Following philosophers like Tim Crane and Uriah Kriegel, letâ€™s call the Problem of Intentionality the problem of motivating the rejection of one of the three propositions in the following inconsistent triad:

1. We think about non-existents

2. One can bear relations only to existents

3. Thinking about is a relation

Part of my interest in the Problem of Intentionality is that a big chunk of the Unicorn Argument involves an acceptance of 1 & 2 and a rejection of 3.

Iâ€™ve gotten grief from philosophers like Chase Wrenn and Eric Steinhart about whether the Unicorn can be stated in a formal calculus. Such grief can equally be directed at the Problem of Intentionality. We can motivate such grief by formulating what Iâ€™ll call the Steinhart Principle:

**Steinhart Principle:** A set of propositions exhibits logical properties (e.g., validity, inconsistency) only if there is at least one calculus in which the propositions are jointly formalizable.

I have a worry about the applicability of the Steinhart Principle to either the Unicorn or Intentionality that I would like to raise in terms of what Iâ€™ll call the Mandik Principle:

**Mandik Principle:** The adoption of a formalism is philosophically fruitful only if doing so doesnâ€™t beg (pro or con) the question at hand.

Consider, then, the following challenge: State the Problem of Intentionality in a way that simultaneously respects both the Steinhart Principle and the Mandik Principle.

Can this challenge be met? I havenâ€™t made up my mind one way or another, but here are some reasons for doubting that the challenge can be met.

Consider that meeting this challenge would involve formulating the three propositions in a way that doesnâ€™t require one to assign a particular truth-value to any of them. Now consider proposition #1. It is very difficult to see how to proceed with its formalization without also taking a stand on the truth of 1, 2, or 3. For exampleâ€¦

Suppose that we formulate 1 as

($x)($y)(Px & ~Ey & Txy)

where â€œ($x)â€ is the existential quantifier, â€œPxâ€ is â€œx is a personâ€, â€œExâ€ is â€œx existsâ€, and â€œTxyâ€ is â€œx thinks about yâ€.

Lots of problems arise aside from the fact that one may be squeamish about an existence predicate. In particular, formulating 1 in terms of the two-place â€œTxyâ€ presumes the truth of proposition 3.

On the other hand, we might try to formulate 1 as

($x)($y)[Px & Tx & ~($z)(Uz)]

where â€œUxâ€ is â€œx is a unicornâ€ and â€œTxâ€ is a predicate we construct by presuming a language of thought and an apparatus of thought-quotation giving us â€œx is thinking â€˜($z)(Uz)â€™â€.

On this formulation lots of problems arise aside from the fact that we are quantifying into the opaque context of thought quotation. In particular, it looks like such a formulation in terms of a one-place thinks predicate presumes the falsity of 3.

Letâ€™s suppose for the sake of conversation that there is no formalization of the Problem of Intentionality that satisfies the Mandik Principle. What, then, is the most appropriate response to the Problem of Intentionality? Rejecting it as a non-problem seems itself to beg genuine philosophical questions.