Category: Nominalism and Realism

The Use and Abuse of Occam’s Razor: On Multiplying Entities Beyond Necessity

Self-styled neo-Aristotelian Richard Hennessey's response to my three posts concerning his theory of accidental predication is now online. 

He graciously declines my suggestion that he make use of accidental compounds or accidental unities in his theory despite the excellent Aristotelian pedigree of these items, a pedigree amply documented in the writings of Frank Lewis and Gareth Mathews.  Following Mathews, I characterized accidental compounds as 'kooky' objects with as little pejorative intent as I found in Mathews who defends these items. Hennessey, however, apparently takes the label pejoratively:

I cannot help but agree that the seated-Socrates in question, as a being other than Socrates, is a “‘kooky’ or ‘queer’ object.” And I cannot help but wonder how anyone who rejects universals could be tempted to multiply entities and accept such a “‘kooky’ or ‘queer’ object.”

So before examing the meat of Hennessey's response to me, in a later post, we must first tackle some preliminary matters including the nature of Occam's Razor, its use and abuse, and the role of explanation and explanatory posits in philosophy.

On Brandishing the Razor

I am not historian enough to pronounce upon the relation of what is standardly called Occam's Razor to the writings of the 14th century William of Ockham. The different spellings of his name will serve as a reminder to be careful about reading contemporary concerns into the works of philosophers long dead. Setting aside historical concerns, Occam's Razor is standardly taken to be a principle of theoretical economy or  parsimony that states:

   OR. Do not multiply entities beyond necessity.

It is sometimes formulated in Latin: Entia non sunt multiplicanda praeter necessitatem. The principle is presumably to be interpreted qualitatively rather than quantitatively, thus:

   OR*. Do not multiply TYPES of entity beyond necessity.

Thus it is not individual entities that are not to be multiplied, but types or kinds or categories of entity.  To illustrate.  Some criticized David Lewis' extreme modal realism on the ground that it proliferates concreta: there are not only all the actual  concreta , there are all those merely possible ones as well.  He responded quite plausibly to the proliferation charge by pointing out that the Razor applies to categories of entity, not individual entities, and that category-wise his ontology is sparse indeed.

'Multiply' is a picturesque way of saying posit. (Obviously, there are as many categories of entity as there are, and one cannot cause them to 'multiply.')  And let's not forget the crucial qualification: beyond necessity.  That means: beyond what is needed for purposes of adequate explanation of the data that are to be explained.  Hence:

OR**  Do not posit types of entity in excess of what is needed for purposes of explanation.

So the principle enjoins us to refrain from positing more types of entity than we need to explain the phenomena that need to be explained. It is obvious that (OR**) does not tell us to prefer theory T1 over theory T2 if T1 posits fewer types of entity than T2. What it tells us is to prefer T1 over T2 if T1 posits fewer types of entity AND accounts adequately for all  the data. So there is a trade-off between positing and accounting.

Our old pal Ed over at Beyond Necessity often seems to be unaware of this.  He seems to think that simply brandishing the Razor suffices to refute a theory.  Together with this he sometimes displays a tendency to think that whole categories of entity can be as it were  shamed out of existence by labeling them 'queer.'  I picked up that word from him.  A nice, arch, donnish epithet.  But that is just name-calling, a shabby tactic best left to the ideologues. 

Hennessey is perhaps not guilty of any name-calling or entity-shaming but I note that he too seems to think that merely waving the Razor about suffices as a technique of refutation. One piece of evidence is the quotation above where he states in effect that to posit accidental compounds such as seated-Socrates is to multiply entities.  But this is to ignore the crucial question whether there is any need for the positing. 

What is offensive about Razor brandishing is the apparent ignorance on the part of some brandishers of the fact that we all agree that one ought not posit types of entity in excess of the needs of explanation. What we don't agree on, however, is whether or not a given class of entities is needed for explanatory purposes.  That is where the interesting questions and the real disagreements lie. 

Hennessey eschews universals in the theory of predication, and elsewhere.  Fine.  But he cannot justify that eschewal solely on the basis of Occam's Razor which is a purely methodological principle.  In other words, the Razor does not dictate any particular ontology.  Taken as such, and apart from its association with the nominalist Ockham, it does not favor nominalism (the view that everything is a particular) over realism (the view that there are both particulars and universals).  It does not favor any ontology over any other. 

Nor does it rule out so-called 'abstract objects' such as Fregean propositions.  I gave an argument a while back (1 August 2010 to be precise) to the conclusion that there cannot, as a matter of metaphysical necessity, be nothing at all, that there must be at least one abstract object, a proposition.  Hennessey commented on that post, Thinking about Nothing, and made the objection that I was multipying entities.  But again, the salient question is whether the entity-positing is necessary for explanatory purposes.  If my argument was a good one, then it was.  One cannot refute such an argument simply by claiming that it introduces a type of entity that is less familiar than one's favorite types.

To sum up.  Philosophy is in large part, though not entirely, an explanatory enterprise.  As such it ought to proceed according to the methodological principle formulated above as (OR**).  This principle is not controversial.  Hence it should not be presented to one's opponents as if it were controversial and denied by them.  Nor is it a principle that takes sides on the substantive questions of ontology.  Thus the following argument which is suggested by Hennessey's remarks is invalid:

1. OR**
2. Accidental compounds are a category of particular distinct from both substances and accidents.
Ergo
3. There are no accidental compounds. 

Non sequitur!  He needs a premise to the effect that the positing of accidental compounds is otiose since the explanatory job can be adequately done without them.  He needs such a premise, and of course he needs to defend it.

What I am objecting to is the idea is that by earnest asseverations of a wholly uncontroversial methodological principle one actually  advances the substantive debate.  

My Intentionality Aporia ‘Ockhamized’

Edward of London proposes the following triad

O1. The proposition ‘Bill is looking for a nonexistent thing’ can be true even when there are no nonexistent things.
O2. The proposition ‘Bill is looking for a nonexistent thing’ expresses a relation between two things.
O3. Every relation is such that if it obtains, all of its relata exist.

as a nominalistic equivalent to my

W1. We sometimes think about the nonexistent.
W2. Intentionality is a relation between thinker and object of thought.
W3. Every relation R is such that, if R obtains,then all its relata exist.

Edward imposes the following contraint on aporetic polyads: "The essence of an aporetic polyad is that any proper subset of statements (including the singleton set) should be consistent on its own, and only the whole set being inconsistent."  I accept this constraint. It implies that nothing can count as an aporetic polyad if one of its limbs is self-contradictory. 

My definition runs as follows.  An aporetic polyad is a set S of n self-consistent propositions (n>1) such that (i) any n-1 members of S, taken in conjunction, entail the negation of the remaining member; (ii) each member of S has a strong claim on our acceptance.  Edward's constraint follows from this definition.  For if any member is self-inconsistent, then it cannot have a strong claim, or any claim, on our acceptance.

If I understand Edward, he is urging two points.  His first point is that my formulation of the triad is inept because (W1), unlike (O1), is self-contradictory.  If this charge sticks, then my formulation does not count as an aporetic polyad by my own definition.  His second point is that his version of the triad has a straightforward and obvious solution:  reject (O2). 

Reply to the First Point.  There is nothing self-contradictory about 'We sometimes think of the nonexistent.'  As I made clear earlier, this is a datanic, not a theoretical, claim.  On this score it contrasts with the other two limbs.  It is meant to record an obvious fact that everyone ought to grant instantly. Because the fact is obvious it is obviously self-consistent.  So if Edward denies (W1), then it is not profitable to to continue a discussion with him. 

All I can do at this point is speculate as to why Edward fails to get the point.  I suppose what he is doing is reading a theory into (W1), a theory he considers self-contradictory.    But (W1) simply records a pre-theoretical fact and is neutral with respect to such theories as Meinong's Theory of Objects.  Suppose I am imagining a winged horse.  If so, then it would be false to say that I am imagining nothing.  One cannot simply imagine, or just imagine.  It follows that I am imagining something. We are still at the level of data.  I have said nothing controversial.  One moves beyond data to theory if one interprets my imagining something that does not exist as my standing in a relation to a Meinongian nonexistent object.  That is a highly controversial but possible theory, and it is not self-contradictory contrary to what Edward implies.  But whether or not it is self-contradictory, the main point for now is that

1. BV is imagining a winged horse

Is neutral as between the following theory-laden interpretations

2. BV (or a mental act of his) stands in a dyadic relation to a Meinongian nonexistent object.

and

3. BV is imagining winged-horse-ly.

The crucial datum is that one cannot just imagine, or simply imagine.  We express this by saying that to imagine is to imagine something.  But 'imagine something' needn't be read relationally; it could be read adverbially.  Accordingly, to imagine Peter (who exists) is to imagine Peter-ly, and to imagine Polonious (who does not exist) is to imagine Polonious-ly.  I am not forced by the crucial datum to say that imagining involves a relation between subject and object; I can say that the 'object' reduces to an adverbial modification of my imagining. 

So even if the relational reading of (1) were self-contradictory — which it isn't –  one is not bound to interpret (1) relationally.  Now (1) is just an example of (W1).  So the same goes for (W1).  (W1) is obviously true.  He who denies it is either perverse or confused.

Reply to the Second Point.  One can of course solve Edward's triad by denying (O2). But the real question is whether one can easily deny the distinct proposition  (W2).  I say no.  For one thing, the alternatives to saying that intentionality is a relation are not at all appetizing. All three of the limbs of my triad lay claim to our acceptance, and none can be easily rejected – but they cannot all be true.  That is why there is a problem. 

A Reply to “Ockham’s Nominalism”

The following is a response to "Ockham's Nominalism"  by our London sparring partner, Edward Ockham.  His words are in black, mine are in blue.  Comments are enabled.

At this stage, I should discuss Peter Lupu’s objections (mostly in the extended comment on Vallicella’s blog here) to the nominalist program.

I should first explain what I think the nominalist program is. I am taking my lead from a principle that William of Ockham neatly formulates in his Summa Logicae book I, chapter 51, where he accuses 'the moderns' of two errors, and says that the root of the second error is “to multiply entities according to the multiplicity of terms and to suppose that every term has something real (quid rei) corresponding to it”. He says grumpily that this is erroneous and leads far away from the truth. ('Radix est multiplicare entia secundum multitudinem terminorum, et quod quilibet terminus habet quid rei; quod tamen abusivum est et a veritate maxime abducens'). See also an early definition of nominalism here.

What does he mean? Well he says that it is an error. He implies it is a common one, by attributing to the moderns and by the fact he mentions it all. Thus he implies that there exist terms which do not have something real corresponding to them.

A net that snags every fish in the sea brings in too large a catch.  The trouble with the above explanation of nominalism is that it will be accepted by almost all philosophers, including plenty who would not identify themselves as nominalists.  For few if any philosophers hold that for each word in a sentence there is a corresponding referent.  Consider

1. Nobody came to the party.

No one will take 'nobody' in (1) as a name.  ("Well, I'm glad to hear that at least one person showed up.  How is Nobody doing these days?")  (1) is easily analyzed so as to remove the apparent reference of 'nobody.'  And the same goes for a long list of other synsemantic or syncategorematical expressions.  Would any philosopher say that in

2. I'm a day late and a dollar short

every word has a referent?  Edward needs to give examples of philosophers who hold that 'nobody' in (1) and 'and' in (2) have referents.  Let us hope he does not weasel out of this challenge.  Since no one assumes that every term has something real corresponding to it, the above definition of 'nominalism' is too broad to be of any use.

If Ockham is correct, the relevant distinction to draw is between queer and straight terms. Straight terms have something real corresponding to them, queer terms don’t. Furthermore, there must at least be some temptation to imagine that queer terms refer to or denote something, otherwise there would be little point in making it.

There is no need for this bizarre terminological innovation.  We already have 'autosemantic' and 'synsemantic' and equivalents.  Do not multiply terminology beyond necessity!

And let us note that synsemantic terms have useful semantic roles to play despite their not referring to anything.  There is a rather striking difference between 'I will come' and 'I will not come,' a difference that rides on the synsemantic particle 'not' which, as synsemantic, does not refer to anything.

Which brings me to the main point raised by Peter Lupu, who asks “What are ‘queer-entities’ and how do we determine whether a given entity is “queer” or “straight”? There are two parts to his question. In answer to the first, there are no such things as queer entities, if Ockham is right. There are only ‘queer terms’. These, by definition, are terms that don’t refer to or denote anything, and so by implication there are no ‘queer entities’.

In other words, synsemantic terms do not refer.  True by definition.

This is what makes any debate with realists difficult. Realists, namely those who think that queer terms refer, will persist in using the queer terms as if they did refer, and so will ask what kinds of thing are referred to, what is their ‘ontological status’ and so on. Ockhamists will naturally refuse to use these terms as if they referred, and refer the names of the terms instead, typically by using real or scare quotes.

No, realists are not those who think that queer terms refer since no one thinks that queer, i.e., nonreferring terms, refer.  Edward needs to explain the criteria for deciding whether a given term is queer or straight.  Is 'Edward' a queer term?  If not, why not?

[. . .]

That deals with Peter's first question. What are queer entities? We can't say, because there are no such things, just as we can't say what kind of things ghosts are. But we can say what 'queer terms' are. These are terms that are categorical, but which (a) have no reference or denotation and (b) appear, or are believed by many, typically on grounds of reason alone, to have a reference or denotation.

This doesn't advance the discussion at all.  First of all, we are not told what 'categorical' means.  More importantly, we have not been supplied with criteria for distinguishing queer from straight terms, to acquiesce for the nonce in this idiotic terminology. 

Peter’s second point, on how we determine whether given entity is “queer” or “straight”, I will leave for the next post, although clearly the first point applies here also. If the nominalist is right, we cannot ask this question of anything, just as we cannot ask whether a UFO came from Alpha centauri or Betelgeuse. We can only ask whether a given term is queer or straight. More to follow.

This doesn't get us anywhere.  We can ask, of a given term, whether or not it has a referent.  But then we need to be supplied with some method for answering this question.  Consider

3. Wisdom is a virtue.

Presumably, Edward will put 'wisdom' down as queer.  But on what grounds?  Is it because  he just knows (again by what method?) that everything that exists is a particular, and that if 'wisdom' has a referent then it must be a universal?  Or is there something about the word itself that tips him off that it is nonreferring? 

Is he appealing to some paraphrastic method?  Is he suggesting that what (3) expresses can be expressed salva significatione by a sentence containing no term making an apparent reference to a universal?  And in particular, would he accept the following paraphrase:

3*.  If anyone is wise, then he is virtuous?

So far, then, Londonistas 0, Phoenicians 1.

Two Questions About the Bundle Theory Answered

On the bundle-of-universals theory of ordinary concrete particulars, such a particular is a bundle of its properties and its properties are universals.  This theory will appeal to those who, for various ontological and epistemological reasons, resist substratum theories and think of properties as universals.  Empiricists like Bertrand Russell, for example.  Powerful objections can be brought against the theory, but the following two questions suggested by  some comments of Peter Lupu  in an earlier thread are, I think, easily answered.

Q1.  How may universals does it take to constitute a particular?  Could there be a particular composed of only one or only two universals?

Q2.  We speak of particulars exemplifying properties.  But if a particular is a bundle of its properties, what could it mean to say of a particular that it exemplifies a property?

A1.  The answer is that it takes a complete set.  I take it to be a datum that the ordinary meso-particulars of Sellars' Manifest Image — let's stick with these — are completely determinate or complete in the following sense:

D1. X is complete =df for any predicate P, either x satisfies P or  x satisfies the complement of  P.

If predicates express properties, and properties are universals, and ordinary particulars are bundles of properties, then for each such particular there must be a complete set of universals.  For example, there cannot be a red rubber ball that has as constituents exactly three universals: being red, being made of rubber, being round.  For it must also have a determinate size, a determinate spatiotemporal location, and so on.  It has to be such that it is either covered with Fido's saliva or not so distinguished.  If it is red, then it must have a color; if it is round, it must have a shape, and so on.  This brings in further universals.  Whatever is, is complete.  That is a law of metaphysics, I should think.  Or perhaps it is only a law of phenomenological ontology, a law of the denizens of the Manifest Image.  (Let's not get into quantum mechanics.) 

A2.  If a particular is a bundle of universals, then it is a whole of parts, the universals being the (proper) parts, though not quite in the sense of classical mereology.  Why do I say that? Well, suppose you have a complete set of universals, and suppose further that they are logically and nomologically compossible.  It doesn't follow that they form a bundle.  But it does follow, by Unrestricted Summation, that there is a classical mereological sum of the universals.  So the bundle is not a sum.  Something more is required, namely, the contingent bundling to make of the universals a bundle, and thus a particular.

Now on a scheme like this there is no exemplification (EX) strictly speaking.  EX is an asymmetrical relation — or relational tie:  If x exemplifies P-ness, then it is not the case that P-ness exemplifies x.  Bundling is not exemplification because bundling is symmetrical: if U1 is bundled with U2, then U2 is bundled with U1.  So what do we mean when we say of a particular construed as a bundle that is has — or 'exemplifies' or 'instantiates' using these terms loosely — a property?  We mean that it has the property as a 'part.'   Not as a spatial or temporal part, but as an ontological part.  Thus:

D2. Bundle B has the property P-ness =df P=ness is an ontological 'part' of B.

Does this scheme bring problems in its train?  Of course!  They are for me to know and for you to figure out.

 

The Hatfields and the McCoys

Whether or not it is true, the following  has a clear sense:

1. The Hatfields outnumber the McCoys.

(1) says that the number of Hatfields is strictly greater than the number of McCoys.  It obviously does not say, of each Hatfield, that he outnumbers some McCoy.  If Gomer is a Hatfield and Goober a McCoy, it is nonsense to say of Gomer that he outnumbers Goober. The Hatfields 'collectively' outnumber the McCoys. 

It therefore seems that there must be something in addition to the individual Hatfields (Gomer, Jethro, Jed, et al.) and something in addition to the individual McCoys (Goober, Phineas, Prudence, et al.) that serve as logical subjects of number predicates.  In

2. The Hatfields are 100 strong

it cannot be any individual Hatfield that is 100 strong.  This suggests that there must be some one single entity, distinct but not wholly distinct from the individual Hatfields, and having them as members, that is the logical subject or bearer of the predicate '100 strong.'

So here is a challenge to William the nominalist.  Provide analyses of (1) and (2) that make it unnecessary to posit a collective entity (whether set, mereological sum, or whatever) in addition to individual Hatfields and McCoys.

Nominalists and realists alike agree that one must not "multiply entities beyond necessity."   Entia non sunt multiplicanda praeter necessitatem!  The question, of course, hinges on what's necessary for explanatory purposes.  So the challenge for William the nominalist is to provide analyses of (1) and (2) that capture the sense of the analysanda and obviate the felt need to posit entities in addition to concrete particulars.

Now if such analyses could be provided, it would not follow that there are no 'collective entities.'  But a reason for positing them would have been removed.

Scholastic Realism and Predication

This post continues our explorations in the philosophy of The School. What is a scholastic realist? John Peterson (Introduction to Scholastic Realism, Peter Lang, 1999, p. 6) defines a scholastic realist as follows:

S is a scholastic realist =df i) S is a moderate realist and ii) S believes that universals exist in some transcendent mind, i.e., the mind of God.

A moderate realist is defined like this:

S is a moderate realist =df i) S denies that universals exist transcendently and ii) S affirms that universals exist immanently both in matter and minds.

Peterson A universal exists transcendently just in case it exists "independently of matter and mind." One who holds that universals exist independently of matter and mind is a Platonic or extreme realist. A moderate realist who is not a scholastic realist Peterson describes as an Aristotelian realist. Such a philosopher is a moderate realist who "denies that universals exist in some transcendent mind."   In sum, and interpreting a bit:

Platonic or extreme  realist:  maintains that there are universals and that they can exist transcendently, i.e., unexemplified (uninstantiatied) and so apart from matter and mind.

Moderate realist:  denies that there are any transcendent universals and maintains that universals exist only immanently in minds and in matter.

Scholastic realist: moderate realist who believes that there is a transcendent mind in which universals exist.

Aristotelian realist:  moderate realist who denies that there is a transcendent mind in which universals exist.

Continue reading “Scholastic Realism and Predication”

Why not be a Nominalist?

0. This post is a sequel to Truthmaker Maximalism Questioned.

1. On one acceptation of the term, a nominalist is one who holds that everything that exists is a concrete  individual.  Nominalists accordingly eschew such categories of entity as: universals, whether transcendent or immanent, Fregean propositions, Castaneda's ontological operators, mathematical sets, tropes (abstract particulars, perfect particulars), and concrete states of affairs.  Nominalists of course accept that there are declarative sentences and that some of them are true.  Consider the true

1. Peter is hungry.

Nominalists cheerfully admit that the proper name 'Peter' denotes something external to language and mind, a particular man, which we can call the 'ontological correlate' of the subject term.  But, ever wary of "multiplying entities beyond necessity," nominalists fight shy of admitting an ontological correlate of  'hungry,' let alone a correlate of  'is.'   And yet, given that (1) is true, 'hungry' is true of Peter.  (In a simple case like this, the predicate is true of  the the referent of the subject term iff the sentence is true.) Now philosophers like me are wont to ask:  In virtue of what is 'hungry' true of Peter?  Since 'hungry' applies to Peter in the way in which 'leprous,' 'anorexic,' and other predicates do not, I find it reasonable to put the same question as follows:  What is the ontological ground of the correct application of 'hungry' to Peter?

2. In answering this question I introduce two posits that will enrage the nominalist and offend against his ontologcal parsimoniousness.   First of all, we need an o-correlate of 'hungry.' I admit of course that 'hungry' in our sample sentence functions differently than 'Peter.'  The latter is a name, the former is what Frege calls a concept-word (Begriffswort).  Nevertheless, there must be something in reality that corresponds to 'hungry,' and whatever it is it cannot be identical to Peter.  Why not?  Well, Peter, unlike my cat, is not hungry at every time at which he exists; and for every time t in the actual world at which  he is hungry, there is some possible world in which he is not hungry at t.  Therefore, Peter cannot be identical to the o-correlate of 'hungry.' 

We are back to our old friend (absolute numerical) identity which is an equivalence relation (reflexive, symmetrical, transitive) governed by the Indiscernibility of Identicals and the Necessity of Identity.

3. But why do we need an o-correlate of 'hungry' at all?  I asked: in virtue of what is 'hungry' true of Peter?  One sort of nominalist, the 'ostrich nominalist,' will say that there is nothing in virtue of which 'hungry' is true of Peter.  For him is is just a 'brute fact,' i.e., an inexplicable datum, that 'hungry' correctly applies to Peter.  There is no need of an ontological ground of the correctness of this application.  There is no room for a special philosophical explanation of why 'hungry' is true of Peter.  It just applies to him, and that's the end of the matter.  The ostrich nominalist of course grants that Peter's being hungry can be explained 'horizontally' in terms of antecedent and circumambient empirical causes; what he denies is that there is need for some further 'philosophical' or 'metaphysical' or 'ontological' explanation of the truth of 'Peter is hungry.'

If a nominalist says that 'hungry' is true of Peter because Peter is hungry, then I say he moves in a circle of embarrasingly short diameter.  What we want to understand are the ontological commitments involved in the true sentence, 'Peter is hungry.'  We need more than Peter.  We need something that grounds the correctness of the application of 'hungry' to him.  To say that 'hungry' is true of Peter because Peter is hungry presupposes what we are trying to understand.  Apart from this diversionary tactic, the ostrich nominalist is back to saying that there is nothing extralingusitic that grounds the correct application of 'hungry' to Peter.  He is denying the possibility of any metaphysical explanation here.  He is saying that it is just a brute fact that 'hungry' applies to Peter.

4.  As for my second posit, I would urge that introducing an o-correlate for 'hungry' such as a universal tiredness does not suffice to account for the truth of the sample sentence.  And this for the simple reason that Peter and tiredness could both exist withough Peter being tired.  What we need is a concrete state of affairs, an entity which, though it has Peter and tiredness as constituents, is distinct from each and from the mereological sum of the two. 

5.  Now one can argue plausibly against both posits.  And it must be admitted that both posits give rise to conundra that cast doubt on them.  But what is the alternative?  Faced with a problem, the ostrich sticks his head in the sand.  Out of sight, out of mind.  Similarly. the ostrich nominalist simply ignores the problem.  Or am I being unfair?

Perhaps the issue comes down to this:  Must we accept the truth of sentences like (1) as a 'brute fact,' i.e. as something insusceptible of explanation (apart, of course, from causal explanation), OR is there the possibility of a philosophical account?

6. Finally, it is worth nothing that the nominalist blunders badly  if he says that Peter is hungry in virtue of 'hungry''s applying  to him.  For that is a metaphysical theory and an absurd one to boot: it makes Peter's being hungry depend on the existence of the English predicate 'hungry.'  To avoid an incoherent, Goodmanaical, linguistic idealism, the nominalist should give no metaphysical explanation and be content to say it is just a brute fact that Peter is hungry.