Hinge Propositions and Their Epistemic Importance

Reply Thu 19 May, 2011 06:52 am
In this short philosophical paper I will try to set out a theory which enunciates a certain set of propositions as the foundation of our epistemic system. I am not claiming anything original in my thesis, except that there are a certain group of propositions that I believe Wittgenstein has identified in his notes; and that these propositions form the substructure of our epistemic system. They provide a kind of backdrop that allows us to form more sophisticated language constructs. For example, our understanding of knowledge and how we use phrases like “I know that such and such is the case” and “I doubt that such and such is the case” in certain contexts and not in others; and how not understanding these contexts can cause philosophical confusion.

My main source of information will be Wittgenstein’s final work called On Certainty and his response to Moore’s papers, Proof of an External World and A Defense of Common Sense in which Moore lists a number of propositions that he claims to know with certainty. Propositions such as the following: “Here is one hand” and “There exists at present a living human body, which is my body”1 – Moore continues to enumerate other propositions that he claims to know, with certainty, to be true. These propositions provide for Moore a proof of the external world, and as such, they supposedly form a buttress against the skeptic. However, as we shall see, it is not only Moore’s claim to knowledge that Wittgenstein criticizes, but he also critiques the skeptic, and specifically their use of the word “doubt.”

It is my opinion that Wittgenstein’s response to Moore’s propositions is not entirely unsympathetic, although he argues that Moore’s propositions do not accomplish what Moore thinks they do, namely, to provide a proof of the external world; which in turn is supposed to undermine the doubts of the skeptic.

On Certainty begins with the following statement:

“If you do know that here is one hand, we’ll grant you all the rest.”2

So Wittgenstein grants that if Moore knows what he claims to know, then Moore’s conclusion follows. Nevertheless, Wittgenstein argues throughout the book that Moore does not know what he thinks he knows. However, I think we are all inclined to agree with Moore. After all, if we do not know this is a hand, then what do we know? It is this inclination to use the word “know” as Moore uses it that causes the dispute.

“Now, can one enumerate what one knows (like Moore)? Straight off like that, I believe not.—For otherwise the expression “I know” gets misused.”3

The disputes with Moore’s propositions are not only problematic; they are also very subtle disputes, which means that they are difficult to flush out. One of the problems is that we sometimes fail to see the connection between the use of the word “know,” and the use of the word “doubt,” and the logic behind that use. It is the kind of logical link that is also seen between rule-following and making a mistake - one cannot happen without the other. To know what it means to make a mistake in following a rule one must also know what it means to follow the rule correctly. Otherwise any procedure that is said to follow a rule, would be the same as following a rule. Thus there would be no difference in thinking one is following a rule, and actually following a rule. So the link between rule-following and making a mistake in following a rule is one of necessity. This can be clearly seen in mathematics where rule-following is a crucial part of understanding how to solve problems. Rule-following tells us something important about what it means to have knowledge of mathematics, and making mistakes in mathematics also tells us something important about one's knowledge of mathematics. The two go hand-in-hand.

In the following quote from Wittgenstein we can see some slight differences in the use of the word “know,” and how it accomplishes the purpose of thwarting the misgivings of another.

“’I know what kind of tree that is.—It is a chestnut.’ ’I know what kind of tree that is.—I know it’s a chestnut.’ The first statement sounds more natural than the second. One will only say ‘I know’ a second time if one wants especially to emphasize certainty; perhaps to anticipate being contradicted. The first ‘I know’ means roughly: I can say.

“But in the other case one might begin with the observation ’that’s a …’, and then, when this is contradicted, counter by saying: ‘I know what sort of a tree it is’, and by this means lay emphasis on being sure.”4

One use of the word “know” is to alleviate doubt, or even to eliminate doubt as we participate in our everyday interactions. For instance, if I say that “I know that George is guilty,” then I am simply saying that I have the proper grounds for my knowledge. Hence, if you agree, you too will acknowledge that “I know that George is guilty.” If you acknowledge that I know what I claim to know, then presumably this lets the air out of the proverbial balloon of doubt; and if you disagree with my claim, then the doubt remains. So if I make a claim to know what DNA is, and I have never studied biology, then it makes sense to have a question about my claim to knowledge. If on the other hand, you know that I have a PhD in biology from MIT, then it is very unlikely that you will doubt my claim to knowledge as it pertains to biology. Is not Moore trying to accomplish this very thing when he makes his claim to knowledge, that is, Moore is trying to negate the doubt of the skeptic by saying that he does have proof of the existence of his hands, which in turn leads to his conclusion that there is an external world. He is claiming to be in a position to know, and of course it is this assertion that Wittgenstein disputes.

Moore’s proof is supposed to show that the conclusion follows necessarily, and if it does, then the skeptic’s doubts are supposed to vanish. The proof would look something like the following:

1) Moore has knowledge that he has two hands.
2) Moore makes the inference from the fact that he has two hands, to the conclusion that there exists an external world.
3) Hence, Moore knows that an external world exists.

Wittgenstein is challenging the first premise in the above argument; more specifically, he is challenging Moore’s claim that he has knowledge of his two hands. Having knowledge of something presupposes that there are good reasons to believe it, but exactly what is it that Moore has knowledge of? He claims to have knowledge of the existence of his hands, but what would count as evidence for such a claim? Do I know that I have hands because I check to see if they are there every morning? Do I make a study of my hands, and thereby conclude that I do indeed have hands? I have knowledge of chemistry, physics, history, epistemology, and other subjects, and there are ways to confirm my knowledge. However, in our everyday lives do we need to confirm that we have hands? And do we normally doubt such things?

“When Moore says he knows such and such, he is really enumerating a lot of empirical propositions which we affirm without special testing; propositions, that is, which have a peculiar role in the system of our empirical propositions.

“Even if the most trustworthy of men assures me that he knows things are thus and so, this by itself cannot satisfy me that he does know. Only that he believes he knows. That is why Moore’s assurance that he knows…does not interest us. The propositions, however, which Moore retails as examples of such known truths are indeed interesting. Not because anyone knows their truth, or believes he knows them, but because they all have a similar role in the system of our empirical judgments.

“We don’t, for example, arrive at any of them as a result of investigation.”5

Wittgenstein’s argument is not only with Moore’s use of the word “know,” but also with the use of the word “doubt” by the skeptic. I believe Wittgenstein is not only saying that Moore’s use of the word “know” is senseless,6 but also that the skeptic’s use of the word “doubt” is senseless. The first question we need to ask ourselves is - “Does it make sense to doubt?” For example, does it make sense to doubt whether the earth is more than 100 years old? What would a doubt here look like? Do we question whether or not our desks still exist when we are not looking? Do people who have known us for years question whether our name really is what we say it is? If one is to doubt, then one needs good reasons to doubt, just as one needs good reasons for knowledge claims. We could understand the doubt of the skeptic if occasionally there were reasons to doubt that we lived on the earth, or that occasionally my hands actually turned out to be someone else’s hands, but we do not observe anything of the kind. And even in cases where we can understand doubting such propositions, the circumstances that give rise to such doubts tend to be very unusual. The point is that we recognize the difference. Both of these activities (knowing and doubting) are rule-governed, and take place within a practice of making empirical judgments. Our system of doubt and knowledge are formed because the world stands fast for us. If it did not, then we would not be able to form a coherent system of knowledge and doubt. One wonders if language would even get off the ground.

Another point made by Wittgenstein in relation to Moore’s propositions is the following:

“Moore’s view really comes down to this: the concept ‘know’ is analogous to the concepts ‘believe’, ‘surmise’, ‘doubt’, ‘be convinced’ in that the statement ‘I know…’ can’t be a mistake. And if that is so, then there can be an inference from such an utterance to the truth of an assertion. And here the form ‘I thought I knew’ is being overlooked.—But if this latter is inadmissible, then a mistake in the assertion must be logically impossible too. And anyone who is acquainted with the language-game must realize this – an assurance from a reliable man that he knows cannot contribute anything.”7

What Wittgenstein seems to be asserting is that Moore’s use of the word “know” seems to force us to conclude that he knows based on his assertion that he knows. Wittgenstein continues with:

“It would surely be remarkable if we had to believe the reliable person who says, ‘I can’t be wrong’; or who says ‘I am not wrong’.”

Later Wittgenstein states that if one knows that something is the case, then it must be shown objectively. Again, ones claim to knowledge contributes nothing.9

It is as though Moore’s propositions come down to a state of knowing – a feeling of certainty, which is subjective; and this needs to be juxtaposed to the kind of certainty that is a result of objective verification. Wittgenstein seems to point this out when he remarks that

“…’I know’ gets misused. And through this misuse a queer and extremely important mental state is revealed.”10

Moore’s propositions appear to be more the result of an inner feeling of certitude, or an inner conviction. For example, my subjective certainty that I have hands, or that I have a body is a certainty that is shown by the way I act, as opposed to having arguments that prove it. One can see this kind of certainty even in animals. For instance, an animal will express its belief or certainty that it is about to be fed by its actions – the wagging of its tail, or the action of jumping up and down as the food is prepared. I may express my belief or certainty propositionally, but what is going on is an outer expression (my actions or the dog’s actions) of an inner belief.

The problem is that when we try to express our subjective beliefs with one another in the course of dialogue, the only way to do it is with statements or propositions. I am inclined to say “I know” because of an inner feeling of certainty, and herein lay the crux of the problem; because knowing and doubting only occur in language-games, and language-games only take place between people. The proposition that “I have hands” is not the result of my knowledge, but is the result of an inner certitude out of reach of any objective evidence. The beliefs that Moore claims he knows are based on a causal connection between our sense experiences, which take place as we interact in the world, and the beliefs that are formed as a result of those experiences. They are not a matter of knowing. Moore's inclination to say that he knows is one that proceeds from his subjective certainty, and this is much different from knowledge, which is the result of objective facts.

“One says ‘I know that he is in pain’ although one can produce no convincing grounds for this.—Is this the same as ‘I am sure that he…’?—No. ‘I am sure’ tells you my subjective certainty.”11

A further point is that we do not play the language-game of “knowing” and “doubting” by ourselves, because knowing and doubting is an activity that happens between people. It is not a language-game that you can do alone; I believe this is similar to the idea that Wittgenstein put forward in The Philosophical Investigations, namely, that we cannot have a private language, which goes to the notion of making mistakes and rule-following.12 Compare this with “knowing” and “doubting,” which can only take place where there is resolution. One does not play the language-game of resolution (that is, resolving knowledge claims and doubts) with oneself.

If Moore’s propositions are not the kind of propositions that can be known or doubted – what are they? After all, a basic definition of a proposition is that it is a statement that either asserts that something is the case, or that something is not the case; and since Moore’s statements do not seem to fall into the category of being true or false (as Wittgenstein defines them), then they must be something else – but what? I am going to refer to these propositions as “hinge propositions.” Wittgenstein makes reference to “hinge propositions” in his notes On Certainty (paragraphs 341, 343, 655, etc), so I will borrow the phrase from him.

What are hinge propositions? We already have a clue, because Moore has given us some examples of these kinds of propositions unknowingly. The following is a list taken in part from Wittgenstein’s <span style="font-style:italic;">On Certainty</span>:

1) I live on the earth.
2) I am a person.
3) My name is Bill Smith.
4) This is a tree.
5) 2x2=4

According to Wittgenstein justification comes to an end,13 however, I want to say that justification ends with hinge propositions, which in turn brings us to bedrock. I say "part of the foundation," because I believe the world is also foundational. Hinge propositions are the result of our subjective certainty, and it is from here that we launch into a world of objective certainty (knowledge) as language takes hold between people. Therefore, what forms the backdrop or launching point for us - is the world, and in particular - hinge propositions.

What makes hinge propositions foundational is that they lay outside our epistemic system, and we build our epistemic system on top of them. They lay outside our epistemic system because they can neither be known nor doubted, which means that they can neither be justified nor disbelieved. If they cannot be sensibly justified nor disbelieved, then justification ends with hinge propositions.

Another facet to Wittgenstein’s method is to show that when we justify any proposition using evidence, we do so with propositions that are stronger than the propositions we are defending. We do not do it with weaker propositions – weaker propositions do not support stronger propositions. Wittgenstein illustrates this point in the following passage:

“One says ‘I know’ when one is ready to give compelling grounds. ‘I know’ relates to a possibility of demonstrating the truth. Whether someone knows something can come to light, assuming that he is convinced of it. But if what he believes is of such a kind that the grounds that he can give are no surer than his assertion, then he cannot say that he knows what he believes.”14

Bedrock is the strongest part of the foundation, or the structure; one does not use 2x4’s to support 10x10’s, which is the point of the passage. What holds up bedrock? Nothing holds up bedrock, which is why it is called bedrock. Again, we have come to the end of justifications, and we have arrived at hinge propositions, which form the bedrock of our epistemic system.

In his paper Wittgenstein On Skepticism Duncan Pritchard says that one of the problems with the non-epistemic approach to hinge propositions has to do with the closure principle.15 The closure principle simply states the following:

If S knows that p, and S knows that p entails q, then S knows that q.

The problem is that when we use the closure principle we can seemingly justify hinge propositions. Consider the following example based on what Wittgenstein says in the following passage:

“It is certain that after the battle of Austerlitz Napoleon … Well, in that case it’s surely also certain that the earth existed then.”16

So using the closure principle we can supposedly justify hinge propositions in the following way:

If John knows that the battle of Austerlitz occurred in 1805, and John knows that the battle of Austerlitz entails that the earth has existed for a long time, then John knows that the earth has existed for a long time.

And since the proposition that “The earth has existed for a long time” is a hinge proposition – it follows then that one can know, what one is not supposed to know. Is this really a problem; are we in fact justifying a proposition that cannot be justified? It certainly seems so.

If it is true that hinge propositions are a matter of subjective certainty, then the closure principle really does not apply. My subjective certainty is neither strengthened nor weakened by the closure principle. There may be causes of my inner certainty, but I do not infer from other propositions that I have knowledge of my hands.

These propositions have nothing to do with reason, and this becomes clear if we consider the following example: Suppose I was the only living person, and also suppose that there is no language, after all who would I talk too, one could still imagine that I would have the subjective certainty that I have hands, or that I had a body, etc. This would be the case without any formal knowledge. There would be no one to convince; I would not conclude by any formal system of knowledge that something was or was not the case. All of my beliefs would be subjective certainties. Hence, to conclude that John could infer from some fact that he knows the earth has existed for more than 100 years is to not understand the nature of hinge-propositions - anymore than a dog’s subjective belief that it is about to be fed could be strengthened by some objective fact. That is not to say that objective facts are not part of what is being observed, it is only to point out that one does not infer from the objective facts to the conclusion that I have two hands. The nature of these subjective beliefs is not a matter of reason. I simply find that I believe these propositions (hinge propositions) based on causal interactions with the world, and the evidence that I believe them is in my actions.

Another important point to be made is that because we are able to describe bedrock beliefs in terms of propositions, this does not mean that bedrock beliefs are like other beliefs based on propositions. Think of the example I gave earlier about the dog's belief that it is about to be fed. Even though it is true that I can describe the belief using propositions, this does not mean that the belief itself occurs within language. It is quite prior to language. In fact the dog will never develop a language, nor will it develop an epistemic structure that can be used to justify beliefs. Understanding how these beliefs are formed is crucial to understanding if they can be justified; and this is true even if you <b>can</b> plug them into the closure principle. Can we plug the dog's belief into the closure principle and justify them in the same way? If not, why not?

If these beliefs are not based on reasons or evidence, then how do these beliefs form? The answer to this question is that there is a causal connection between our sense experiences and the world around us. Causally based beliefs provide an explanation as opposed to giving a reason. For example, Mary believes that snakes are to be feared because she was bitten by one - this is a causally formed belief. There is a causal relation between being bitten and her belief that snakes are to be feared. This explains her belief, but does not give reasons for it. If Mary was to give reasons for her beliefs she would say something like the following: I believe snakes are to be feared because they bite, because some are poisonous, and because some can squeeze the life out of their victims with their powerful constricting muscles. These are reasons or evidence for a belief as opposed to forming a belief based on causes.

These causally based beliefs are clearly seen in my earlier example of the dog's belief. The dog is not able state its belief, and yet we are clearly able to observe what it believes by watching its actions. This same feature can also be observed in the actions of babies or toddlers. As a baby interacts with the world through its senses it forms beliefs. The baby learns to interact with the world by moving its limbs. As time goes on the baby learns that it can pick things up with its hands. The baby will even show its beliefs, as the dog did, when preparing its food. All of these beliefs are causally formed by the interaction of the child through its sense experiences and the world.

These causally formed beliefs are what form the bedrock of all our knowledge. They are subjective certainties that allow us to progress in terms of language. Then language allows us to create more sophisticated beliefs (language-games) in terms of knowledge. However, this is only done within the scope of language.

The foundation then of our epistemic system is not a set of propositions that are justified, or known to be true or false by any epistemic method. They are not justified by argument, inference, or proof; they are not justified by testimony; they are not justified by experience; they are not justified linguistically; nor are they tautologically justified. They are simply subjective certainties that are shown by our interactions with one another, and our interactions with the world. I believe they also form the basis from which we build a language, and from which we form our systems of knowledge and doubt. And it is in this sense that they are important to our epistemic considerations; and it is in this sense that they are foundational, or more to the point, they are bedrock.


1 Published in Contemporary British Philosophy (2nd series), ed. J.H. Muirhead, 1925, Reprinted in G.E. Moore, Philosophical Papers (1959), p. 1.

2 Wittgenstein, L. (1969), On Certainty, (eds.) G.E.M. Anscombe & G.H. von Wright, (tr.) D. Paul & G.E.M. Anscombe, Blackwell, Oxford, p. 1.

3 Wittgenstein 2.

4 Wittgenstein 77.

5 Wittgenstein 20.

6 Wittgenstein 10.

7 Wittgenstein 5.

8 Wittgenstein 5.

9 Wittgenstein 4.

10 Wittgenstein 2.

11 Wittgenstein 74.

12 Wittgenstein, L. (1958), Philosophical Investigations, (eds.) G.E.M. Anscombe & R. Rhees, (tr) G.E.M. Anscombe, Blackwell & Mott, New York, p. 81.

13 Wittgenstein, L. (1969), On Certainty, (eds.) G.E.M. Anscombe & G.H. von Wright, (tr.) D. Paul & G.E.M. Anscombe, Blackwell, Oxford, p. 27.

14 Wittgenstein 32.

15 Pritchard, D. (forthcoming) Wittgenstein On Scepticism in the Oxford Handbook to Wittgenstein, (ed.) M. McGinn, OUP, p. 15-17.

16 Wittgenstein, L. (1969), On Certainty, (eds.) G.E.M. Anscombe & G.H. von Wright, (tr.) D. Paul & G.E.M. Anscombe, Blackwell, Oxford, p. 26.



Moore, G. E. ‘A Defense of Common Sense’, Contemporary British Philosophy (2nd series). Edited by J. H. Muirhead, Allen and Unwin, London, 1925.

Pritchard, D. Wittgenstein On Scepticism in the Oxford Handbook to Wittgenstein. Edited by M. McGinn, OUP, (forthcoming).

Wittgenstein, L. On Certainty. Edited by G. E. M. Anscombe & G. H. von Wright. Translated by D. Paul & G. E. M. Anscombe, Oxford: Blackwell, 1969.

Wittgenstein, L. Philosophical Investigations. Edited by G. E. M. Anscombe & R. Rhees. Translated by G. E. M. Anscombe, Blackwell & Mott, New York, 1958.

June 21, 2009

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