Do Logic and Existence Go Together?

It's said by some (or most) logicians that “logic must handle every possible state of affairs” and hence that it “can't imply the existence of anything” (Dale Jacquette). That almost sounds like a non sequitur. Yes, logic must handle “every possible state of affairs”. Nonetheless, how does it follow from this statement that logic can't imply the existence of anything? Why can't logic be able to handle every state of affairs and imply the existence of something (or one thing)?

Is it because if logic is applicable to everything, then implying the existence of something would pollute its ability to handle all states of affairs (note the jungle of quantifiers here)? Or is is it that the case that something (or these things) would somehow make logic contingent (or empirical) in nature? Nonetheless, implying (or allowing) the existence of something that's contingent (or empirical) isn't the same as arguing that logic itself is contingent (or empirical). Logic can still be applied to the the contingent (or empirical) even if isn't itself contingent (or empirical).

Does it mean, instead, that if logic implies the existence of anything (or even something) that it would somehow depend on that something? And, if logic did imply the existence of anything, then its logical purity would somehow be sullied?

In that sense, quantificational logic (or first-order logic) is far from being pure. Quantifiers in logic have existential import (or have ontological commitment). That is, a quantificational proposition is about the existence (or non-existence) of something (or of many things). Even free logic accepts abstract objects of various kinds. It can also be said that logical statements about self-identity have existential import. That is, the proposition (x) (x = x) has existential implications. And, more obviously, so too does, (∃y) (y = y).

It seems to follow from the acceptance of quantificational logic that an empty universe is excluded – nay, it's logically impossible. However, do these facts about quantificational logic necessarily apply to the more generic “logic” we began discussing? Perhaps quantificational logic is actually a deviant logic!

Lewis Carroll's Premises Paradox

The British writer, mathematician and logician Charles Lutwidge Dodgson (which was Lewis Carroll’s real name) worked in the fields of geometry, matrix algebra, mathematical logic and linear algebra. Dodgson was also an influential logician. (He introduced the Method of Trees; which was the earliest use of a truth tree.) For some time Dodgson was Mathematical Lecturer at Christ Church, Oxford University.

And, of course, Dodgson (under the name Lewis Carroll) also wrote Alice in Wonderland, Alice Through the Looking Glass and many other books and poems.

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Lewis Carroll (I’ll use Dodgson’s better-known pen name from now on) formulated his premises paradox in 1895. (The argument was advanced in Carroll’s paper ‘What the Tortoise Said to Achilles’; which was published by the journal Mind.) This paradox refers to the possibility of infinite premises being required in order to reach a single conclusion.

Firstly, two or more premises are usually linked to a conclusion in a logical argument.

So how are they linked?

Now that can be a question of the philosophical nature of the link between premises and conclusion: whether it’s an example of entailment (or logical consequence), implication (or material implication) or whatnot. However, that wasn’t the point that Lewis Carroll was making. He was making a purely logical (not a philosophy-of-logic) point.

To put this simply: in order to justify (or explain) how any given premises are related to a conclusion (or how the premises entail or imply the conclusion), then a further premise will need to be brought into the argument in order to do so. Moreover, another premise will be required in order to tell us (or show us) how (or why) it’s the case that if the premises are true, then the conclusion must follow and also be true.

Now that added explanation (or justification) will itself be a premise within the argument.

Of course the same problem will repeat itself.

Just as we brought in a premise to link two, three or more premises to a conclusion: now we have to say how this new premise is itself linked to those previous premises. Or, alternatively, we’ll need to know how all the premises (when taken together) are linked to the conclusion.

A solution has been offered to this logical paradox.

That solution is simply to say that no added premises are needed in the first place. That is, the link between the premises and the conclusion doesn’t need to be explained (or justified) by a further premise.

So why is that?

The (or one) answer is to say that the premises and conclusion are simply linked by a rule of inference. That rule itself explains (or shows) the relation between the premises and the conclusion. Nonetheless, that sounds (at least at a prima facie level) like a cop-out. To simply say that premises are linked to a conclusion by a rule of inference doesn’t appear to be saying anything… much. Surely that rule -again! — will need to be explained by a further premise.

It can also be argued that saying that premises are linked to a conclusion by an inference rule is itself a further premise.

Yet that’s unless that rule of inference somehow works without any justification or explanation.

In other words, it’s not a justification: it’s just a rule. It’s something that “can be shown but not said” (to use Wittgenstein’s much-quoted phrase); just as the nature of the logical constants can’t be said, only shown.

Does the Mind-as-Computer-Programme Idea Support Mind-Body Dualism?

“Yes, I am a confirmed "dualist" at this point in my journey, i.e., I understand my mind to be separate from my body/brain, analogous to the way an application program and its data are separate from the computing infrastructure they depend on.” - Chasw

Does believing your mind to be separate from your body/brain automatically mean you're a dualist? That would depend on what the word 'separate' means. The mind simply being (fundamentally) different from the body wouldn't commit anyone to dualism.

Dualism is a commitment to the idea that mind and brain are fundamentally different ontological categories or 'substances'. That creates the problem of mind-body interaction. If mind and brain (body) were fundamentally different, then how could brain-to-mind and mind-to-brain interactions be explained?

Dualists are also committed to minds being separable from brains, not just being separate and different. I don't think the 

mind = programme/data 

and the 

brain = hardware

comparison works here because, after all, even programmes and data are physical. Programmes and data depend on physical syntactic devices which encode data/info and which themselves rely on physical processes to implement that data (as well as to send that data, electronically, around the hardware/infrastructure). The programme-hardware/mind-brain analogy works only to show us that the same programme can be instantiated in different kinds of hardware: from brains to computers to coke machines. In itself, it's not an argument for dualism; which is specifically about the mind being of a different substance/category than the brain. When it comes to computer programmes and their different hardware juxtapositions, there are no such deep ontological problems as there are for mind-brain/body dualism.

The Cartesian Circle

Rene Descartes' basic position can be summarized in the following manner:

 

i) I can only know (or be certain) as to whether or not some statement or proposition (p) is true if I already know (am certain of) that God exists and is not a deceiver.

 

ii) I can only know (or be certain) that (i) God exists and is not a deceiver if I already know (am certain of) that every proposition I clearly and distinctly perceive is true.

 

That encapsulates the "Cartesian circle".

In other words, i) depends on ii) and ii) depends on i). Neither i) nor ii) can get off the ground without the prior existence of i) or ii). Or, in other words, i) can't get off the ground without ii) and ii) can't get off the ground without i). It seems to follow, then, that neither can get off the ground.

 

In more detail, one would need to ask why Descartes has already assumed God's existence, let alone the fact that He's not a deceiver. It could be said that written into God's nature and existence, as it were, is the fact that He can't be a deceiver. But since Cartesian Doubt is supposed to begin at rock bottom, Descartes could hardly have assumed any of these things.

 

In terms of ii), we would need to know what Descartes mean by 'clear' and 'distinct'. How does clarity and distinctness guarantee truth? How did he know that he clearly and distinctly perceived certain propositions? And what did he mean by “perceive” here? (He wasn't talking here about external objects such as trees or chairs.)

 

Descartes, or at least philosophers defending Descartes, have said that metaphysical or logical certainly isn't required at the beginning of Cartesian Doubt. Or, more correctly, metaphysical or logical certainty isn't required to take one to the existence of God. Instead only psychological certainty is required: presumably to take you to God and be certain about the aforesaid propositions.

 

From psychological certainly you can reach metaphysical or logical certainty about both God's existence and the truth of clear and distinct propositions. This, of course, leaves out entirely what the nature of this psychological certainty is and whether or not it's meaty enough to take us to both God's existence and nature and the truth of these propositions.

 

It also leaves out the Cartesian circle: why talk about taking oneself to God's existence at all when God hasn't been proven in the first place? Surely even the assumption of God's existence can't be accepted in Cartesian Doubt. Yet here we are assuming God's existence in the very process of arguing about psychological certainly taking us to the existence of God. That means that God's existence is assumed not only before metaphysical certainty: it's also assumed before psychological certainty (whatever that is).

 

Nonetheless, philosophers have defined what metaphysical certainty is. This is one definition:

 

A proposition P is metaphysically certain if and only if there is no other proposition R that is a reason for doubting P.

Firstly, this definition is completely psychological in nature. The Cartesian wouldn't deny that. What I mean by that is that there could be a proposition R (or even many propositions) that would give S reasons to doubt P if he were aware of them. However, S isn't aware of them. In addition, R could be a logical reason to doubt P even though S doesn't take R as a logical reason to doubt P. Nonetheless, taken non-psychologically, R is logically a contradiction of P which S may not be aware of at all.

 

Indeed, in the post-Cartesian world, the very locution “metaphysically certain” has a strange psychological ring to it. Some philosophers or metaphysicians would ask: What has certainty (psychological or otherwise) got to do with metaphysical reality? In addition, R could contradict P without having any metaphysical reality as such; just as contradictions can be formulated in logical systems from symbols or formula which don't have any (metaphysical or empirical) content.

 

However, none of that is strictly relevant if all we're talking about is the Cartesian's move from psychological certainty to metaphysical certainty because that metaphysical certainty can be deemed to be just as psychological as the prior psychological certainty. That is, the metaphysical certainty that is derived from the psychological certainty is done so in an equally psychological manner – in what other manner could it be derived?

 

In an case, most of that is a sidetrack.

The Cartesian move is that, yes, we begin with only psychological certainty as to various clear and distinct propositions. The first thing we do with these psychologically certain propositions is prove that God exists. Then, with God's help, as it were, they become metaphysically certain as well. The question here, however, is that even if we accept psychological certainty, how is it, exactly, that such certainty “proves” God's existence? After all, psychological certainty alone can't prove God's existence or anything else for that matter. Only valid and true arguments can do that.

Then the Cartesian seems to move in another circle within the general Cartesian Circle. By proving God's existence from psychologically certain and therefore true propositions, we're giving a reason, apparently, for doubting all possible reasons for doubting those very propositions which prove God's existence. The propositions which took us to God are then blessed by God and therefore become certain. Thus:

 

God + psychological certainty = metaphysical certainty.

This could be seen as a virtuous, rather than a vicious, circle. Certain propositions lead us to God and God leads us the those very same propositions. And that, surely, is a classic case of the Cartesian Circle. I simply can't see how anyone has broken out of this very vicious Cartesian Circle. All that's has happened is we've expressed and codified it, not solved it.

Perhaps it all hinges on how psychologically certain propositions (if that's what they truly are) somehow “prove” God's existence. Clearly, simple psychological certainty of one or a hundred propositions can't prove anything, as I said. It all depends on what these propositions are. It also depends on whether or not these propositions assume the existence of God as well as the ability of God's existence to somehow give metaphysical legitimacy to the prior psychologically-certain propositions.

 

Another part of this Cartesian Circle is that reasons for doubting P also have to be certain. That is, not-P, or R, also has to be clearly and distinctly perceived. Clearly, if not-P is clearly and distinctly perceived to be true, then P is false, according to the Cartesian. This seems to imply that not-P or R is not clearly and distinctly perceived to be true. Therefore P must be true. Again, all this depends on what P is and what not-P (or R) is. In addition, the Cartesian requires more than one P and must defend itself against more than one not-P: there will be many not-Ps.

 

Of course one not-P is that God is a deceiver. Can I clearly and distinctly perceive that God is a deceiver? Not according to the Cartesian. (Really? Even if I'm an atheist?) That can't be true: there are many reasons for doubting clear and distinct propositions. One reason is their very existence as adumbrated by Descartes himself. Another thing we can doubt is that psychological certainty leads to metaphysical certainty, God's existence or anywhere else (as I have said).

 

Again, the Cartesian only accepts any not-P if it is certain. Alternatively, the Cartesian must be certain that not-not-P is certain (or -–P). Here again, and not surprisingly, it's all about psychological certainty, even if that can lead us to all sorts of other things. And, again, the only not-P that Descartes appears to consider is that God is a deceiver.

 

Proof and Doubt: A Non-Technical Introduction

i) Introduction

ii) Proof and the Law

iii) Descartes: Doubt, Contradiction and Definitions

iv) Analytic Truths

v) Truth and Doubt

vi) Popper: Proof and Scientific Theories

vii) C.S. Peirce: Abduction

viii) Quine: the Underdetermination of Theory by the Evidence

ix) Conspiracy Theories

The notion of proof is over-used and little understood by the non-philosopher. Put plainly. He/she often demands proof when proof is impossible. Not only that: he/she often doesn’t have a clear conception of what it is, precisely, that s/he wants.

Proof and the Law

Take the case of the law. In law we never really have proof that so-and-so is guilty or not guilty. All we have is that Mr X is guilty "beyond reasonable doubt". Or that it is beyond reasonable doubt that Mr X was in vicinity Y on the night in question. But do we have a proof that Mr X was at that place? What would constitute such a proof? Even considered theoretically, we can see the problems here. 

For example, it may be the case that Mr X was caught on camera. But do we have proof that the man caught on video really is Mr X? Perhaps it's his twin brother.

Descartes: Doubt, Contradiction and Definitions

Descartes, for one, believed that he had a proof of something if he couldn't possibly doubt its truth or existence. Thus he couldn't doubt his own thinking. He had proof that thought existed. More specifically, if his "ideas" were deemed to be "clear and distinct", then he had proof of their truth or existence.

Instead of relying on the Cartesian and psychologistic notion of doubt to establish proof, 20^th century logicians and philosophers dealt with proof in terms of contradiction and non-contradiction. Put simply. Something has a proof if its negation constitutes a logical contradiction. Thus it's not the case that I can't doubt that 

1 + 1 = 2. 

Or, rather, it may well be true that I can't doubt this truth. However, what really matters, logically, is that its denial would constitute a contradiction. To say that 1 + 1 = 3 is to utter a statement that contradicts itself. But how, precisely, does the equation 1 + 1 = 3 contradict itself? It all boils down to definitions. If we define each symbol and number in the equation, we'll soon find that 3 is the wrong answer to the addition 1 + 1. That is, 1 + 1 must equal 2. Thus if:

i)                    ‘2’ df. = the number which doubles the number 1

ii)                  ‘1’ df. = the first positive number

iii)                ‘+’ df. = the sign for the addition of numbers

iv)                ‘=’ df. = the sign which signifies the identity, or equality, of both sides of an equation.

If 2 is the number which is double the number 1, then 1 + 1 states that it's the doubling the number 1 and that it must therefore equal 2. Similarly, if the ‘=’ symbolises equality or identity, then if we have 2 + 1 = 4, we can see that we have ‘3’ on the left side and ‘4’ on the right. Clearly, then, 3 can't be identical to 4. The ‘3’ of the ‘2 + 1’ contradicts the ‘4’ on the right side in the sense that it's not equal, or identical, to the ‘3’ on the left side of the equation.

Analytic Truths

We can apply the same kind of reasoning to non-mathematical "analytic truths", such as the well-known

All bachelors are unmarried.

This is also true because of the identity (or synonymy) of the words:

i)                    All bachelors are unmarried

ii)                  [bachelor] = [unmarried]

iii)                2 + 1 = 3

iv)                3 = 3

i) above is an analytic truth solely because of the synonymy of the words ‘bachelor’ and ‘unmarried man’. And like our ‘2 + 1 = 3’, we do not need empirical research to constitute its truth and that's why it too is analytic. Thus, again as with our ‘1 + 2 = 4’, the statement "All bachelors are married" contradicts itself just as "1 + 2 = 4" does.

Truth and Doubt

However, it's still true that in the Cartesian sense it's the case that we can't doubt that 2 = 2 is true; though we can easily doubt, if only initially, the truth of a difficult or complex equation. So non-doubt may be of value for 2 + 1 = 3, but be of no relevance for difficult or complex equations.

We should doubt the Cartesian epistemic maxims:

i)                    non-doubt = truth

ii)                          doubt = falsehood

Not only that, despite the earlier reference to the logical notions of contradiction and non-contradiction,

i)                    What we can't doubt (a psychological notion) may still be wrong.

More strongly:

ii)                  What we can't doubt or deny without engendering what seems to result in a contradiction may still be wrong.

For example, it's no doubt (!) the case that very many people, both today and throughout history, can and couldn't doubt the existence of God. They found it impossible, psychologically speaking, to believe the statement "God does not exist" (forget Plato’s beard!). Bringing God’s existence or non-existence into the equation shows us that doubt or non-doubt (belief) is clearly a psychological, not a logical, notion. We can say that non-doubt didn’t bring God into existence, as it were. Even universal and absolute non-doubt wouldn't do so! More relevantly. We may find it hard or even impossible to doubt an equation or a truth of maths but it still may be false. Similarly, we can easily doubt the truth of an equation which is in fact true. (It's worth stating here that many 20^th century logicians and philosophers have questioned or even denied the Law of Excluded middle. They've questioned the truth of p or not-p, or, more strongly, A or not-A. Some logicians, e.g., dialethic logicians, have even said that A and not-A is - or is possibly is - true in certain cases. [see G. Priest’s 2002])

Perhaps the introduction of the notion of doubt into logic, maths and philosophy itself was the prime vice and mistake of what Frege, Husserl and others took to be "psychologism". Proof for these logicians is based on the notion of contradiction and non-contradiction; which also determined a logical system’s validity and consistency. A contradiction in a system would make that system inconsistent and thus rejectable. In addition, the use of doubt (or even the reality of doubt) within maths and logic would make those disciplines far too psychologistic in nature for many late 19^th century logicians. The laws and truths of logic were deemed by them, after all, to be mind-independent and not ultimately dependent on minds at all – even if it's minds that come to know and notate these abstract non-spatiotemporal truths and laws [see Frege’s 1884 and Husserl’s 1900].

We can also go on to say that it's possible to doubt just about anything if we so desire. And this was precisely the kind of radical (or global) scepticism that Descartes reacted against - thus he came up with his famous Cogito. 

For example, we can doubt that we're truly sane; that we're not actually awake but asleep; that we're not a brain in a vat. And so on. Descartes, again, reacted against global scepticism by using doubt itself to defeat doubt. His "method of doubt" was Descartes’ attempt to prove that we can't doubt our own doubting or thinking. Modern logicians, however, simply dispensed with the whole notion of doubt vis-à-vis logic and maths.

As the late Wittgenstein [1969] argued, radical or global doubt isn't possible anyway. Radical doubt, if actualised, would render all communication - and even thought itself - impossible or senseless.

In tandem with the notions of contradiction and non-contradiction in the domains of logic and maths, we also see the importance of definitions (as stated earlier). We've already said that it's ultimately definitions that constitute the nature of proof and contradiction. Thus, from our explicit definitions of numbers (or logical principles and logical components) we derive logical laws and truths and ultimately whole logical systems. We can see, then, that definitions in this sense are the axioms of logical systems. And the same is the case with geometry and its definitions.

On the other hand, contradiction and non-contradiction are of little or no value when we come to empirical statements and those of science as a whole. 

Popper: Proof and Scientific Theories

For example, it's an established scientific fact that the earth revolves around the sun. This truth of science has been recognised for over 400 years. However, if I were to say that the sun revolves around the earth this wouldn't be to utter something that is a contradiction of the reverse scenario:

i)                    The sun revolves around the earth.

doesn't contradict the statement that

ii)                  The earth revolves around the sun.

The former doesn't contradict ii) in the strict logical sense we have covered. It's simply the case that i) is a scientific falsehood, not a contradiction of ii).

There's also another sense in which proof in empirical matters (or science) is different to proof in logic. Take our examples again. We don't really have a proof that the earth revolves around the sun. Strictly speaking, we have no proof that this is so. In fact it's difficult to even imagine what could constitute a proof of that scientific fact. It could be the case that all our scientific theories are false. Indeed, historically speaking, this has been the case. It can also be argued that proof in science would prove to be counter-productive in the long term. That's because it was the eventual refutations and rejections of well-established scientific theories that pushed science, as a whole, forward. If scientists really believed that they had iron-cast proofs of their theories (which couldn’t then be called by that name!), then new theories would never have been accepted if they negated the established ones. Thus science would have atrophied at the time of Copernicus or even at the time of the pre-Socratics. Instead, scientists have come to accept that science (or its theories) are all fallible. Scientists are, or should be, fallibilists. They should thus reject (or even do without) any strict notions of proof in science. Proof is the game which only logic and maths play. Science shouldn't play that game. 

We can conclude positively that a lack of scientific proof of a theory is no reason to throw it overboard. There's no proof that Darwinian evolution [see Popper’s 1974] was and is the case in the natural world. 

On the other hand, our inability to disprove a theory in no reason, on its own, to accept it. We can say that the Big Bang theory hasn't been disproved (how could it be?). However, this negative compliment is no reason – on its own! – to accept this theory. Quite simply, no scientific theory can be proved to be true. 

However, we don’t need proof in science. And if proof is unobtainable because of the incompleteness of a theory (or its lack of a 100% truth-content), this is no reason to reject a theory. 

For a start, an incomplete theory is better than no theory at all. That theory may have much to tell us - even if incomplete. Similarly, a 90% truth-content (or even only a 50% truth-content) is better than no truth-content at all. We can say, as with Popper [1963/72], that Newton’s theory of gravitation has less than a 100% truth-content. And yet this theory has proved to be immensely important and successful in scientific history and has provided us with countless benefits in technology. And if we see Einstein’s theory of relativity as its successor, it is still the case that this theory doesn’t have a 100% truth-content either - even if the percentage is higher than that of Newton’s theory. Perhaps a 100% truth-content is impossible in principle. Indeed what would that even mean? What would constitute its 100% truth-content?

Similarly, an inability to prove something wrong is no reason to accept that something. As we said earlier, global scepticism can't be conclusively refuted. However, that's no reason (on its own) to accept it because if we did, communication - and even thought itself! - would be rendered impossible or senseless. More particularly, we have no strong or good reason to really believe that we are brains in a vat, dreaming when we think we're awake, or that other people have no minds. As Wittgenstein [1969], and Hume [1739] before him, argued, we just can’t help but believe these things anyway [see Strawson’s 1985]. And, again, if we did deny other minds, etc., we would need to become - or be - solipsists. In practice that would prove (!) to be impossible too.

We can't prove God’s non-existence. We can't prove His existence. But proof alone doesn’t give us a strong or good reason to either believe or disbelieve in God’s existence. I can't prove that a teacup floats around a distant planet (as in Russell’s example [Russell]). And neither can I disprove the assertion that "there is an invisible pink elephant dancing on this book in front of me" [Baggini, 2002]. Just as Wittgenstein’s Tractatus tautologies don't even allow the possibility of their negation, so many sceptical scenarios can't be disproved in the strict logical sense [Wittgenstein, 1921]. Indeed, many sceptical hypotheses are designed by philosophers to be irrefutable or beyond disproof (and proof!) [see A. J. Ayer’s 1936]. 

What would make living as brains in vats today differ from yesterday when we weren't brains in vats? What could differentiate a Cartesian dream-state from the state of being awake? How could mindless persons differ from persons with minds? In addition, if Russell’s scenario of a five-year-old earth (replete with fake sciences of age but which are nevertheless duplicates of actual signs of age) be different from a planet that is billions of years old? In the case of the pink elephant dancing on this book in front of me, the sceptic makes it being disproved in that he claims that it "has no weight, no colour, smell, or texture". We can now ask the sceptic:

How does a weightless, colourless, odourless and texture-less thing differ from nothing – or no thing?

As Wittgenstein put it. A nothing will do as well as a something in such a scenario [1953]. Similarly, how does Russell’s teacup (or the metaphysical realist’s ‘future contingent’) differ from nothing? Neither have truth-conditions. So who cares if they're still either true or false? Future contingents are non-verifiable and have no truth-condition – in principle [see Dummett’s 1982].

If proof is impossible - even in principle - when it comes to these statements about the world, the future, other minds, brains in vats, pink elephants and inter-galactic teacups, then we've no need for proof in such contexts. Thus we can erase the word ‘proof’ from these ‘contexts’ [see D. Lewis’s 1996] of empirical and scientific discourse and leave it where it belongs – in logic and mathematics! Indeed not only is proof impossible in the case of these sceptical hypotheses: the belief in it has proved to be destructive in science and philosophy. Proof (like certainty and "ultimate foundations") is a malignant demon when it comes to these disciples. Thus it's far from being a coincidence, then, that not only was Descartes concerned with proof in his philosophy, he also based his philosophical reasonings (or so he claimed or thought) on the deductive systems of maths, geometry and logic [see Descartes’ 1641].

In Hume’s words, "matters of fact" can never be conclusively proved; whereas his "relations of ideas" may well be (if only on Hume’s terms). And as Tractatus Wittgenstein might have put it. We have proof in logic and maths precisely because their propositions are not world-directed – they aren't about the experiential or empirical world!

C.S. Peirce: Abduction

The acknowledgement that proof is impossible (or counter-productive) outside logic and maths is well captured by C. S. Peirce’s technical term "abduction" [Peirce, 1992 and Hookway, 1985]. When we use abductive logic in science and philosophy, what we're essentially looking for is the "argument to the best explanation". We aren't looking for an argument which we can prove; and neither are we looking for an argument (or theory) that has a 100% truth-content and is therefore complete. Instead, we're simply looking for the best argument, piece of evidence or theory we have at a particular point in time. So even though our argument (or theory) is incomplete and not 100% true, it may still be superior to other arguments (or theories) with less completeness or truth.  In Popper terms [Popper, 1963/72]:

theory¹ = 90% truth-content

                10% falsity-content

theory² = 50% truth-content

                50% falsity-content

It's acceptable to ask oneself here how it is, exactly, that we can discover such precise percentage levels in scientific and other theories.

It can be argued that if we somehow know that we only have a 90% truth-content in the case of theory¹ above, there must be a sense that we implicitly have 100% knowledge of its truth in that in order to make that distinction between a 90% truth-content and a 10% falsity-content, we would need to know why it is the case that 10% of the theory is in fact false. But how could we know that this is the case if we don’t also know what it is that makes 10% of this theory false? Wouldn’t we need to know what are the facts (or pieces of evidence) which make 10% of this theory false? We surely can only know what is false if we also know what makes it false. And what makes 10% of our theory false may be knowing what makes this slice of the theory false will take us half way to knowing what it is that would make it true. Thus we have a seemingly paradoxical case of holding a theory that is both 10% false and 100% true! 

However, we could know that 10% is false without having to know what, precisely, makes it false. Similarly, we don’t know the 10% truth-content which makes, as it were, the theory only have a 90% truth-content. We know that it is 10% false; though we don’t know the nature of the truth-content that could or would supersede that 10% negative score. 

For example, we may know that 848 x 68 = 1,000,000 is false without at the same time knowing what is the correct answer to this multiplication. Perhaps we could know it to be false for purely intuitive reasons – that is, the incorrect answer simply seems too high a number to be the answer to the equation. However, we don't know why we think that. We simply have an intuition (whatever that is!) that it is, or that it must be, false!

Quine: the Underdetermination of Theory by the Evidence

Another deflationary and fallibilistic reality of scientific schemes is that there may be many competing theories that deal with the same evidence and data. Scientists happily accept this lively competition [see Quine’s 1953 and 1969]. They think that it's a good thing. What this is called (in technical terms) is the well-know thesis of the "underdetermination of theory by the evidence". After all, perhaps the favourite theory has less truth-content than its neglected rivals; even if that's not always a case of comparing truth-content with truth-content. 

For example, even if theory² has only a 70% truth-content to the 80% of theory¹, the former may be preferred because of its simplicity, explanatory power or even because of its aesthetic appeal. So scientists as a matter of course accept rival or even complementary explanations and theories even if they don’t themselves utilise them. They simply acknowledge the well-accepted fact that they are "often presented with more than one possible explanation for an event or a state of affairs with no conclusive way of knowing which one is correct". If that's indeed the case, then the scientist may simply accept the "best explanation" or theory even if that has less truth-content that some or its rivals. It may, for example, be simply that other theories are less revolutionary - or more revolutionary [see Quine’s 1953 and 1969].

In terms of "explanatory power" (i.e., instead of proof), we can't prove that other people have minds (or that the earth is not five years old); though we can safely assume that they have minds (or that the earth is billions of years old). We can do so because believing that other people have minds "explains why it is they talk like they do, act like they do, have the same physiology as us" [Baggini, 2002]. Similarly, considering the not inconsiderable amount of evidence for the earth’s old age and the absurdity of Russell’s hypothesis (even if non-refutable), it's quite simply rational to accept the scientists and laugh at the sceptics who truly believe the sceptical scenario (or just its possibility). In other words, the hypothesis (or theory) that other people have minds and that the earth is ancient have more explanatory power than the theories and hypotheses which deny them. Again, in terms of Peircian abduction, theories are "arguments to the best explanation". They're superior to all the arguments and theories that would deny – if not entertain – the fact (?) that other people have minds or that the earth isn't the age of a toddler. However, we still don't have proof that other people have minds and that the earth is old. We may not even need proof.

Conspiracy Theories

Take the interesting case of conspiracy theories [see Baggini, 2002]. Such things generally have less explanatory power than their generally-accepted rivals. We can offer a list of factors and reasons which should make us - even more - suspicious of the majority of such conspiracy theories:

i)                    Their ‘facts’ are not firmly established - or established at all.

ii)                  Conspiracy theorists hypothesise huge amounts of supposedly "suppressed information".

iii)                Conspiracy theories don't have available the requisite evidence or data. (This, ironically, is often seen, by conspiracy theorists, as evidence for the conspiracy theory!)

iv)                Conspiracy theories are often not simple: they are complex instead (almost by definition).

       v)         The complexity of conspiracy theories often make them more exciting and  pleasing to conspiracy theorists (admittedly this is a psychological point).

All the above give us good reasons to reject most conspiracy theories.

References and Further Reading

Baggini, J – (2002) Making Sense, BCA

Descartes, R – (1641) Meditations on First Philosophy, various editions

Dummett, M – (1982) ‘Realism’, in Synthese 52, pp. 55-112

Frege, G – (1884/1950) Foundations of Arithmetic, trans. J. L. Austin, Oxford

Hookway, C – (1985) Peirce, London

Hume, D – (1739) A Treatise of Human Nature, various editions

Husserl, E – (1900/1970) Logical Investigations, tr. London

Lewis, D – (1996) ‘Elusive Knowledge’, in Australasian Journal of Philosophy 74, 4, pp. 549-67

Moore, G. E – (

Peirce, C. S – (1992) Reasoning and the Logic of Things, Cambridge Mass.

Popper, K – (1974) ‘Darwinism as a Metaphysical Research Programme’, in his Unended Quest, Fontana

                  - (1963/1972) Conjectures and Refutations, Routledge and Kegan Paul