## An Analysis of On Certainty

Discussions on the nature of being, existence, reality and knowledge. What is? How do we know?

### Re: An Analysis of On Certainty

At one time, Wittgenstein claimed that he had not read Aristotle but that he in fact had read Plato! How can any philosopher not have read Aristotle, even if only nothing more than as a foil for Plato? Not so surprisingly, this attitude is reflected in Wittgenstein's work. So much so, that an understanding of Wittgenstein requires reference back to Plato's epistemology.

In one of the earlier dialogues, the Meno, Plato has the Socrates character working to develop the nature and mechanics of formal relations in a world of universal abstractions. Similarly, in the Tractatus, Wittgenstein goes on to develop the logic of a world of universal language.

In the Meno, Socrates asks: What would it take to teach Virtue? Of course, one would first have to know what Virtue is. Many people have the correct opinion, but to know is rare if not unique. According to Plato exceedingly high standard, it is not enough to have justification one's belief, like I learned it from a wise teacher, but it must also be bound by aitias logismos, by a worked out explanation. This hints at understanding rather than just knowledge by aquaintance.

Wittgenstein, in On Certainty says
11. We just do not see how very specialized the use of "I know" is.
12. - For "I know" seems to describe a state of affairs which guarantees what is known, guarantees it as a fact.

However,
14. That he does know remains to be shown.
15. It needs to be shown that no mistake was possible. ... it needs to be objectively established that I am not making a mistake about that.

Of course, Moore knows no such thing. He has true belief. But what is his belief based on? How does he know?
9. Now do I, in the course of my life, make sure I know that here is a hand - my own hand, that is?

### Re: An Analysis of On Certainty

For those of you who are interested in a more complete thread on Wittgenstein go to http://forums.philosophyforums.com/thre ... 41631.html.
Sam26
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### Re: An Analysis of On Certainty

If one takes truth to be that which is immune from refutation, knowledge cannot be a belief that is both justified and true; for no belief can be free of all doubt. The same may be said of falsity, if one takes it to be that which is immune from refutation. There is no infallible arbiter of truth that holds court for mere mortals.

Unfortunately, the human condition is such that truth can be no more than a justified belief. However, one man’s justification is another’s man nonsense. Therein lies the problem.

Plainly put, we say that a belief is justified when virtually everyone finds it credible and those who claim to find it incredible act as though it is true. Here I refer to that thing for which all philosophers have the greatest contempt—namely, “common sense.” The latter really refers to the common experience of all mankind.

In the final analysis, all logic consists of inferences derived from that experience. Thus, no argument in support of any claim of truth or falsity cannot but presume some feature of experience common to us all. If this were otherwise, all logic would proceed from hypothesis, and truth would be no more than supposition.

It is part of that common experience that each of us exits, that others with similar dispositions also exist and that we are able to communicate with them by means of language. To say otherwise is to render “proof” meaningless, for we are always directing proofs to others.

Indeed, when we speak of language and even “language games,” we are presuming that others exist; for language is the vehicle of communication with others, and if we are “playing language games” we must be playing them with others that exist.

Thus, to say that we can prove that others exist is to presume that they exist, for proofs are meant to convince others. Obviously, we cannot prove to others that they do not exist. The mere fact that we would go through such an exercise is itself a demonstration that we do in fact believe that they exist. I do not know how to put it plainer than that.

Thus, Kant, Wittgenstein and even Berkeley were constrained to presume that others exist, for to do otherwise would be to render their “proofs” utterly incredible.

It is part of my experience of the world (that I suspect is shared by many others) that people like Berkeley who claim that the body is illusory are the first to run to a doctor to treat an injury to their “imaginary bodies.” In other words, they deny that they have bodies but act as though they do. This exposes what they cannot help but believe. Indeed, only a madman actually believes that he does not have a body.

Who really believes that our senses are deceiving us completely because they place all in a context of space and time when space and time do not exist outside of us? Kant would be the last person to stand in front of a speeding train to express his belief in such a proposition. Regardless of what he said, he could not really believe it; for the very constitution of his humanity forbad it.

Does this mean that all our thinking and analyzing is no more than “a mind game”? I think not.

To my way of thinking, the whole matter is reduced to a question of burden of proof. Who has the burden to prove that our senses do not in any way provide a truth corresponding to that which lies outside of us? Is it the one who proposes it or is it the collective experience of all mankind that opposes it?

This is the crucial question, for neither the proponent nor opponent of such a proposition can really prove his case. Surely, the general experience of all mankind raises at least a “prima facie” case for the opponent. This cannot but shift the burden of proof to the proponent who must face the fact that he cannot possibly prove his case.

However, this only means that we are justified in accepting the truth of the fundamental experiences common to us all—not that they are absolutely true.” They are “true” only in the sense that they appear to be true and cannot be proved to be false and not in the sense that we can prove that they are true. For “proof” cannot apply to that which we cannot help but believe. What we call “proofs” are really inferences derived ultimately from such shared beliefs. This expresses the fundamental limitations of the human condition.
Neri
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### Re: An Analysis of On Certainty

I appreciate your critical attitude toward standard concepts, in this case the accepted formula that knowledge is justified true belief (JTB), which is usually repeated and defended by rote without adequate critical consideration. The greatness of Wittgenstein is partially in his critical insight into this concept. JTB originates in Plato's Theaetetus where he rejects a number of interesting candidates for the definition of knowledge, including the ones you propose. In the end, he leaves this definition hanging, open for further discussion.

There are two general classes of propositional, descriptive knowledge, which is all that is under consideration in Plato and also in modern analytic philosophy. Propositions are formal statements of fact, much more restrictive than normal speech.

The first class is scientific knowledge or publicly acknowledged facts. The second derived from personal observation or deduction. Plato and Aristotle were generally concerned with the first type, which produces definitions and universals. JTB does not apply equally to both of these types (Moore's error).

There are plenty of scientific facts that are justified. Otherwise these would not have become facts. To be considered public knowledge, they only have to be considered as provisionally true and justified by a consensus of experts. Universal belief is not required.

For me to know any of these facts does require that I believe the facts to be true and justified, and to accept that my justification is valid as well. If I believe some proposition because I read it in a book, then that book must also be authoritative. In reverse, If I know as a fact that I know, then all the above are necessarily true.

### Re: An Analysis of On Certainty

YY,

What is a “fact” if not a true statement? This only returns us to the question, “What is truth”?

I argue that truth cannot refer merely to coherent thinking--that it must refer ultimately to a correspondence of our beliefs to that which lies outside of us. When I say “us/we,” I refer to human kind. When I say “outside of us,” I mean outside of the consciousness of all individual human beings.

We are justified in believing that we can recognize a real object, because the representation it stimulates in our consciousness (sense object) is duplicated each time the same or similar real object is encountered. It follows, if this is so, that the relations among sense objects correspond to the relations among real objects.

Because the last paragraph sets forth the convictions common to all mankind, those who would propose otherwise have the burden of proof--a burden they cannot satisfy. Rather, they take the position that because such common beliefs cannot be proved, that they are false. In other words, they conspire to transfer a burden that rests with them.

“Scientific knowledge or publicly acknowledged facts,” like all knowledge, is rooted in sense impressions, which I call “direct observation.”

When I say all knowledge is rooted in direct observation, I do not mean that all knowledge is limited to direct observation. Clearly we have the power to infer the existence of things not directly observed. However, we must have facts from which we infer other facts, and this process must ultimately regress to facts directly observed. Otherwise, deductive reasoning would be impossible.

My views on JTB are to be found in the topic, “JTB is Rubbish,” to be found on page 6 of this section.
Neri
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### Re: An Analysis of On Certainty

It is usually held that facts, whatsoever they are, are not true statements themselves but the things in virtue of which true statements are true; their truthmakers. Now, the phrase, "it is a fact that…" may simply be a null sentential operator, behaving much like the truth predicate does according to deflationary theories of truth. This is not to say that the common notion of facthood is a linguistic matter however.
Consider, as a trivial example, the publicly-acknowledged facts you cite. If such things as these are to be identified with types of true statement, ergo true sentence, then I would be in a position to acknowledge two facts and not just one if I understood both the true sentences, "Der Schnee ist weiß" and "snow is white", for these are clearly different sentences. It is needless to say that this is counter-intuitive, which indicates the problem with considering facts as kinds of statements.
Zin5ki

### Re: An Analysis of On Certainty

Zin,

At the risk of quibbling, I will say that a statement is a declaratory sentence that purports to be true (a proposition). If we say a proposition is true only if it corresponds to a fact, we are making the metaphysical commitment that--

(1) Facts exist independently of us and do not depend upon our contemplation of them and, as a consequence, the world consists of facts.

And the epistemic commitment that--

Commitment (1) has an immediate intuitive appeal. After all, we know that “facts are stubborn things.” For example, if one’s physician declares--“you have lung cancer”—no amount of disbelieving, wishing or hoping can change the fact to which the physician’s declaration corresponds.

Thus, we seem constrained to admit that the existence of a fact does not require our assent, for a fact is a thing whose reality does not depend on our awareness of it.

One assumes, of course, that the physician’s declaration is conclusively established by X-rays and other diagnostic tests, as well as by a pathologist’s analysis of biopsied lung tissue [commitment (2)].

But what are we calling a fact in this example?

We are referring to a change in the composition of the lung, such that some of its cells have changed their appearance in a way that makes them recognizable as cells having the capacity to grow so rapidly that they can cause wide-spread interference with bodily functions and threaten the continuation of life.

Thus, what actually exists outside of our thoughts is a process, a series of events that changes the character of the entity we call a body. There is no singular “fact” at work. What we call a fact is nothing more than our acknowledgment that this process is continuing at the time the fact is stated. Facts are the linguistic things by which we singularize:

(a) A process, event or thing; or
(b) The relations included in an event or process; or
(c) The relations among individualized things.

To individualize a thing, we must be able to recognize it by the sensation it causes in our brains. The qualities we give to a thing depend upon the extent to which we are sensitive to aspects of it. Aspects of a thing exist, but not necessarily in the way that we perceive them.

[For example, “white” as a color exists only a sensation; yet it corresponds to the fact that snow reflects a certain wave-length of electromagnetic radiation. Thus, both “Snow is white” and “Der Schnee ist weiss” purport to be true in the sense that each claims a correspondence to the same fact.]

However, the world does not consist of facts, as such. Facts express reality in a way that is peculiar to our mode of thinking, which is to construct summarized declarations that are true in the sense that they correspond, in a general way, to (a), (b) or (c) above--the presumption being that the latter are realities independent of our contemplation of them.

So that, if, after a biopsy and a whole battery of tests, one is told by his physician, “you do not have lung cancer”-- one might say that “his not having lung cancer” is a fact. Yet, it cannot be the case that “his non-lung-cancer” exists as a singular entity independently of anyone’s consciousness of it. In other words, a fact can exist but a “non-fact” cannot; for the latter refers only to the non-existence of a fact. Thus, “a fact” is seen to be a kind of linguistic convention.

More significantly, not everyone is prepared to make the commitments referred to above. For example, as to commitment (2) Kant argued:

:"(...) Truth, it is said, consists in the agreement of cognition with its object. In consequence of this mere nominal definition, my cognition, to count as true, is supposed to agree with its object. Now I can compare the object with my cognition, however, only by cognizing it. Hence my cognition is supposed to confirm itself, which is far short of being sufficient for truth. For since the object is outside me, the cognition in me, all I can ever pass judgement on is whether my cognition of the object agrees with my cognition of the object. [Kant, Immanuel (1801), The Jäsche Logic, in Lectures on Logic. Translated and edited by J. Michael Young (Cambridge: Cambridge University Press, 1992), pp. 557-558.]

Further, philosophers of the stature of George Berkeley have rejected both commitments (1) and (2).

The question is presented, therefore: Can commitments (1) and (2) be properly regarded as unimpeachable? They clearly cannot, when great minds have presented imposing arguments to the contrary.

Some (myself included) have argued that the burden of proof rests with those who would deny these commitments; for if they cannot be disproved, it may be said that we are justified in believing them. However, if we cannot prove what we believe, we cannot properly make the claim that we have captured truth.
Neri
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### Re: An Analysis of On Certainty

Thank you kindly for your detailed response, Neri. I appreciate your dedication.

Your thesis that facts are linguistic entities is, as I take it, motivated by two broad concerns.

Firstly, the problem of which objects "come together" in such a way as to instantiate a given fact, such as the fact conveyed by the assertion, "you have lung cancer".
Secondly, the related problem of which facts correspond to negative assertions, such as "you do not have lung cancer".

These are indeed valid concerns, especially to a logical atomist such as Russell. I fail to see how these suffice to dispel the notion that facts are non-linguistic though.

Concerning the first issue, it indicates only that identifying the parts of which facts consist, and the relations in which such parts stand, is not a straightforward task, for it will often involve citing universals and abstract objects (inter alia). Of course, the world as it is may not be as it appears to us, as your Kantian concern would indicate, though this would turn facthood into something somewhat anthropocentric, without eo ipso turning it into something strictly peculiar to language.

Concerning the second issue, it only serves to underline my previous concession that there are uses of the term "fact" that are merely linguistic devices: "His not having lung cancer is a fact" is, I grant, merely used in a deflationary fashion to assert that he doesn't have lung cancer. This does not demonstrate that all uses of the term "fact" are to be understood in this fashion though. Pace the Kantian concerns you cite, there are still many cases where readily identifiable states of affairs are intuitively appropriate to identify as facts. In these cases, we wish to say that the term "fact" successfully denotes some such thing, as opposed to assigning the word a less substantial role.
Zin5ki

### Re: An Analysis of On Certainty

Zin,

I should like to make a few points of clarification (which are no doubt necessary because of the imprecision of my explanations). A good place to start is with Kant.

I do not believe that this philosopher used “fact” in connection with his concept of truth. In a sense, Kant did position truth as anthropocentric; for to him a proposition could only be “true to us” and never--by reason of a correspondence to what lies outside of us-- “true in itself”.

Kant’s truth arises from our peculiarly human way of thinking. Because, the latter is expressed through our languages, to him there existed a parity between the content of human languages and the content of human thoughts. His truth was no more than the coherence of our thinking when taken as a whole, as expressed through language.

In a certain way, I adopt this epistemology; but in another more important way, I reject it.

First of all, the notion that the world consists of facts seems a bit silly. Facts are not concrete things. We cannot weigh or measure facts nor can we capture them in a jar like insects. The world consists of matter, energy, events, recognizable things and the relations among them. Facts are justified statements about such things.

If we say that a proposition is true only if it corresponds to a fact [and if we ignore the contradiction inherent in saying that a single fact may be multiple] the following will hold:

The proposition, “I have cancer,” is true only if it corresponds to the fact that I have cancer.

On the other hand, if we assume that I do not have cancer, the following will hold:

The proposition, “I do not have cancer,” cannot be true only because it corresponds to a fact; for it is true precisely because it does not correspond to the fact that I have cancer. This would be otherwise only if non-facts were real entities, and we amended the analysis to say that a proposition is true only if it corresponds either to a fact or to a non-fact. However to say that non-facts exist is to equate existence with non-existence, and this is nonsense.

Yet, there must be such a thing as truth, for a declaration that affirms a proposition and one that denies the same proposition cannot both correspond to reality. That which distinguishes propositions such as, “I have cancer” from “I do not have cancer” is truth. Both propositions cannot be true, but one must be true. In this way, truth is seen as a certainty. However, even if we grant that there is such a thing as truth, the question remains: Is truth something within our grasp?

Kant observed that "(...) Truth, it is said, consists in the agreement of cognition with its object.” [ibid.] It can also be stated as “the agreement of a statement with reality” or even “the correspondence of a proposition with a fact.”

Statements and propositions, of course, are not only linguistic but also cognitive. They are conscious judgments. “An object,” like “a fact” and “a reality,” are said to lie outside of us.

However, Kant argued that this correspondence definition of truth is only nominal, because we have no way of comparing real things with the judgments we make of them. All we have are the judgments themselves. To put it another way, he claims that we have no access to what lies outside of us and hence cannot know what is true by way of correspondence. This says, in effect, that the senses are useless.

Because this argument has been widely accepted, it has brought metaphysics to a dead end. Nonetheless, there is a viable alternative.

Most will admit that when a given thing outside of us excites the senses, it puts in motion a process that eventually causes the brain to create a conscious experience (sensation) which the brain assigns to that thing by way of memory. This is a representation which persists long-term in memory.

It is certainly reasonable to believe that whenever the same or similar thing is before us, a same or similar representation will again be assigned to it in memory. When the current representation (sensation) is compared with the past representation consigned to long term memory (conception), we are able to recognize that the perception agrees with the conception. Thus, although we are only comparing cognitions, we are able to know when their objects are the same or similar.

Because we can, in this way, identify what Kant called “objects of cognition,” we are also able to know when such objects of the same sort are interacting with each other in time and space. Further, we are able to know the relations among all objects of cognition, simply because the relations among their cognitive representations will necessarily agree with the relations among the objects they represent. This is our window to reality.

Of course, this analysis will not appeal to those who believe that nothing material exists and that, as a consequence, we do not have bodies. Certainly, the conclusions I have just put forward can neither be proved nor disproved beyond all doubt. [The same may be said of the Kantian view.] However, because my analysis is logically justifiable, does not render the senses useless and gives us a foothold in reality, it should appeal to reasonable minds.
Neri
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### Re: An Analysis of On Certainty

Thank you for your clarifications, Neri. Alas, there remain several persisting points of contention between us.
Neri wrote:First of all, the notion that the world consists of facts seems a bit silly. Facts are not concrete things. We cannot weigh or measure facts nor can we capture them in a jar like insects. The world consists of matter, energy, events, recognizable things and the relations among them. Facts are justified statements about such things.

I see not how this demonstration follows. You make the straightforward point that facts, unlike spaciotemporal objects, lack certain worldly properties. You then make the point, amenable to many except Wittgenstein, that the world is not made of facts. These premises are insufficient, however, to motivate the position that facts are to be type-identified with linguistic entities. Everything you have stated is consistent with what Russell said of facthood in his first 1918 lecture on logical atomism, and therein Russell explicitly avoided the anthropocentricity you posit.

Now, whilst it is appropriate to use the problem of "false facts" as grist for your mill, it should be stated that there exists an initial response to it. Consider Russell again:
Bertrand Russell wrote:If I say, “Socrates is dead”, my statement will be true owing to a certain physiological occurrence which happened in Athens long ago. If I say, “Gravitation varies inversely as the square of the distance”, my statement is rendered true by astronomical fact. If I say, “Two and two are four”, it is arithmetical fact that makes my statement true. On the other hand, if I say, “Socrates is alive”, or “Gravitation varies directly as the distance”, or “Two and two are ﬁve”, the very same facts which made my previous statements true show that these new statements are false. (The Philosophy of Logical Atomism, Routledge, p.7.)

In your case, it would be the fact that your body is healthful in relevant respects—a fact that owes itself to measurable, concrete objects, events and relations—that renders the proposition, "I do not have cancer" false. In this way there is scope for retaining the notion that only facts, as opposed to non-facts, are the sole determiners of every proposition's truth value.

Of course, Russell's programme encounters difficulties when we consider the relation between facts and propositions, which is where the Tractatus rears its baffling head.

I wish now to turn to another matter.
Neri wrote:Because this argument has been widely accepted, it has brought metaphysics to a dead end.

I do not actively study Kant, but I am nevertheless sceptical of this. As the history of the analytic tradition shows, metaphysics has hardly lingered at a dead end since the initial popularity of the first Critique.
Zin5ki

### Re: An Analysis of On Certainty

Zin,

If I say, “the tooth fairy does not exist,” and you say, “the tooth fairy exists,” what are the very same positively existing facts that make one statement true and the other false?
Neri
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### Re: An Analysis of On Certainty

In this case, we would have to consider a large conjunction of states of affairs. Consider the state of affairs according to which none of the properties, or sets of properties, you instantiate are sufficient for you to be the tooth fairy. Moreover, certain properties you do instantiate preclude it being true of you that you are the tooth fairy. Now consider the broader state of affairs according to which this is the case for you, and for me, and indeed for every other thing that exists. It is this conjunction of obtaining states of affairs that determines the truth values of the utterances you consider.

To put this into context, if we wish to follow Russell's account of denoting phrases from On Denoting, uttering the statement "the tooth fairy does not exist" would assert a quantifier expression towards the effect of this: For all things, those things are not the tooth fairy, or something akin. We make a statement about all objects failing to be sufficient to be identified with the entity in question, and we do so in such a way as to specify that it is the things which are true of existent objects that determines this.

It might strike one as odd that we are making a generalising statement about all objects when declaring something not to exist, but the strength of such a claim—that there are no tooth fairies in the entirety of existence—would require this, and this is respected in the epistemology relating to it.

I hope that this illuminates how positive facts, such as those according to which object instantiate or fail to instantiate particular properties, act as the truthmakers for negative existential claims.
Zin5ki

### Re: An Analysis of On Certainty

Zin,

As near as I can tell, what you are saying amounts to no more than this:

All of our experience of the world is inconsistent with the existence of a tooth fairy--so that while the proposition that “the tooth fairy does not exist” is true, it does not itself correspond to a fact.

But if the proposition that “the truth fairy does not exist” bears truth but does not itself correspond to a fact, it violates the correspondence theory of truth which holds that a proposition is true only if it corresponds to a fact. Therefore, your argument is self-defeating.

What you are talking about is not correspondence but justification. In essence, you are saying that the evidence (so far as we may know it) does not justify a belief in tooth fairies. This is a judgment (cognition, as Kant called it) which finds expression in “the tooth fairy does not exist.” There is a parity between the judgment and the statement (in whatever language the latter may appear). In another words, the truth of the statement arises from the judgment which gives it voice.

This is made all the more evident in statements such as “Big Foot does not exist;” or “the Loch Ness Monster does not exist.” There is nothing in our general experience of the world that would forbid the existence of creatures such as Big Foot or the Loch Ness Monster. However, because the evidence is so far insufficient to establish the existence of these creatures, we are justified in believing that they do not exist. Therefore, the quoted statements may properly be taken as true in the absence of convincing evidence to the contrary.

Returning to the Bertrand Russell quote--Is the proposition that “gravitation varies inversely as the square of the distance” unimpeachably true? Indeed, is the proposition that “gravitation is covariant with respect to arbitrary continuous transformations of space-time co-ordinates” unimpeachably true? As inductions, we know that both are subject to falsification by newly discovered data. In other words, scientific theories, like everything else are determined judgmentally by the weight of available evidence and hence cannot be taken as “absolutely true.” They are true only in the sense that they are presently justified.

Is 2+2=4 true in the sense that it corresponds to a fact?

It is interesting to note that the Japanese language has both “counting numbers” and abstract numbers. For example, there is a word for two books and another word for two sweets. If one adds the word for two books to the word for two sweets, one does not get four of anything. One simply gets an assemblage of two books and two sweets. Of course, if one adds the abstract “2” to the abstract “2,” one gets the abstract “4.” The first approach refers to concrete things outside of us. The second refers to ideas.

Because in English, we only have abstract numbers, our numbers are only ideas. This does not mean that 2+2 does not equal 4. It means only that this simple equation does not correspond to an existing entity outside of us. It is true to us all by reason of a judgment immanent to the human thought process.
Neri
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### Re: An Analysis of On Certainty

It behoves me to state, on the contrary, that I have given an account of what a fact to which the truth of the sentence in question corresponds would be: a very large conjunctive state of affairs according to which the world, in effect, excludes the tooth fairy.

I must refute your claim that I have issued an account of epistemic justification instead of a metaphysical sketch, through which you dismiss my claim. The ontology of facthood, which concerns me currently, is a distinct issue to that of how we may come to believe in a certain fact. What you note about our experiences being insufficient to exclude the existence of Big Foot (et cetera) does nothing to undermine my account of what it would be for there to be a fact that makes the statement "Big Foot does not exist" true. Your claims instead moot the possibility that there may be no such fact, i.e., that for all we know, Big Foot exists. Your counterargument rests on the confusion of these notions.

To disambiguate, the speech act in which I assert the sentence "Big Foot does not exist" is an act that states a belief, and in such a case epistemic matters are highly germane to interpreting what has been expressed, but our discussion concerns not the beliefs our assertions express, which is what Kant’s notion of judgement may be taken to concern, but instead the epistemically neutral domain of what makes such assertions true or not. Hence our focus on propositions as opposed to token utterances.

It may indeed be the case, as you rightfully suspect, that gravitation is not how the proposition quoted describes it. Epistemic limitations perhaps demonstrate that when presented with such propositions, we are not always able to identify them as facts, but again, this does not suffice to indicate that our concept of facthood itself, as opposed to our access to facts, is to blame. Consider this: to address your later question, the very same concept of facthood is employed in declaring the statement "2+2=4" as a statement of fact as in the case of "Big Foot does not exist", but we only suffer worries of justification in the former case.

You may immediately ask me to specify what the "entity outside us" is that makes the proposition "2+2=4" a fact. In response to this, I can follow Russell in holding that the correspondence theory of truth (which, for the record, is not the theory of truth I officially endorse) doesn't require all facts to be spaciotemporal. Perhaps you hold that correspondence theorists cannot avoid Platonism of mathematical entities, but that would ground a separate discussion.

Allow me, in parting, to give one of my tutors' favourite examples:

The number of grains of sand on Brighton beach is even.

I can happily accept that there is either a fact that renders the above sentence true or a fact that renders it false. It would be absurd for epistemic reasons for me to decide which of these disjuncts to endorse, and hence for me to assert this sentence or its converse, but again it is not the proposed notion of facthood that is responsible for any such absurdity.
Zin5ki

### Re: An Analysis of On Certainty

Zin,

I perceive a certain disconsonance in what you regard as the constitution of the truth of any statement. On the one hand, you take as true, statements such as “the tooth fairy does not exist,” because “a very large conjunctive state of affairs according to which, in effect, excludes the [existence of the] tooth fairy.” This is a far cry from saying the proposition “the truth fairy does not exist’ is true because it corresponds to a fact.

Thus, you seem at first to claim that the determiner of truth is “a very large conjunctive state of affairs.” If the latter excludes what is proposed, it is false. Presumably, if it includes what is proposed, it should be true. However, this would include all that is possible. Accordingly, such a truth determiner is reducible to: Whatever is impossible is false, and whatever is possible is true. Yet clearly, this is error; for all possible things need not be real. Thus, the proposition, “Big Foot exists,” is possible but need not be true.

In the face of this realization, you seem to retreat to your former stance on truth-bearing by declaring that there must be a fact that determines the existence or non-existence of Big Foot, even if we do not know what it is. Thereby, you seek to divorce logic from knowledge.

You observe that the number of grains of sand on Brighton Beach must be either odd or even, regardless of whether or not we know which is the case. However, this only means that the proposition--“the number of grains of sand on Brighton beach is either odd or even”-- is true. On the other hand, the propositions--“the number of grains of sand on Brighton Beach is even” and “the number of grains of sand on Brighton Beach is odd”-- can be called neither true nor false owing to our ignorance. The matter becomes further complicated when one realizes that odd and even numbers are only ideas.

Hence, our inability to know whether or not a proposition corresponds to a fact affects our ability to determine the truth content of that proposition. Therefore, any endeavour to assign truth or falsity to any proposition must take into account our ability or inability to know the fact to which the proposition refers. To do otherwise would be to give “fact” a purely nominal significance. This is a pivotal consideration, for human ignorance is boundless. Indeed, there are grounds for scepticism that we can establish beyond all doubt any meaningful fact. This would certainly impact “our concept of factness.”
Neri
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### Re: An Analysis of On Certainty

You raise some interesting points, Neri. It is of merit for me to issue responses on certain matters. Allow me to list them.

Firstly, for a proposition to be true by virtue of a given obtaining state of affairs, on the account I have given, just is for there to be a fact to which it corresponds. My entire enterprise of elucidating such a state of affairs has been in order to identify it with the fact required, should such a state of affairs obtain. This convention of considering facts to be obtaining instances of states of affairs is made explicit in the Tractatus, and has been commonplace ever since.

Secondly, you worry that the conjunctive state of affairs used in the tooth fairy case extends beyond the actual and includes all that is possible. This is a misconception. I have attempted to describe the fact (if there is one) corresponding to the truth (if there is such a truth) of the proposition, “the tooth fairy does not exist”. I have not described the fact corresponding to the truth of the very different proposition, “it is possible that the tooth fairy does not exist”. As I am not making a modal claim, the state of affairs I adumbrate would be formally stated without the use of any modal operators.

Thirdly, you correctly characterise me in holding that there is a fact determining either the existence or non-existence of Big Foot, in spite of not knowing which disjunct obtains. I fail to see how this is a problematic notion, for I can be in a position to assert p or q without being in a position to assert p or to assert q.

Fourthly, you propose that “the number of grains of sand on Brighton Beach is even” has an indeterminate truth value. Now, following Frege and later Peter Strawson amongst others, the theory that there are “truth-value gaps” has become quite orthodox, especially after having been formalised into many-valued logics. However, saying that the propositions whose truth or falsity we are ignorant of thereby have indeterminate truth values lacks any such orthodoxy, as far as I’m aware. I’m sceptical as to whether such a thesis could be defended.

Finally, you are correct to state that “any endeavour to assign truth or falsity to any proposition must take into account our ability or inability to know the fact to which the proposition refers”. Any such endeavour is an epistemological one though, given that assigning truth to a proposition is intuitively connected with coming to know it. Contra your assertion, we are not burdened with the job of reflecting on whether a given fact is knowable or not when merely attempting to describe facthood. I see no evidence that Frege, Russell, Wittgenstein or everyone following in their tradition would disagree with me on this matter. Conversely, I struggle to identify acolytes of your position.
Zin5ki

### Re: An Analysis of On Certainty

Zin,

(1) I now understand you to say that the truth-determiners are “obtaining instances of states of affairs” and that it is only a convention to refer to this plurality as “a fact.” Because I am not quite clear as to what all of these obtaining instances of states of affairs may be in the case of the proposition--“the tooth fairy does not exist”—please list them all without exception.

(2) Do all the obtaining instances of states of affairs referred to in (1) above render it impossible that the tooth fairy exists? If not, why are these so-called states of affairs no more than a justification for believing that the tooth fairy does not exist--rather than a full determination that the proposition that “the tooth fairy does not exist” is true.

(3) Consider the following questions:

(a) If it is true that “Big Foot does not exist,” but it is possible that he does exist--where exactly does the truth lie?

(b) Is the proposition, “God exists,” true or false? If it is false, is the proposition true that “It is possible that God exists”?

(c) Is the proposition true or false that “a statement is true only if it corresponds to a fact”? If it is true, is the proposition true or false that “It is possible that a statement is true even if it does not correspond to a fact”?

(d) How do we determine as true the proposition that “a statement is true only if it corresponds to a fact”-- without “lifting ourselves by our own bootstraps”?

(4) There certainly are “truth-value gaps.” Indeed, they are far wider the some are prepared to admit.

Take the following propositions:

(a) Emeralds are green.
(b) Emeralds are not green.

There would seem to be the following two alternatives:

ALTERNATIVE (A) If the colour, green, does not represent anything real outside of us, emeralds will be green to those with “normal vision” but false to those who are completely colour blind. Thus, if “green” is only an idea, the proposition—“Emeralds are green”—can be both true and false.

[In such case it cannot be that “normality” determines truth, for normality refers only to an overwhelming majority, and truth cannot be only a matter of majority opinion. Indeed, if the overwhelming majority of mankind was mad by present standards, you and I might well be considered mad for believing in such things as time, space and causation.]

ALTERNATIVE (B) If the idea, green, represents a wave length of electro-magnetic radiation whose existence in no way depends on how it is experienced--it will be impossible that the proposition—“Emeralds are green”—can be both true and false.

The question is presented:

How can we know with certainty whether Alternative (A) or (B) is the actual state of affairs?

It is implicit in Alternative (B) that “a wave length of electro-magnetic radiation” is something that exists outside of us—that it is something more than just an idea. But how can we know this?

Clearly, if we were a blind species incapable of language, we would have no concept of wave lengths of electro-magnetic radiation. Indeed, all of science depends upon confirmation by observational and experimental data. But the latter are nothing more that sense experiences. This brings us face to face with the Kantian dilemma: we can only compare cognitions and cannot compare cognitions with their objects. Hence, we cannot know whether Alternative (A) or Alternative (B) is the actual state of affairs.

I have suggested a resolution to this dilemma, which is based upon the conviction that whenever a similar object is before us it causes a similar sensory representation. While this conviction may be justified because it preserves the utility of the senses, it is by no means a certainty. Indeed, all we can say of any proposition is that it is justified or not justified.
Neri
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### Re: An Analysis of On Certainty

Your questions are most trenchant. I shall discuss each.

I begin with a disambiguation: By my use of "possibly", I cite the metaphysical as opposed to epistemological concept. The latter of these, roughly, takes "possibly P" to be tantamount to "for all I know, P", which is not what I have in mind. Brian Weatherson knows a lot about this distinction. Perhaps you've been concerning epistemological possibility thus far, which would explain many of our disagreements.

To heed your first request, allow me to list the conjunctive state of affairs formally. Take the set $T$ of properties $\left \{\ T _{1} , \ T_{2} , \ldots , \ T_{n} \right \}$ such that if $\left $$\ T _{1} x \vee \ T_{2} x \vee \ldots \vee \ T_{n} x \right$$$, then $x$ is the tooth fairy.

Now consider the set $S$of all existent objects $\left \{\ x_{1}, \ x_{2}, \ldots, \ x_{m} \right \}$. We then state the following. For all members of the set $P$ of properties $\left \{\ P _{1} , \ P_{2} , \ldots , \ P_{q} \right \}$ such that $P _{i} x _{j}$ for a particular $P _{i} \in P$ and $x _{j} \in S$, where $(1 \leq i \leq q)$ and $(1 \leq j \leq m)$, $P _{i} \not{\in} T$. The proposition expressed in the preceding sentence is equivalent to a list of all the relevant states of affairs which, if obtaining, correspond to the fact required. (Put more loosely, we may say that all instantiated properties are insufficient for their bearers to be the tooth fairy.)

To answer your question from (2), the set $S$ only includes objects that exist, and not those objects that possibly exist. Thus the relevant set of states of affairs obtaining does not render it impossible that the tooth fairy exists, just that she doesn't exist.

Alas, I do not understand why you worry that such a conjunctive state of affairs is "no more than a justification for believing that the tooth fairy does not exist". Justifications, whatsoever they are, are things which support our beliefs about states of affairs; I do not hold that they are identical to the states of affairs our beliefs concern.

My answer to question (3a) is provided by the demonstration by which I started this post. We arrive at a state of affairs according to which all instantiated properties are insufficient for their bearers to be Big Foot. This would, of course, be insufficient to exclude truth of, "possibly, Big Foot exists", given my appeal to metaphysical and not epistemological possibility.

Concerning (3b), I would rather not take a stance on whether it can be false that God exists but true that it is possible that God exists. Doing so plunges one deeply into the debates surrounding the Modal Ontological Argument, which would make for a discussion quite orthogonal to the current one.

Under the current proposal, my answer to (3c) is that both statements are true, but that the latter question is only true if we construe "it is possible that" as an application of metaphysical possibility. Unless one's views on modality are very austere, à la Spinoza for example, it can be possibly true that Q even when Q is false.

Question (3d) is highly intriguing, as it calls for a metaphilosophical account of how we go about determining whether one metaphysical theory is correct a priori. On a whim, one might try to show that one's account of facthood enjoys all of the strengths of rivalling views, vis-à-vis logical consistency, intuitive force and so on, but fewer of the flaws. One subsequently endorses it as an inference to the best explanation of the concept of facthood. The views on facthood that I have described may prove false, but only through showing that I commit some sort of fallacy or other irreconcilable error. This might sound much like bootstrapping to you, but it is hard to see how any plausible rival views can claim to have a more decisive process of argument in their favour.

Question (4) revolves around the following concern: we do not have the tools, in spite of Locke's legacy of the primary/secondary quality distinction, to ascertain whether to be realists about ascriptions of colour. This does not motivate a third category of truth values to be assigned to propositions about colour though. At best it demonstrates that we do not know whether the facts corresponding to statements about colour inherently include facts about judging or speaking subjects as component parts, or more succinctly, whether such facts are subjective in nature. In either case bivalence can be retained; at worst we would have to state that different statements about an object's colour state different propositions in spite of their identical surface syntax.
Zin5ki

### Re: An Analysis of On Certainty

Zin,

Your exquisitely reasoned response says no more than this:

(1) A proposition is true if it supported by the weight of the evidence, yet it may possibly be false.

(2) A proposition is false if it is not supported by the weight of the evidence, yet it may possibly be true.

However this argument equates justification with truth; for a proposition cannot possibly be false if it corresponds to a fact, when “a fact” is taken to be a reality independent of our contemplation of it. Similarly, a proposition cannot possibly be true if it is contradicted by a fact, when “a fact” has the same meaning. To say that the expression, “a fact,” is a convention referring to a whole body of states of affairs does not alter these conclusions. Indeed, to say that a proposition is true because it is justified by a whole body of states of affairs is to say no more than it is supported by the weight of the evidence; for only in such case can it possibly be false.

Traditionally, truth has been distinguished from justification. Thus, a meteorologist who predicts rain tomorrow based upon satellite imagining, barometric readings, computer models, the opinion of the National Weather Service and the like, is justified in his prediction. Yet, it cannot be said that his prediction is true until tomorrow. If it rains, it is true. If it does not, it is false. [As we know, both Former President Bush and Former Prime Minister Blair have insisted on this distinction in connection with their position that Saddam Hussein possessed weapons of mass destruction.]

Of course, if we take Kant’s point of view—even if we are standing in the rain tomorrow, we cannot know if the cognition, “it is raining,” represents anything real outside of us; for we cannot compare that cognition with its object. We can only compare the cognition, “it is raining” with the cognition, “it is not raining.” This is why Kant favored the coherence and not the correspondence theory of truth.

It seems clear that the proposition that “a-proposition-is-true-only-if-it-corresponds-to-a-fact (p1)--does not have the same meaning as the proposition that “a-proposition-is-true-if-it-is-supported-by-the-weight-of-the-evidence” (p2). These are two entirely different accounts of truth.

Significantly, p2 does not have the rather serious problems associated with p1. The latter, while it purports to establish truth by way of correspondence, cannot itself be established in this way but instead relies upon a justified belief. In a round-about way, you concede this in your last post.

If we say that p1 is true because it corresponds to a fact, we are begging the question by presuming the truth of the very correspondence theory provided by p1. In other words, we are taking for granted the very thing we have set out to prove.

Further, if we say that the proposition that “p-1 is true because it corresponds to a fact” (p1a), then it follows that the proposition that “p1a is true because it corresponds to a fact” (p1b), and so forth for p-1c, p-1d, etc. in infinite regression. Hence, the whole business is ungrounded in meaning.

On the other hand, p2 does not refer to a correspondence to reality. It refers only to a justified belief in a correspondence to reality. That is, it refers to an extent of knowledge and not a theory of truth. It is for this reason that I have taken the position that “JTB is rubbish,” for all the human condition allows as knowledge is a justified belief. As I have often said, “there is no infallible arbiter of truth who holds court for mere humans.” Unimpeachable truth is something beyond our grasp.

If there is such a thing as truth in the context of our limited access to external reality, it can be no more than a justified belief. In this sense, I agree with you. Yet, truth, as so understood, is always a work in progress and not something capturable by quasi-mathematical reasoning.
Neri
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### Re: An Analysis of On Certainty

I must admit to being puzzled that you take my account of facthood to equate to a quaint 'evidentialist' theory of truth, if such a thing can be conceived of. Had I wished to describe truth in this misguided fashion, my appeal to what facts are would have been an idle cog. What it takes for something to be evidence, and what it takes for a subject to possess evidence, are matters on which the correspondence theory of truth remains silent. In the tooth-fairy case, none of the propositions $P _{i} x _{j}$ are determined by what is or could be evidence, but by the brute matter of what actually obtains.

Given my explicit avoidance of epistemological matters, chiefly my avoidance of i) the questions of when and how an agent can be in a position to declare the truth of a proposition and ii) the issue of what an agent's declaration to that effect actually expresses, I must request that you demonstrate how (1) and (2) follow from my positions on truth and facthood.
Zin5ki

### Re: An Analysis of On Certainty

Zinski...

I think it's one of those funny things about philosophy that we mix up ontological claims with epistemological ones. And it is in the use of 'fact' that often spurs such confusion (also of 'true'). For some reason philosophers, who are always questioning things, having their mind opened to alternative views, perhaps, or maybe they are just skeptics, often get tripped over their use. Facts are all around us. What would we be without them? However, as a cross-examiner, we are quite within our right to ask: "Are you sure?". But, as a philosopher, we should be attending to the question at hand, whether they be existential questions or those of a semantical nature, or of value, or whatever, and not draw in every other area of philosophy. Philosophy would get nowhere, were that the case. In delving into facts, we should assume there are some and the target would be what makes them facts, or possibly what their truth conditions are. (And even in expressing it in just this fashion should cause us to pause that we are straying. From this, I suspect there is a better way of expressing it.) In any case, if we are delving into fact-claims, we have a different target, one that deals with how we can come to acquire their truth or what it means to possess its truth.

James
owleye

### Re: An Analysis of On Certainty

Zin,

As I stated previously, the notion that a proposition is true only if it corresponds to a fact requires both an ontological and an epistemic commitment. The former commitment expresses the idea of necessary and not just possible truth.

If one makes the claim that the truth or falsity of any proposition depends on its correspondence to a fact whether or not we are capable of knowing facts—one makes the former commitment and not the latter. This leaves him with a truth in name only [an “idle cog,” if you like]. Kant pointed this out better than I.

In other words, if one does not make the epistemic commitment, one cannot say that any proposition is necessarily true or false--only that it must be either true or false (without knowing which is actually the case).

When confronted with the circular reasoning inherent in the correspondence theory of truth, you yourself resort to what you disparage as a “quaint evidentialist” argument.

You state that your “account of facthood enjoys all the strengths of rivalling views...but fewer of its flaws”; that it is “the best explanation of facthood”; that “it may prove false, but only through showing that I commit some sort of fallacy or other irreconcilable error”; that “it is hard to see how any plausible rival views can claim to have a more decisive process of argument in their favour.”

If this is not an evidentiary argument (an attempt at justification), I have never seen it in forty years at the bar of court.
Neri
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### Re: An Analysis of On Certainty

I must admit to failing to understand much of what you have written today. My puzzlement may be summarised by the following list of questions:
• What is this epistemological commitment with which correspondence theorists are lumbered?
• What does it mean for a commitment to express "the idea of necessary and not just possible truth"? How can commitments express anything?
• How does my position that the correspondence theory holds regardless of whether we are be able to know any facts lead to truth being an idle cog?
• If your argument against the correspondence theory is somehow grounded in Kantian exegesis, how come B82 of his first Critique, which you have cited, is commonly taken to be an endorsement of such a theory?
I could attempt to refute your claims in sequence, though as I fail to grasp the inference you draw in your first three paragraphs, I doubt that I would do you justice. I humbly request that in lieu of addressing the questions above, which may well be little more than expressions of confusion, you rephrase your entire argument against me.

I am in a position to say this much at present: as it stands there is no problem with the correspondence theory when it comes to stating that p is necessarily true. A correspondence theory can accommodate the uncontroversial axiom that:

p is necessarily true iff p corresponds to the fact that F, where F is the case in all possible worlds.

This is simply a special case of the relation that needs to hold for a given p to be true.

As regards your final two paragraphs, I see not how my abductive attempt to justify my theory of facthood involves the notion of evidence. Pace your appeal to your professional experience, the justification of an a priori matter, such as the matter of whether a given philosophical theory is accurate, is not the sort of feat provided by 'evidence'. Evidence seems to be called upon only in empirical claims, which I am not making.
Zin5ki

### Re: An Analysis of On Certainty

Neri wrote:If there is such a thing as truth in the context of our limited access to external reality, it can be no more than a justified belief. In this sense, I agree with you. Yet, truth, as so understood, is always a work in progress and not something capturable by quasi-mathematical reasoning.

How then can some beliefs be true but unjustified (i.e. true by accident), or justified but untrue? Truth is orthogonal to justification.

Suppose I believe something without evidence, and it then turns out to be true. If (as you claim) truth can only be a justified belief, then an "unjustified true belief" (i.e. one that is simultaneously unjustified and true) is a contradiction. Conversely, if I have very good evidence for a belief, which then turns out false for reasons I could not have been aware of, my belief would on your criterion be both justified and unjustified (because it was simultaneously justified and false).

Neri wrote:In other words, if one does not make the epistemic commitment, one cannot say that any proposition is necessarily true or false--only that it must be either true or false (without knowing which is actually the case).

You concede that it is possible to say that the proposition must be either true or false. But if so, the words "true" and "false" must have a non-epistemic meaning. Otherwise, knowledge of what is true would be equivalent to knowledge of knowledge of what is true, and so on in an infinite regress.

A justified belief must be justified by evidence of an external state of affairs. Your idea of truth as justified belief would make justification self-referential; a belief would be justified by evidence that it was justified.
Positor
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### Re: An Analysis of On Certainty

Zin,

What follows are answers to your questions in the order in which you presented them. You will note that I have already covered many of these issues.

(A) On 7th March, I stated:

“If we say a proposition is true only if it corresponds to a fact, we are making the metaphysical commitment that--

“(1) Facts exist independently of us and do not depend upon our contemplation of them and, as a consequence, the world consists of facts.

“And the epistemic commitment that--

(B) On 21st March, I stated:

“... a proposition cannot possibly be false if it corresponds to a fact, when “a fact” is taken to be a reality independent of our contemplation of it. Similarly, a proposition cannot possibly be true if it is contradicted by a fact, when “a fact” has the same meaning.”

(C) If we accept that “facts exist independently of us and do not depend upon our contemplation of them” but do not accept that “our sense experiences and the inferences ultimately derived from them give us access to facts”--we are saying that, while there may be an external reality, our human limitations give us no window to it. In such case, we would not be in a position to know whether any proposition whatever is either true or false by way of correspondence.

(D) On 9th March, I stated:

“...Kant argued that this correspondence definition of truth is only nominal, because we have no way of comparing real things with the judgments we make of them. All we have are the judgments themselves. To put it another way, he claims that we have no access to what lies outside of us and hence cannot know what is true by way of correspondence.”

I remind you of Kant’s own words:

:"(...) Truth, it is said, consists in the agreement of cognition with its object. In consequence of this mere nominal definition, my cognition, to count as true, is supposed to agree with its object. Now I can compare the object with my cognition, however, only by cognizing it. Hence my cognition is supposed to confirm itself, which is far short of being sufficient for truth.” Ibid.

Note that Kant held that the correspondence theory provided only a “nominal definition” of truth, for he maintained that we have no access to external reality. It is for this reason that he subscribed to the coherence theory of truth.

The remaining portion of this post treats the other issues you raised.

Frankly, I find rather fanciful the idea that “p is necessarily true iff p corresponds to the fact that F, where F is the case in all possible worlds.” Reality consists of what actually is, not of what can possibly be. Surely, at every instant, the world could have conceivably taken a different course. [The uncertainty principle of QM has even led to some to theorize that an infinity of words is created at every instant. However, this is no more than a far-fetched attempt to make possibilities somehow certain, when actualities are the only certainties.]

If we say that “necessary truth” is correspondence to a fact that is the case in all possible worlds, we are saying that correspondence to the actual state of affairs (reality) does not necessarily yield truth simply because such a state of affairs could possibly have been otherwise. If truth is a correspondence with reality, “necessary truth” is a redundancy. While the notion of “all possible worlds” may be a matter of logical coherence (a tool of thought), it cannot be a matter of metaphysical correspondence; for what is real is necessarily what is actually the case.

If one is employing abductive reasoning, one is claiming to provide the best explanation, given the available evidence. This is exactly what we ask of a jury in a criminal case. Both Inductive and abductive reasoning have in common the property that they provide only a justification for believing that a proposition corresponds to a fact and not a certainty that it does so. To provide a justification by way of abduction, one must have evidence, information, a set of circumstances, or whatever else you wish to call it. Thus, an abductive argument is essentially an evidentiary argument.

However, if one employs abductive reasoning, he cannot properly reach the conclusion that it is true that “a proposition is true only if it corresponds to a fact,” when such a conclusion necessarily involves circular reasoning and infinite regression (as I described previously); for such a conclusion would hardly provide the best possible explanation.
Neri
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### Re: An Analysis of On Certainty

Positor,

My position is that nothing ever really “turns out to be true.” Such a thing is implied in the traditional JTB analysis of knowledge, which I reject. A belief that is justified by the current state of the evidence may be taken as true, while at the same time conceding that it cannot be true in the sense that it corresponds to reality.

Newly discovered evidence may establish the falsity of such a belief and demonstrate that a different belief is justified, yet it cannot establish the truth of the new belief as a matter of correspondence. In other words, truth is a work in progress. We get closer to it, but it always eludes us. In this regard, I make no distinction between empirical, logical and mathematical truths. All are derived ultimately from our uniquely human way of cognizing what we experience.

When I say that a proposition cannot be both true and false I make the ontological claim of realism. In other words, I say that there is such a thing as certain truth. On the other hand, I make the epistemic claim that our human limitations are such that we cannot capture it completely.

Kant’s position on the matter is somewhat different. To him we have no real capacity to know truth as a correspondence with what lies outside of us; because, he says, it is impossible for us to compare a cognition with its object. To him, truth was no more than the coherence of our cognitive processes. In other words, Kant maintained that a proposition can only be true to us but never true in itself.
Neri
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### Re: An Analysis of On Certainty

Thank you kindly for your lucid summary. I believe some degree of precision is now attainable on my part.

I accept (A)(1), but I believe that upholding (A)(2) is not a concomitant requirement of correspondence theorists. (Certainly, it wasn't for Russell or Wittgenstein.) That is to say, it is not qua correspondence theorist that one might accept (A)(2).

My views on (B) are that a contingent proposition can be possibly false even if it corresponds to a fact, viz., even if it is true. I see not any intuitive issue with holding that $\left (p \wedge \neg \box p \right ) \rightarrow\diamond \neg p$, unless we confuse metaphysical possibility with epistemic possibility.

Concerning (C), I can certainly accept that “our sense experiences and the inferences ultimately derived from them give us access to facts” is true for many facts, but again I don't hold that this commitment is part of what the correspondence theory of truth per se demands of its adherents. In spite of the Lockean tradition, there is logical space to hold that we have access to certain a priori facts by means aside from sense-data and inferences therefrom, and thus a Cartesian could adopt the correspondence theory if she so desired. In any case, I hold that there are more facts for propositions to correspond to than only the ones knowable 'externally'.

Now to matters modal. One can articulate talk of "possible worlds" without being a Lewis-style modal realist. Few people adopt the view that possible worlds exist in any way, but the terminology is convenient. A further discussion on this, alas, would concerning the ontology of possibilia and not facthood itself. If one wishes, one might simply view possible worlds in the more neutral fashion of ways our world could have been. (As an aside, I must state that possible worlds as philosophers conceive of them are different to the plurality of worlds one may find in popular science: the former entities bear no causal influence on anything outside of themselves by stipulation, whereas this doesn't always hold for the latter.)

Your worries about the necessary truth of a proposition having a trans-world fact as its truthmaker might lead to an impasse of sorts. Is reality limited by the actual? Perhaps, perhaps not. Many are willing to accept that there are states of affairs that hold in all possible worlds, such as axioms of geometry. Though I do not implore you to share this view, it would certainly do justice to the nature of the sort of fact on which necessary truths seemingly turn.

Your complaints of the limits of attempting to abductively justify that a proposition is true only if it corresponds to a fact are quite germane. They do not lead to circularity though. Even if our justification involves a spot of hand-waving, we can still hold that according to the theory we're attempting to justify, there is a fact corresponding to the proposition, "a proposition is true only if it corresponds to a fact": the conjunction of all instances of facts corresponding to obtaining states of affairs in all possible worlds, along with the absence of anything else obtaining therein. "The Great Fact", as one could call it. Wittgenstein's somewhat arcane declarations regarding facts and 'pictures' are illuminating in this case.

Had I instead been proposing a verificationalist theory of truth, according to which p is true if and only if there exists a means of verifying or falsifying p, I would indeed succumb to your charge of circularity, for in such a case the theorem itself would fail to attain a truth value by its own maxim. (Verificiationalism has, of course, been dead for some time.)
Zin5ki

### Re: An Analysis of On Certainty

Zin,

You say that (A)(2) is not required for correspondence theorists. My questions are these: If the human condition gives us no access to what lies outside of us, how can we possibly know any fact? How can we say there is correspondence to facts we know not of? If facts are only concoctions of our own minds, what do they correspond to? Without (A)(2), how is anything other than a coherence theory of truth possible?

As to (B), I have the following question: How is truth possible as correspondence with a reality independent of our contemplation of it, if we claim the correspondence is to that which does not actually exist?

As to (C), I ask: If we were devoid of all sensations, would we have any experience of so-called a priori truths? If so, how? In such case, could we possibly have any notion of the distinction between necessary and contingent propositions? Could we possibly have any notion of facts? Indeed, could we possibly know anything?

I mention the QM doctrine of multiple worlds only parenthetically. The notion of other worlds in analytic philosophy is much more rudimentary. I suspect, however, that this trendy scientific jargon has found its way into this philosophy. Be that as it may, I have the following question: What is the meaning of reality if it includes that which does not actually exist?

Are “pictures,” in the analysis Wittgenstein later repudiated, only cognitive representations, or are they things that actually exist outside of us?

If you are employing an abductive argument to support the seminal proposition, “that-a-proposition-is-true-only-if-it-corresponds-to-a-fact”, do you not thereby admit that the seminal proposition, though likely true, may also be false? If it may be false, how can you say that it corresponds to a fact? If it may be false, does it not follow that everything that flows from it may also be false?

If there is a fact corresponding to the proposition, ["a proposition is true only if it corresponds to a fact"] does it not follow that there is a fact corresponding to the proposition, [“that there is a fact corresponding to the proposition, that ‘a proposition is true only if it corresponds to a fact’] and so forth ad infinitum? If this is so, how is “correspondence to a fact” any more than a mere makeweight? In other words, can we capture certain truth by way of correspondence or are we left with only likely truths by way of justification through abduction, induction and the like?
Neri
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### Re: An Analysis of On Certainty

Thank you for your questions. Whilst they spur one to pause for thought, their subject matters aren't quite attuned to the purely metaphysical issues posed by theories of truth. Allow me to demonstrate.

Firstly, your epistemic questions. If we spent our lives in sensory deprivation, there would still in principle be plenty of knowable facts, and thereby plenty of propositions we could identify as true. Basic mathematical principles and axioms of simple logics would be examples of such. Recall, if you will, Russell's explicit avowal of such things as arithmetical facts to contrast with physiological ones. Now, there would certainly be some facts that would be unknowable if we had no sensory access to anything, but what we could know would still suffice to grasp adequate conceptions of propositionality, of facthood and of correspondence. That twice two is four would be an example of a fact to which a the proposition "two plus two equals four" would correspond, and conversely the proposition "two plus two is seven" would illuminate a failure of correspondence. If you require examples of knowable contingent propositions, cases abound: that one is aware of the Russell paradox, or of the relation between a natural logarithm and its integral, or of that between an imaginary number and its square, et cetera. Cases of self-knowledge are, for us mortals, metaphysically contingent.
Even if, contra platonism, mathematical objects are mental constructs, the picture of facts and propositions the correspondence theorist requires remains intact. All that would change is that facts about mathematics and its kin would become facts about our internal mental entities and phenomena. We would still have something for a proposition to correspond to, much like how a subjectivist of value theory still considers there to be truthmakers to evaluative sentences.
All this holds for other theories of truth aside the correspondence theory, mutatis mutandis. The maxim, p is true iff ___ would still be retained without the blank being forcibly substituted. Because truth theorists aren't interested in which truths are knowable, scepticism of an external world only forces such theorists to restrict the examples they give, and nothing more.

Now for your modal question. You ask how there can be a correspondence relation between a proposition and something that doesn't exist. My answer is clarificatory remark. When we declare that p is metaphysically possible, we are not making a claim about the truth of p but of the possible truth thereof. A correspondence theorist can happily accept that possible truth is a correspondence between a proposition and a non-obtaining state of affairs, for this doesn't impinge upon her answer to what truth consists of, or more precisely but redundantly, what actual truth consists of. Note that this is separate to the question of how a modal statement can be (actually) true under a correspondence theory, as opposed to how a non-modal statement can be possibly true. Answering the former question is, alas, quite a lengthy matter, as it is not neutral with respect to one's views on possible worlds.

Your question of what reality consists of according to a modal realist may be addressed by appealing to the most lucid of sources on the matter.
David Lewis wrote:Nor does this world differ from the others in its manner of existing. I do not have the slightest idea what a difference in manner of existing is supposed to be. Some things exist here on earth, other things exist extraterrestrially, perhaps some exist no place in particular; but that is no difference in manner of existing, merely a difference in location or lack of it between things that exist. Likewise some things exist here at our world, others exist at other worlds; again, I take this to be a difference between things that exist, not a difference in their existing. You might say that strictly speaking, only this-worldly things really exist; and I am ready enough to agree, but on my view this 'strict' speaking is restricted speaking, on a par with saying that all the beer is in the fridge and ignoring most of all the beer there is. When we quantify over less than all there is, we leave out things that (unrestrictedly speaking) exist simpliciter. If I am right, other-worldy things exist simpliciter, though often it is very sensible to ignore them and quantify restrictedly over our worldmates. (On the Plurality of Worlds, pp.2-3, italics are Lewis'.)

Under this sort of framework, the truth predicate could be rephrased as true-at-our-world, and the possible truth predicate as true at some world. Likewise, an obtaining state of affairs could be qualified as a state of affairs that obtains at the world of discourse, as opposed to possible states of affairs that obtain elsewhere.

Wittgenstein's early use of pictures was for linguistic purposes. Pictures are certainly representations of things which possess pictorial forms within themselves and which that share a logical form with the worldly states of affairs they represent, but they are not essentially cognitive. This is to say nothing of his theory's problems though.

Your penultimate question lacks force. I do grant that the correspondence theory might be false for reasons we have not yet discussed. (Indeed, I prefer a deflationary theory of truth.) Now, for me to doubt whether the correspondence theory is true is perfectly permissible, as there's no general problem with employing a certain concept in an assessment of an analysis of that concept itself. A sceptical utilitarian can doubt whether utility is the good without considering something problematic or meaningless, contra Moore, and likewise a truth theorist can wonder whether our conception of truth is fully served by the biconditional she advocates as an analysis thereof. That we can doubt the suitability of an analysis doesn't change the consequences of such an analysis itself, independently of our endorsement thereof.

Regarding your final question I have this to say. Under the correspondence theory we must assert that $\forall x(True(x) \leftrightarrow \exists y(Fact(y)\wedge Corresponds(x,y)))$. Let us call this proposition $P$. You are right to hold that given this, we must assert that $\exists z(Fact(z)\wedge Corresponds(P,z))$, which we might identify as proposition $Q$, and thus assert that $\exists \alpha(Fact(\alpha)\wedge Corresponds(Q,\alpha))$ and so on. I think, in such cases, that the aforementioned "Great Fact" can easily be identified with all of the facts from $z$ and $\alpha$ onwards that this process requires. To illuminate, consider how if there is a fact corresponding to "it is true that p", there needn't be any other facts, save those regarding the meaning of the relevant terms, for "it is true that 'it is true that p'" to eo ipso be true, and so on for iterative embeddings. A regress is only apparent.
Zin5ki

### Re: An Analysis of On Certainty

Zin,

I have endeavoured to restrict myself to matters metaphysical and epistemic in our discussion and have tried to avoid semantic hair splitting. Whether or not I have succeeded, remains to be seen.

Without intending to be offensive, I will say that it is preposterous to make the claim that a person born without the capacity for sensations of any sort would have “plenty of knowable facts, and thereby plenty of propositions we could identify as true,” including “basic mathematical principles and axioms of simple logics.”

Clearly, to be conscious, one must be conscious of something. To be conscious of nothing is to be unconscious. One cannot possibly have any content to his consciousness if one has never sensed anything. It takes much time and considerable experience before the brain can learn to give meaning to what is presented to it by way of the senses. Basic mathematical principles and axioms of logic are abstractions that come much later, after a child learns to speak and understand language. Certainly, a person who has been deprived of sensory experience for all of his life would be incapable of language. He would not only be incapable of understanding spatial and numerical relations but would also be conscious of nothing.

Thus, all things that are the content of our consciousness are rooted in sensory experience. This does not mean we are limited to such experience. However, it does mean that without a grounding in sensations, logical and mathematical principles [your so-called “necessary truths”] would not be possible. All knowledge is derived from sensations and the inferences derived therefrom by means of our peculiarly human cognitive processes.

With all due respect to the late David Lewis, to make the outlandish claim that “all possible worlds” actually exist as concrete entities, borders on madness. To say that such worlds exist only as a matter of “discourse,” as you have suggested, at least positions the matter rationally. Further, if different possible worlds are causally and spatio-temporally isolated and non-interactive, there would be no reason for the possible-worlds analysis in the first place; for so-called a priori judgments (which are the claimants of necessary truth) need not have the same meaning in such other worlds.

Kant, on the other hand, presented a far more cogent rendition of the a priori. He maintained that, although they are native to our particularly human cognition, they correspond to nothing real in their own right. So that, by his lights, it was possible—within this same universe—to have animated creatures whose cognition differed so radically from ours that they would have their own set of a priori judgments differing from the human kind. In other words, although these other creatures would live in the same world as we, they would nonetheless experience an entirely different one—the presumption being that neither would experience the world as it really is. I do not necessarily agree with Kant on this point. However, one cannot deny that his reasoning was sound (at least so far as it went).

Wittgenstein conflated spatio-temporal relations among representations (pictures) with logical relations. Spatio-temporal relations exist in the real world. Logical relations are purely a matter of cognition—of how we look at things. Representations themselves are sensory experiences created in the brain. Of course, Kant would have said that time and space themselves are only matters of cognition. The truth probably lies somewhere in between.

As I have said, the correspondence proposition cannot itself be established by correspondence, for this would assume the very thing which is sought to be established. It can only be justified by abduction, which is not the same as correspondence. The latter implies certain truth. The former claims to provide the best explanation given the circumstances at hand and, as such, admits the possibility of error. Further, the regression I referred to is not merely a matter of repetition and is more than apparent; for it involves the meaning of the relevant term, “fact.” That is, the regression shows that term to be ungrounded in meaning.
Neri
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