Question

when formalizing an argument, do not be generous, i.e., only formalize the premises as stated and do not add premises to the arguments.

question 8 (1 point)
consider the following argument:
p1. something orbits earth and something orbits jupiter.
p2. earth is a celestial object and jupiter is a celestial object.
p3. celestial objects are orbited by all less massive celestial objects.
p4. all celestial objects can have their masses compared.
p5. only celestial objects orbit celestial objects.
c. therefore, there are at least four celestial objects.
choose the correct classification of this argument from the options below.

• valid in tfl.
• valid in fol, but not in tfl.
• sound.
• invalid.

Explanation:

1. TFL (Truth - Functional Logic) Limitation: TFL deals with simple truth - functional connectives (like and, or, not) and treats sentences as atomic units. The argument here involves quantifiers ("something", "all", "only") and predicates (e.g., "orbits", "is a celestial object"), which TFL cannot handle. So it's not valid in TFL.
2. FOL (First - Order Logic) Analysis: FOL can handle quantifiers (∃, ∀) and predicates. Let's break down the premises:

• P1: ∃x(x orbits Earth) ∧ ∃y(y orbits Jupiter)
• P2: Earth is celestial ∧ Jupiter is celestial
• P3: ∀x∀y((x is celestial ∧ y is celestial ∧ y < x in mass)→ y orbits x)
• P4: ∀x∀y((x is celestial ∧ y is celestial)→ mass of x and y can be compared)
• P5: ∀x∀y((x orbits y)→ (x is celestial ∧ y is celestial))
• From P1, we have at least two celestial objects (the ones doing the orbiting: let's say A orbits Earth and B orbits Jupiter). From P2, Earth and Jupiter are celestial. So in total, A, B, Earth, Jupiter are at least four celestial objects. The reasoning requires FOL's ability to handle quantifiers and predicates, which TFL lacks.

1. Soundness Check: Soundness requires the argument to be valid and all premises to be true. While the conclusion might seem reasonable in the real world, the premise "Celestial objects are orbited by all less massive celestial objects" is not actually true (e.g., not all less - massive celestial objects orbit a given celestial object in reality). So the argument is not sound.
2. Invalidity Check: As shown in the FOL analysis, the conclusion follows from the premises when using FOL's capabilities, so it's not invalid.

Answer:

Valid in FOL, but not in TFL.