Two years ago, KeithS, who surely needs no introduction here, mounted a skeptical argument in a thread on Uncommon Descent. The argument purported to show that we should never claim absolute certainty for any thought – a very strong conclusion. It was not until today that this argument came to my attention, when I read a comment by KeithS in a post by Colin over at TSZ, on self-evident truths.
In this post, I will not be arguing that there are any self-evident truths. My aim is a more modest one: to show that the strong version of skepticism defended by KeithS does not follow from the premises in his argument.
KeithS’s skeptical argument
To give credit where credit is due, I have to say that the argument put forward by KeithS was carefully crafted. (Readers with a philosophical background will recognize it as a refinement of Descartes’ “deceiving God” argument, coupled with his “evil demon” argument. Unlike Descartes, KeithS does not think that there are any indubitable truths.) Unfortunately, however, KeithS is not a philosopher, and there are a couple of important distinctions relating to modal logic which he has overlooked.
Without further ado, let us examine here is the argument advanced by KeithS:
In the hopes of making some progress in this thread, let me lay out my argument systematically, with numbered statements, so that it will be easier for people to specify exactly what they disagree with and why.
1. It’s possible that God exists. (or Satan, or demons, etc.)
2. If God (or Satan, etc.) exists, then it is possible that he has the power to deceive us.
3. If he has the power to deceive us, then he might be exercising that power at any particular time.
4. Being human, we cannot reliably determine when he is deceiving us and when he isn’t.
5. Any particular thought we have might coincide with a time when God/Satan/the demon is deceiving us.
6. Thus, any particular thought might be mistaken.
7. If we claim to be absolutely certain of something that isn’t true, we have erred.
8. Therefore we should never claim absolute certainty for a thought that might be mistaken.
9. Since any particular thought might be mistaken (by #6), we should never claim absolute certainty for any thought.
Note that this argument can also be made simply by appealing to the imperfection of human cognition, but it’s more fun this way.
Also note that the argument applies to atheists and theists equally. Atheists don’t think there is a God, of course, but it is still possible that there is a God, and possibility is all that is necessary for the argument to work.
One point which I would like to make at the outset is that KeithS’s argument could still work even for atheists who don’t admit the possibility of God, Satan or demons. Atheists who deny the possibility of supernatural entities would surely acknowledge that there may well be intelligent corporeal beings (e.g. aliens) with technologies that are far more advanced than our own, who have the power to deceive us by manipulating our thought processes, and that these beings might be exercising this power at any given time. I should also remind readers of physicist Paul Davies’ argument that if the multiverse is real, then the universe we are living in is probably a Matrix-style simulation.
I would also like to point out, in passing, that certain Biblical texts which have been quoted by skeptics (including KeithS) in support of their claim that God Himself (assuming that He exists) has the power to deceive us, in reality show no such thing. The matter has been addressed in some detail by the Christian apologist Glenn Miller in his article, How can God not lie and still Deceive the Wicked? Miller concludes:
God permits deceptive forces to enter someone’s life if they are COMMITTED to deception already, and if they have demonstrated a culpable history of that destructive dishonesty (and so deserving censure–hopefully corrective… cf. 2 Tim 2.25-26). But even with that permission, God often sends a counter-balancing message of truth–alerting the recipient of the danger of deception.
I should add that Hebrews 6:18 states that “it is impossible for God to lie” and Titus 1:2 additionally declares that God “does not lie,” as does 1 Samuel 15:29, when it says: “He who is the Glory of Israel does not lie or change his mind; for he is not a human being, that he should change his mind.”
In short: if the skeptics wish to argue that God is capable of deceiving us, then they would had better appeal to reason, rather than Scripture, as the Bible does not support their case.
Some preliminary remarks about indubitable truths
When KeithS originally put forward the argument, some commenters at Uncommon Descent pointed out to him that not even an Arch-Deceiver could deceive me into believing that I exist. For in order for anyone to deceive me, there must be an “I” which is capable of being deceived. This is an old argument which goes back to St. Augustine (354-430), and which was revived much later in a modified form by the French philosopher, Rene Descartes (1596-1650). Countering the skeptics of his day, St. Augustine argued in his City of God, Book XI, chapter 26, that even if I am mistaken about almost everything, one indubitable truth will remain: the fact of my own existence. “For it is certain that I am if I am deceived.” The point that St. Augustine was making here appears to have been that being deceived logically presupposes the existence of a “self” who is capable of holding false beliefs. And even if we replace the term “deceived” – which assumes the existence of an agent who deceiving me – with the more neutral term, “mistaken,” St. Augustine’s point remains: the notion of a mistake logically presupposes the existence of an individual who is making it.
Descartes’ own Cogito, ergo sum argument (“I think, therefore I am”) is, in my opinion, less successful than St. Augustine’s, for it doesn’t even get us this far. In a recent article in The Philosophers’ Magazine titled, A New and Improved Cogito Argument, Professor Stephen Mumford highlights the key flaw in Descartes’ argument: “To be brief, for these issues are well known, if one asserts I think, therefore I am, then the premise assumes the very thing – the I – which the conclusion purports to prove. The argument cannot, therefore, demonstrate the existence of the individual subject, on pain of circularity.” St. Augustine’s argument is not guilty of the same circularity, in my view. For while one might dispute whether the notion of thought presupposes the notion of a thinker, there can be no gainsaying the fact that the notion of a mistake, or error, logically presupposes the notion of a person who is making it.
However, the chief problem I have with St. Augustine’s argument is that it tells me nothing about myself. Knowing that I am is utterly uninformative, unless I also know what I am, and the argument doesn’t tell me that. Indeed, as Descartes himself pointed out much later, an argument of this sort fails to even establish that I am an embodied being, let alone a human being. For all I know, I might be real, but my body might be an illusion. Nor does the argument tell me anything about the existence of other minds, or of an external world. In the seventeenth century, Descartes attempted to circumvent these difficulties by reasoning his way up to the existence of a Perfect Being Who would not allow him to be systematically deceived about the world at large. However, Descartes’ ontological argument has few defenders today, even among theists: its chief defect, as David Banach has pointed out in a 1982 essay, is that it fails to demonstrate that the notion of God reresents something which is ontologically possible. Without such a demonstration, the argument cannot get off the ground. (Godel’s ontological argument constitutes a major improvement in this regard.)
But perhaps we have been starting at the wrong place, by reasoning purely on the basis of introspection, and ignoring the other individuals around us. Maybe our interactions with these individuals can tell us something about ourselves and about the world at large. In his article, A New and Improved Cogito Argument, Professor Mumford build a case for the reality of other minds and of causation, with the help of some crucial insights from the philosopher Ludwig Wittgenstein about the relation between thought, language and society. Mumford argues as follows:
If there is cognition, there is language. If there is language, there is a society. And if there is a society, then there is causation. The argument then goes through: cogito ergo causalitas. From thinking, I know that causation is real. It is. It exists. And even though I have reasoned to causation from the existence of my own thought, and before that from the existence of society, the conclusion is not that causation in any way depends on these things. It is the opposite. Real, mind-independent and society-independent causation is a pre-condition of there being any thought and of there being any society. Thinking, language and society depend on there being causation. And given that these evidently do exist, then so too does causation.
Mumford’s first premise, that if there is cognition then there is language, follows if we grant that at least some of our cognition is conceptual. As Mumford puts it: “There are many things I can think only because I have the concepts or words for them, for example, when I wonder what suit I will wear to my meeting on Thursday morning.” The second premise, that if there is language then there is a society, rests upon a key Wittgensteinian insight about the impossibility of there being a purely private language: “A solitary individual could not be a language user because they could not know whether they were using a word correctly or not. Other language users are required to enforce the norms of the language.” The final step in the argument, that if there is a society, then there is causation, follows from the fact that the members of a society continually interact with one another:
A society, as I understand it, is more than just a plurality. What turns this into a society is that it’s an interacting plurality. And the notion of interaction is, again, an obviously causal notion. The individual members of a society affect, and are affected by, each other. How can they do so unless causation is real?
One apparent weakness of Professor Mumford’s argument is that while it establishes the reality of causation, it fails to establish the reality of material objects, and of physical causation. However, Mumford could respond by arguing that words referring to material objects get their sense from the fact that these objects are publicly shareable, within the community of language users: we can all see, hear and feel them, and we can talk about their physical properties. Thus it is the linguistic community to which I belong that decides whether I am using words correctly when I speak of material objects, and how I and other people in my community can relate to those objects.
Nevertheless, a really hard-headed skeptic might object that firstly, it is possible that the linguistic community within which I grew up has been subjected to mass deception (e.g. by demons or advanced aliens) about the nature of reality, and that the world they perceive around them is actually an illusion, like that of The Matrix; and secondly, it is possible that I have been deceived about the very existence of the linguistic community with whom I have been conversing all my life. Perhaps the “people” I have been talking to are fictional characters created by cunning aliens, who cleverly devised computer programs incorporating these fabricated characters, in order to teach me the meaning of the words in my language (which they created for me). One could even go further, and suppose that the aliens who created my illusions are themselves fictional characters inside a super-program created by “meta-aliens,” who exist in a plane of reality which is two (or more) levels up from my own. On this account, then, I can be absolutely certain of that I exist (as someone capable of following the rules of spoken discourse), that some other agents exist (on either my own level of reality, or some higher level), and that these agents are capable of causally interacting with me – but not necessarily in a physical manner. But there is more. Deception cannot go “all the way up.” There must be some ultimate level of intelligent beings who do not exist within a simulation, and whose perception of reality is veridical.
This is a significant result. However, it is a fairly modest one. I can still entertain doubts about what I am, or what the “someone else” who interacts with me is, or how many levels of reality there are. And what I can be certain of is something which is still too meager to be expressed in the symbolism of propositional logic.
I haven’t said anything so far about the truths of logic or mathematics. Very briefly: the best candidates for absolutely certain logical truths are the law of identity (A = A) and the law of non-contradiction (not[A and not-A]). A skeptic might respond that (a) while they are certain, these statements are merely definitions which define the meaning of “equals” and “not” respectively; (b) in any case, these laws are meta-propositions rather than propositions. Regarding the truths of mathematics, it should be pointed out that “analytic” does not imply “absolutely certain,” as any conclusion obtained via a chain of reasoning depends on the reliability of our memories. Hence the number of mathematical truths which are indubitably certain will be very small.
But these skeptical doubts should not worry us, on a practical level. Knowledge is not the same thing as certainty, and in everyday life, we commonly claim to know many things which are not absolutely certain. The reason why such claims are justified is that the things we claim to know are certain beyond reasonable doubt. A skeptic might wonder whether he is living inside a simulation, but the mere possibility that he is right does not make his doubt reasonable. A prudent and sensible person would adopt the maxim of assuming, on a day-to-day basis, that the world around us is real, and that we do not exist inside a simulation.
KeithS might happily adopt this maxim, but he could also point out that his argument does not claim that we don’t know anything. Rather, what he claims is that we cannot be certain of anything. Indeed, he is very clear about this distinction in a recent comment of his, where he writes: ” if God lies it doesn’t mean that you can’t know anything — it simply means that you can’t be absolutely certain of anything.” But we saw in the previous section that there are solid grounds for saying that there are some facts whose falsehood is inconceivable. These facts we may hold as absolutely certain. But we have yet to address the argument put forward by KeithS. This I shall now do.
So, what’s wrong with KeithS’s argument?
Before I proceed, I would like to make a brief observation about the fuzzy terminology used in KeithS’s argument. KeithS attempts to demonstrate that any of our thoughts might be mistaken. Logicians don’t usually talk in that way. The term “thought” is too vague: it may be a mental image, a word, a question, the answer to a problem, a meaningful sentence, or more specifically, a proposition which can be expressed in logical symbolism. Logicians are more accustomed to using terms such as “belief” and “proposition.” A belief may indeed turn out to be “mistaken,” but if we are talking about propositions, then we normally describe them as being either true or false.
Having made that clarification, let us go on. It seems to me that KeithS’s argument suffers from several defects:
1. The argument presupposes the notion of causation. It attempts to show that we should hold nothing certain because at any given time, we may be being deceived by some being (God or Satan) who is capable of making us believe statements which are false. But such an act by the Arch-Deceiver (whoever he may be) would constitute a form of causation: to make me believe something false is to cause me to believe something false. Hence even if I am being deceived, causation is still real. It seems, then, that I cannot be mistaken about that.
At this point, KeithS’s best tactic would be to concede that we cannot be wrong about the fact that causation is real, but to deny that this statement is a proposition, since it cannot be expressed in the symbolism of propositional logic. KeithS could then attempt to defend the more restricted claim that any proposition which we believe might turn out to be mistaken.
2. KeithS’s argument fails to distinguish between epistemic possibility and ontological possibility – that is, between what might be true for all we know and what is possible in the real world. Premise 1 of the argument refers to epistemic possibility, while premise 2 mixes the two kinds of possibility, when it declares that it’s possible (for all we know) that there exists some being (God or Satan) who has the power to deceive us. Having a power is an example of real or ontological possibility. From these two premises, then, I cannot conclude that there is a real possibility that I am being deceived right now; at most, all I can say is that I cannot (on the basis of what I know) exclude the possibility that someone is deceiving me now.
3. In order to show that there is indeed a real possibility that I am being deceived right now, one might attempt to argue that either (i) God exists, and He has the power to deceive us, or some of His creatures (e.g. demons) possess this power, or (ii) the multiverse exists, and therefore there exist (in some universe) technologically advanced intelligent beings who have the power to deceive us. But this won’t do. If God exists, it does not follow that He has the power to deceive us; that might be contrary to His nature. Nor does it follow that any of His creatures possesses this power, for He is under no compulsion to create angels or super-human aliens. On the other side, if God does not exist, then it does not automatically follow that the multiverse is real. And even if it is real, and even if there is some universe out there which contains technologically advanced intelligent beings who possess the power to create simulated universes, it does not follow that these beings have the power to deceive us. That would only be the case if we lived inside one of their simulations – which is precisely the point at issue. (Of course, one could argue that the number of simulated universes is likely to exceed the number of real ones, but that’s an epistemic argument, which says nothing about real possibility.)
4. In the course of his argument, KeithS makes some claims which sound perfectly fine in ordinary discourse, but which are nonsensical when expressed in modal logic. For instance, in premise 6, he argues that any particular thought that we have might be mistaken, since any particular thought that we have might happen to coincide with a time when we are being deceived (e.g. by God or Satan). Oddly enough, you can’t say that in modal logic. You can say that every thought we have might be mistaken, and (if you use an existential quantifier instead of a universal quantifier) you can say that some thoughts we have might be mistaken, but you can’t say that any thought we have might be mistaken.
Here’s what KeithS wants to say, where Eipt means “individual i is in error in believing proposition p at time t”:
(i)(p)(t)◇(Eipt)
(For all individuals i, for all propositions p, and for all times t, possibly i is in error in believing p at time t, where ◇ represents the possibility operator.)
However, the problem is that the possibility operator ◇ can only go in front of a well-formed formula, and Eipt isn’t one, since i, p and t are variables, each of which need to be bound by a quantifier: either the existential quantifier (“there exists some x”) or the universal quantifier (“for all x”).
So perhaps we might amend the above formula to read:
◇(i)(p)(t)(Eipt)
(It is possibly the case that for all individuals i, for all propositions p, and for all times t, i is in error in believing p at time t.)
This formula is certainly a well-formed formula, but it’s very strong: it claims that possibly all of our thoughts are mistaken. That’s very different from the claim that any of our thoughts might be mistaken. As we saw above, the latter claim cannot be expressed in modal logic: it simply “does not compute.”
Now, KeithS might attempt to defend the strong claim by arguing that God (if He exists) is capable of deceiving us about everything, if He wishes to do so, since He is omnipotent. But “omnipotence” is a tricky concept, as there are some things which even God cannot do, either because they are logically contradictory or logically incoherent. For instance, God cannot make 2+2=5, or make a stone so heavy that He cannot lift it, or make the past not to have been. And it might turn out to be the case that God is incapable of deceiving us about everything, simply because there are some privileged beliefs about which we cannot be mistaken. If the arguments adduced in the previous section are correct, then I cannot be mistaken about the reality of causation, the existence of other minds or my own existence.
5. In premise 3, KeithS argues that if some Arch-Deceiver (e.g. God or Satan) has the power to deceive us, then He might be exercising that power at any particular time. What KeithS overlooks here is that we need to quantify over propositions as well as times. It’s not enough to claim that for any given time t, the Arch-Deceiver may be deceiving any (or all) of us at that time. What KeithS needs to claim is that for any given time t and for any proposition p, the Arch-Deceiver may be deceiving any (or all) of us into believing p at time t. But if (as argued above) there is a small, privileged set of beliefs regarding which we cannot be deceived, then it simply does not follow that any of our beliefs might be mistaken – let alone all of them.
6. In premise 7, KeithS states that if we claim to be absolutely certain of something that isn’t true, we have erred. However, KeithS hasn’t shown that there are some beliefs that aren’t true; all he has attempted to show is that any particular belief we hold at a given time might not be true. So the question we need to address is: if I claim to be absolutely certain of proposition p, and it turns out that p might not be true (i.e. p is not necessarily true), have I erred? By no means. Any proposition p about the material world might not be true, in the sense that it would not be true if God had chosen not to create this world. This world is contingent upon God’s decision to create it; hence any proposition which describes things existing in this world is also contingent. However, it does not follow from this fact that I (who live in this world) cannot be certain of any proposition which describes this world. Given that God has decided to create this world, there may be many propositions describing this world, about which we can legitimately claim to be absolutely certain – depending on how God has wired our epistemic apparatus.
I conclude that KeithS’s argument is support of radical skepticism is flawed on several counts. It was a brave attempt, but unfortunately it failed.
However, I don’t claim to have established in this post that there are propositions that we can be absolutely certain about. It seems that one have a legitimate debate about whether sentences such as “Causation is real,” “Other minds exist” and “I exist” express propositions that can be expressed in symbolic notation or not. Certainly they are meaningful utterances; but whether they are best construed as propositional or not is another matter.
What do readers think?