A philosopher argues: 'Numbers exist because our best mathematical theories say there exist things called numbers, and those theories are indispensable to science.' Which view of ontology does this argument most closely follow?
ANominalism — the argument shows that number-talk is just shorthand for patterns in physical things
BQuine's criterion of ontological commitment — what exists is whatever our best theories must quantify over (∃x: x is a number)
CPlatonism — numbers exist in an independent abstract realm discovered by pure reason
DEliminativism — the argument exposes numbers as useful fictions that should be paraphrased away
Quine's criterion says: to be is to be the value of a bound variable. If your best theory says '∃x (x is a prime number greater than 2)', you are ontologically committed to prime numbers. The argument in the question is precisely Quinean — it derives ontological commitment from theoretical indispensability. This makes ontology continuous with science rather than a separate a priori inquiry, which is Quine's signature move.
Question 2 Multiple Choice
A neo-Aristotelian philosopher says: 'Both particles and the table they compose exist, but the table is not fundamental — it is grounded in, and explained by, the particles.' What shift in ontological methodology does this represent?
AA move from asking 'what exists?' to asking 'what is fundamental?' — grounding and priority replace mere existence as the central question
BDenying that tables exist — only particles make the final inventory
CAccepting Quine's criterion but restricting it to fundamental physics
DArguing that 'exists' means different things when said of particles versus tables
Neo-Aristotelian metaphysics reframes ontology around priority and grounding rather than mere existence. The claim is not that tables don't exist, but that their existence is derivative — they exist because the particles exist and are arranged table-wise. The real ontological question becomes 'what is fundamental?' rather than 'what is in the inventory?' This shift allows a richer ontology that acknowledges ordinary objects while still insisting on a hierarchical structure of reality.
Question 3 True / False
Quine's criterion of ontological commitment makes ontological questions continuous with scientific inquiry — what exists is whatever our best scientific theories must quantify over.
TTrue
FFalse
Answer: True
This is Quine's central contribution. By tying ontology to the quantificational structure of our best theories, he shifts the discipline from speculative a priori metaphysics to something answerable by examining theoretical commitments. The criterion also generates hard questions: which theory is 'best,' and can theoretical quantification be paraphrased away? But the fundamental move — making existence a matter of theoretical commitment — is Quine's lasting influence on analytic ontology.
Question 4 True / False
The problem of universals — whether properties like redness exist independently of particular red things — is a historical debate that has been resolved and no longer appears in contemporary ontology.
TTrue
FFalse
Answer: False
The problem of universals remains central to contemporary metaphysics. It appears in debates about tropes (particular instances of properties rather than shared universals), about whether laws of nature require universal properties, and about the ontology of mathematics. Nominalists still argue that only particulars exist; realists defend universals or similar entities. The medieval formulations (realism vs. nominalism vs. conceptualism) frame discussions that are actively ongoing in current philosophy journals.
Question 5 Short Answer
What is the difference between asking 'do numbers exist?' and asking 'what does it mean for something to exist?' — and why does ontology need to address both questions?
Think about your answer, then reveal below.
Model answer: The first is a first-order question: a specific claim about which entities belong in our ontological inventory. The second is a second-order methodological question: what criterion distinguishes existing things from non-existing ones? Ontology needs to address both because without an answer to the second, there is no principled way to settle the first. If we have no criterion for existence — no way of determining what it takes for something to exist — then debates about whether numbers, properties, or fictional characters exist are merely verbal disputes rather than substantive ones. Quine's criterion (to be is to be the value of a bound variable) is one proposed answer to the second question, which then generates answers to the first.
This two-level structure is what distinguishes ontology from a mere list of things we believe in. The methodological question (what is existence?) is prior because it constrains how we can even formulate or adjudicate the categorical question (what exists?). Contemporary ontology debates both levels simultaneously — whether quantifier variance makes the second question unanswerable, or whether neo-Aristotelian grounding is a better framework than bare existence.