Knowledge, Number and Reality

Encounters with the Work of Keith Hossack

Nils Kürbis, Bahram Assadian, Jonathan Nassim, Nils Kürbis, Bahram Assadian, Jonathan Nassim

• Publisher: Bloomsbury Academic
• Year: 2021
• ISBN:
  9781350186453
• Edition: 1
• Topic: Philosophy
• Subtopic: Logic in Philosophy

Throughout his career, Keith Hossack has made outstanding contributions to the theory of knowledge, metaphysics and the philosophy of mathematics. This collection of previously unpublished papers begins with a focus on Hossack's conception of the nature of knowledge, his metaphysics of facts and his account of the relations between knowledge, agents and facts. Attention moves to Hossack's philosophy of mind and the nature of consciousness, before turning to the notion of necessity and its interaction with a priori knowledge. Hossack's views on the nature of proof, logical truth, conditionals and generality are discussed in depth. In the final chapters, questions about the identity of mathematical objects and our knowledge of them take centre stage, together with questions about the necessity and generality of mathematical and logical truths. Knowledge, Number and Reality represents some of the most vibrant discussions taking place in analytic philosophy today.

1

A Summary of My Current Views

Keith Hossack

1. Relation dualism

Dualism is the doctrine that the mental is irreducible: the true theory of mind must include something mental amongst its primitives. This mental something need not be the soul: event dualism is the more modest theory that there are irreducibly mental events; still more modest is relation dualism, which only asserts the existence of a relation that is irreducibly mental. Relation dualism is a doctrine in the philosophy of mind, but it has interesting connections with epistemology and also with metaphysics.

2. Awareness as the irreducible mental relation

Relation dualism needs to identify which relation it takes to be fundamental in the theory of mind. Since mind is that which knows, relation dualists can seek the fundamental mental relation by an analysis of the concept of knowledge. If knowledge is warranted true belief, then since knowledge is factive, one’s having warrant excludes the possibility of one’s belief being false. The relation dualist should therefore take the fundamental mental relation to be a relation that warrants belief.

According to Brentano, every mental state presents an object, and this ‘direction toward an object’ is the mark of the mental. Should relation dualism take the fundamental mental relation to be Brentano’s presentation relation? Surely not, for to do so would lead to scepticism about the external world. Brentano says the ‘presented’ object may possess only intentional inexistence – it need not exist in reality. If an external object that is presented might be mere appearance, its being presented does not exclude the possibility of one’s belief being false.

According to the representational theory of mind, the propositional attitudes are the fundamental mental relations. On this theory, an experience as of an external object is a psychological relation to a proposition that represents a circumstance. But relation dualism should not take propositional attitudes to be the fundamental mental relations, for that would again open the door to scepticism. If the fundamental mental relations are relations to propositions, there is a veil of propositions between the mind and the world: a Cartesian deceiver could undetectably remove the external world without disturbing the veil. So one’s standing in a mental relation to a proposition that represents a circumstance does not exclude the possibility that the circumstance does not exist.

If we are to avoid scepticism, we must suppose that the fundamental mental relation is a relation to a fact, i.e. to the circumstance itself. If one stands in a mental relation to a circumstance – if one is in actual ‘mental contact’ with it – then one’s mental state does exclude the possibility that the circumstance does not exist. So to avoid scepticism, relation dualism should postulate that there is a mental relation to a circumstance which warrants one’s belief in the circumstance. Call this relation the awareness relation. There is then the following connection between knowledge and the awareness relation: S knows that A if S’s true belief that A is warranted by S’s awareness of the circumstance that A.

3. Circumstances

Taking the fundamental relation to be awareness allows relation dualism to avoid scepticism, for awareness is a relation between a mind and the circumstance itself, which foils the Cartesian deceiver. If the external world is removed, the circumstances it contained are removed too, so one would not stand in the same mental relations, so one’s mental state would be different. Standing in the mental relations to the external world in which one actually stands excludes the possibility that the external world does not exist.

A truth, a true proposition, can be about a time, but is not itself in time. In contrast, a circumstance is a being that exists in time: a temporary circumstance exists only at a particular time, an eternal circumstance exists at every time. Temporary circumstances include events, states and processes; eternal circumstances are those whose existence can be known by logical, mathematical and ethical reasoning.

4. Epistemological ramifications of relation dualism

4.1 Consciousness

If S has a conscious experience, there is something it is like for S to have that experience. This property of the experience is called its phenomenal character. If a mental state has a phenomenal character, then necessarily the subject of the state is aware of its having that character. For example, a state could not be pain unless it was felt as pain. Conversely any state that is felt as pain really is pain – even ‘phantom limb pain’ really is pain. We can account for the necessary connection between having a pain and feeling the pain by supposing that the pain and the feeling of pain are one and the same identical event. This account, which I call the identity theory, entails that, necessarily, a mental state with phenomenal character occurs if and only if its subject is aware of its occurrence.

4.2 Faculties

Conscious states are self-announcing, since awareness of a conscious state is identical with the state itself. But most circumstances of which we are aware are known by the operation of some faculty and are not self-announcing. For example, if a subject sees that the cat is on the mat, the circumstance of the cat’s being on the mat must have caused the subject’s faculty of vision to cause their awareness of the circumstance.

The operation of the human visual system gives rise to a visual experience and to awareness of the cat’s being on the mat. How are the experience and the awareness related? Disjunctivists say that they are one and the same thing – the experience just is the subject’s being visually aware of the cat on the mat. Disjunctivists say it is conceivable that there could be a perfect hallucination subjectively indistinguishable from the experience. Such a hallucination would not be awareness, so they say it would not be the same mental state as the veridical experience, although it would be subjectively indiscriminable. But it seems more natural to say that the veridical experience and the hallucinatory experience are identical mental states, since by hypothesis they have exactly the same functional role and exactly the same qualitative character. The experiences differ only in their effects: when veridical, the experience causes awareness, occurring as it does in an epistemically favourable context; when hallucinatory, the same experience does not cause awareness, because it occurs in an unfavourable context. Thus the relational state of the subject of the veridical experience is different from the relational state of the subject of the hallucinatory experience, although it is the same experience in both cases. This analysis allows the awareness theory to reject the sceptic’s premiss that in the good and bad cases one’s total mental state is the same.

4.3 Scepticism

Vision is a faculty, a power of the mind to acquire awareness of the visible circumstances. Similarly the other senses give us awareness of the circumstances proper to them. The sceptic may put forward an argument that we do not have such awareness. It is vain to attempt to argue with the sceptic, for an argument needs premisses, and whatever our premisses are, the sceptic will say that relying on such premisses begs the question. Therefore the correct response to scepticism is Moore’s: any valid argument which entails that Moore doesn’t know he has hands must have a false premiss, since the conclusion is ridiculous.

In addition to the senses, other human faculties include intelligence, which gives us scientific knowledge, empathy which gives us knowledge of other minds, and reason, which gives us a priori knowledge. Moore’s way with scepticism allows us to affirm the existence of these other faculties also. Since it’s ridiculous to suppose that Moore doesn’t know that the sun will rise tomorrow, we must acknowledge the faculty of intelligence, which allows us to learn from experience. Since it’s ridiculous to suppose that Moore doesn’t know that other people have thoughts and feelings just as he does, we must acknowledge the faculty of empathy. And since it’s ridiculous to suppose that Moore doesn’t know that twice two are four, that no contradiction is true, and that some things are good and some actions right, we must acknowledge the faculty of reason.

5. Metaphysical ramifications

5.1 Circumstances

Relation dualism says there is an irreducibly mental relation, so relation dualism is false if no such entities as relations really exist. Bradley rejected the theory of relations on the grounds that it could not explain, supposing given some things and a relation, what it would be for the things actually to stand in the relation. Russell answered Bradley by appealing to the category of entities he called ‘complexes’. According to Russell, what it is for the things to stand in the relation is for there to exist the complex whose constituents are the things and the relation. If we interpret Russell’s ‘complexes’ as our circumstances, the reply to Bradley is that, for example, the cat and the mat stand in the is-on relation if there exists the circumstance of the cat’s being on the mat. Thus relation dualism must endorse a metaphysics of the real existence of circumstances. As we are taking awareness to be the fundamental mental relation, for each kind of knowledge that our faculties give us, we must expect there to be a corresponding kind of circumstance, our awareness of which warrants the knowledge.

5.2 Quantities

Events, states and processes are temporary circumstances, and all of them can be objects of visual awareness: one can see an event such as a flash, a process such as a wave, or a state such as the pavement’s being wet. But we can also see such beings as the ‘individual man or horse’, which according to Aristotle fall in the category of substance. So should the awareness theory allow that we can stand in the awareness relation to entities in the category of substance?

According to Aristotle’s hylomorphic theory, an individual substance comes into being when suitable matter receives the proper form. For example a table comes into being when suitable wood is arranged tablewise. Call a state of tablewise arrangement of some wood a ‘table-stage’. A plurality of such states, if properly connected both causally and spatiotemporally, may be said to comprise the life of a table: call such a plurality of stages ‘table-related’.

The awareness theory can say that one sees a table if one’s belief in the table’s presence is warranted by one’s visual awareness of the wood’s being arranged tablewise. But predicates such as ‘arranged tablewise’ are said of a quantity of matter, not of an individual, and predicates such as ‘table-related’ are said of a plurality of states and not of a single state. The subject term of such predications denotes not an individual but a quantity, so a language that can express such predications needs its quantifiers to range over quantities as well as individuals. In the predicate calculus, the quantifiers range only over individuals. A more general logic is therefore required, where the quantifiers range over quantities also. This more general logic is mereology, the pure a priori logic of quantity, as axiomatized by Tarski. The quantities for which Tarski gave axioms were continua – regions of three-dimensional Euclidean space. But his axioms apply equally to discrete quantities, where they emerge as the logic of plurals.

5.3 Mathematics

The logic of quantity allows us to attribute properties to quantities. One obvious property a quantity has is its size, and this leads us to the a priori science of mathematics. We can take a natural number to be the absolute size of a plurality, and a real number to be the relative size of a continuum. The axioms for the natural and real numbers, and for the ordinal numbers also, can then all be deduced from mereology plus the a priori axioms that Euclid calls the Common Notions.

5.4 Logically complex circumstances

The faculty of reason gives us a priori knowledge of mereology and indeed of logic generally. Since our logical beliefs are knowledge, they are warranted by our awareness of logical cir...