals 1d4 damage plus their spellcasting modifier.

A different way to think about this (but which reaches the same conclusion) is that ray of frost is a level 1 cantrip. A cantrip is a spell. Given that the highest level spell slot your level 1 wizard has is also level 1, there is no real possibility of heightening the spell. The cantrips page which you linked to says it this way:

For a typical spellcaster, this means its level is equal to the highest level of spell slot you have.

Spellcasting Archetypes

If a character received basic spellcasting through an archetype, then this may be slightly different. In this case it is possible to have a cantrip heightened to a level beyond the spell slots they have available.

For example, a 4th-level fighter with the basic wizard spellcasting feat has a single level 1 spell slot. However, cantrips are automatically heightened to half their level - making them level 2 ( level 4 / ).

Answer 2

From the rules for Heightening Spells

Other heightened entries give a number after a plus sign, indicating that heightening grants extra advantages over multiple levels. The listed effect applies for every increment of levels by which the spell is heightened above its lowest spell level

So, the basic effect of a cantrip at level 1 (the minimum level it can have) is as listed in the spell description. For Ray of Frost, this is 1d4+spellcasting modifier cold damage. The heightening applies for every multiple of the heighten value over the minimum. Ray of Frost has a Heighten value of +1, so the earliest you could apply the Heightened effect would be at Spell Level 2, which would be at character level 3.