Ludwig Wittgenstein's 'Tractatus': Philosophy In The Service Of Logic & Practical Reason

Ludwig Wittgenstein

In Ludwig Wittgenstein's  masterpiece, 'Tractatus Logico-Philosophicus'  one beholds a unique work, written as   pure philosophy. But which over time has also provided a formidable tool in the service of practical logic and reason.  This has made it possible  to confront the whole domain of irrational folly and illogical bunkum emerging on different fronts.  In this post, I introduce readers to some of his gems and show applications.

First things first. Below I list (as subsets)  some of the key principles from the Tractatus which I  discuss in turn and which we can then examine in conjunction with the others:

1) The substance of the world can only determine a form and not any material properties. 

2) For these are first presented by the propositions—first formed by the configuration of the objects. Roughly speaking: objects are colourless.

The  two principles above, in many ways, underscore the thinking of Wittgenstein, and hence need to be thoroughly grasped before one can proceed to examine his other points.   The key thing to note is that the "substance" defined in (1) is not a material entity.  In this way, Wittgenstein is approaching his arguments from the viewpoint of idealism.  As defined by Euan Squires  ('Conscious Mind and the Physical World', p. 74):

"Idealism is. the simple observation that all knowledge comes from sensations in the conscious mind. Thus, since everything I know, I know through my mind, it follows that in some way my mind is the only certain reality."

Given this definition then it follows (from (2)) that objects lack color, given color is a physical property.    What Wittgenstein is saying then is that the abstract (mental) form of a thing (its "configuration")  comes first in formulating a proposition. Its later elaboration, say in terms of elucidating physical properties, comes later.  

We consider now the next sequence of three principles:

 3) Two objects of the same logical form are— apart from their external properties—only differentiated from one another in that they are different.

 4) Either a thing has properties which no other has, and then one can distinguish it straight away from the others by a description and refer to it; or, on the other hand, there are several things which have the totality of their properties in common, and then it is quite impossible to point to any one of them. 

5) For if a thing is not distinguished by anything, I cannot distinguish it—for otherwise it would be distinguished

We see here Wittgenstein is affirming that 2 things of the same logical form ("configuration") can only be differentiated one from another if the configuration (apart from external, i.e. physical, properties), is different.  So consider 2 circles, A and B, which share the same configuration: circle.  But how would one discern A is different from B if other external (physical)  properties are disallowed? Well, one might draw the circle A (locus of  dimensionless points satisfying: x ²   +    y ²  =   r ² )  inside the circle B (locus of dimensionless points satisfying:  x ²    +    y ²  =      r'  ² where r' > r).   Then one can see the difference on inspection without even the need for measuring.  In this case one can "straight away" refer- say to circle A- by description (i.e. A is smaller than B since it is inside B).  But if  I have several circles, A, B and C, which share all the same properties (e.g. diameter) then it becomes impossible to point out any one of them as distinct from the others. Or, more importantly, to point to the property (diameter) as distinct from the others.  

In effect, if two or even three 'things' (circles, say) cannot be distinguished by any property, then they cannot be distinguished, period.  For if such a property did exist that enabled distinction,  the object(s) would be distinguished.

6)The configuration of the objects forms the atomic fact. In the atomic fact objects hang one in another, like the links of a chain.

 7)In the atomic fact the objects are combined in a definite way.

8) The way in which objects hang together in the atomic fact is the structure of the atomic fact. The form is the possibility of the structure.

9)The structure of the fact consists of the structures of the atomic facts.  

10)The totality of existent atomic facts is the world.

11) The totality of existent atomic facts also determines which atomic facts do not exist.

Here, "atomic facts" is a concept going back to Bertrand Russel, and basically meaning a fact that cannot be broken down any further.  Hence, the general term "logical atomism"to refer to such facts.  Let us note here this is harking back to an antiquated notion of atoms, such as proposed by Democritos, the Greek atomist.  He intuited that matter is composed of  atoms as hard, irreducible entities that can't be further broken down. Of course, with modern quantum theory we know this isn't true and atoms can be resolved further into electrons, neutrons, protons and even quarks etc.  Further, the wave (probabilistic  model of atoms further renders the Greek notion redundant.

In terms of logical atomism, one Stanford website on Russell notes:

"According to logical atomism, all truths are ultimately dependent upon a layer of atomic facts, which consist either of a simple particular exhibiting a quality, or multiple simple particulars standing in a relation."

Further:

"Logical atomism can be seen as endorsement of analysis, understood as a two-step process in which one attempts to identify, for a given domain of inquiry, set of beliefs or scientific theory, the minimum and most basic concepts and vocabulary in which the other concepts and vocabulary of that domain can be defined or recast, and the most general and basic principles from which the remainder of the truths of the domain can be derived or reconstructed.

Metaphysically, logical atomism is the view that the world consists in a plurality of independent and discrete entities, which by coming together form facts. According to Russell, a fact is a kind of complex, and depends for its existence on the simpler entities making it up. The simplest sort of complex, an atomic fact, was thought to consist either of a single individual exhibiting a simple quality, or of multiple individuals standing in a simple relation. "

Basically, Wittgenstein (like Bertrand Russell) held that all meaningful expressions are analyzable into "atomic elements" which refer directly to atomic elements in the real world. For example, "Saturn has rings" is an atomic fact  and also one from which more complex facts (and propositions) can be constructed, i.e. "Saturn's rings are composed of tiny bits of ice, rocks and dust".   The most important of the atomic fact principles is (11)  where we note:  "The totality of existent atomic facts also determines which atomic facts do not exist".  For example, if:

p =  "Fire burns most material things." 

Is an atomic fact, then it must negate the proposition (alternative atomic 'fact'):  

q =  "Fires can burn non-material things (e.g. souls)."

Thus, the totality of related atomic facts (to p) determines that those related to q cannot exist. Hence, the concept of "Hell" is based on atomic facts which do not exist because it requires elements (facts) of the category q, or the ability to "burn nonmaterial souls"  and do so "forever". 

Following this process, one can eliminate all supernaturally based "atomic facts" (or presumed atomic facts) from consideration or any relevance to human concerns and lives.

We go on to the next set of principles of interest:

12) The existence and non-existence of atomic facts is the reality. (The existence of atomic facts we also call a positive fact, their non-existence a negative fact.)

 13) Atomic facts are independent of one another.

14) From the existence or non-existence of an atomic fact we cannot infer the existence or non-existence of another.

15) The total reality is the world. We make to ourselves pictures of facts.  The picture presents the facts in logical space, the existence and non-existence of atomic facts. The picture is a model of reality. 

16) The totality of true thoughts is a picture of the world.  The thought contains the possibility of the state of affairs which it thinks. What is thinkable is also possible. We cannot think anything unlogical, for otherwise we should have to think unlogically.

Following the preceding set, we can say the existence of fire (in terms of burning material things)  is a positive fact, while "supernatural fire" (i.e. which burns non-material things) is a negative fact.  By principle (15) it is clear that any "model of reality" will, of course, encompass both the existence and non-existence of atomic facts in its logical space or discourse.  In  a rational system of thought the true atomic facts are accepted as such while the false atomic facts ("negative"facts) are not - though their existence is acknowledged.

For example, in the model of reality one accepts as a rationalist there is acknowledged a constellation of atomic facts, e.g. "Saturn has rings", "Fire burns most material things",  "Spain is a country" etc. And at the same time we (grudgingly) reckon in a lesser constellation of non-existent atomic facts, e.g. "supernatural fire burns souls", "demons stoke supernatural fires",  "angels dance on the heads of pins." etc. etc.  In effect, this rationalist model of reality accepts the first but not the second, though it acknowledges the presence of the latter.  Well, because so many people in the world are gullible enough to accept them - and we have to deal with these folks.

All models of reality then will ab initio reference all those facts they accept, and all those (negative) facts they do not.  (Evangelical Christians, for example, will include all facts pertaining to Darwinian evolution in their negative fact category. )

Now, the former constellation of  rationalist  positive facts is essentially what Wittgenstein would refer to as "the totality of true thoughts"  and this yields (for us rationalists) a picture of the world.  We also assert that "picture of the world" is faithful to reality for which the other other negative facts are not. 

When in principle (16) Wittgenstein writes "what is thinkable is possible" he means with the proviso that the thinkable is logical, meaning based on the reality of  true thoughts - not false ones.   On the other hand,  that segment of humans who think in terms of supernatural fires and demons stoking them, are thinking "unlogically" - in Wittgenstein's parlance.   (I prefer the term illogically, though Wittgenstein is clearly attaching a specific meaning to his use of his term with 'un-').

Now we regard the final two principles of interest:

17) No proposition can say anything about itself, because the propositional sign cannot be contained in itself (that is the “whole theory of types”).

18)  It used to be said that God could create everything, except what was contrary to the laws of logic. The truth is, we could not say of an “unlogical” world how it would look. To present in language anything which “contradicts logic” is as impossible as in geometry to present by its co-ordinates a figure which contradicts the laws of space; or to give the co-ordinates of a point which does not exist

That no proposition can say anything about itself ought to be self evident. For example:

p=  "The circumference of a circle is greater than its radius"

Says nothing about itself.  What it says concerns the relation (R) between the circumference (C) and the radius (r) such that:  R: C > r

Principle (18) is perhaps one of the most important articulated in the Tractatus, and it bears more generally on deeper issues and questions, such as: Can science and religion have anything to say to each other, or any relationship, period?  One of the most quoted illustrations of the first sentence in (18) revolves around some variation of the question: Could God create a rock that he can't lift?  On the one hand we are informed (by the religious) that God is "omnipotent" so he can do anything, so that creating such a rock ought to be possible. But on the other hand, if it is claimed "too heavy" to lift it contradicts the laws of logic.  In this case, such a world is deemed "unlogical".  In like manner, the very rendering of such an example is preposterous or better, meaningless.

Natural science, empirical science would flat assert there can be no existent (or entity)  which creates or exists outside the laws of logic.  And here I am including the laws of quantum logic as well as classical,  e.g.

http://brane-space.blogspot.com/2009/09/foray-into-quantum-logical-and.html

 A majority of religions claim, for example, that a supernatural domain exists and is populated by supernatural entities. However, as we've seen, the constellation of supernatural entities (demons, Satan, souls etc.) are based on entities which contradict the settled atomic (positive) facts that comprise an actual model of reality.   The existence of such elements or entities is therefore  as impossible  as presenting a figure in geometry which contradicts the laws of space, or to "give coordinates to a point that does not exist."

The same can be said for any proposition that claims a "miracle", e.g.

"In the miracle of Fatima the Sun was displaced and whirled around."    

The devotees of the Fatima miracle assert the Sun actually gyrated and moved back and forth before 70,000 devout observers.  But, alas, no telescopes or astrometric instruments anywhere on Earth recorded such a phenomenon. The only conclusion?  It did not occur, did not exist as a positive fact, in this case an observational "atomic" fact. Hence, had to be a mass hallucination.

From a strictly rationalist viewpoint any actual motion of the Sun that day would have to be deemed more miraculous than a mass hallucination.  Hence, it meets David Hume's test for any potential real miracle, i.e.

"No testimony is sufficient to establish a miracle, unless the testimony be of such a kind that its falsehood would be more miraculous than the fact which it endeavors to establish."

This leads us to another (related) proposition in the Tractatus (p. 67):

"If God creates a world in which certain propositions are true, he thereby also creates a world in which all propositions consequent on them are true. And similarly, he could not create a world in which the proposition 'p' is true without creating all its objects"

For example, if the proposition:

p=  "The Sun exhibits no motion specific to one location."

Is true, then it means all propositions attendant on it are also true.  I.e.  all  solar behavior is uniformly visible to all observers at the same time, with observational access to the Sun.   Thus, if the Sun were to suddenly  slow in its rate of rotation, this has to be visible to all solar observers wherever they may be, assuming they have daytime access.  If this proposition be true then no world can be created by a hypothetical deity such that any ancillary aspects of the proposition aren't also true. At the same time, this means by extension that   any claimed unusual motion of the Sun - say gyrations - specified only visible from one special location (e.g. Fatima) must be false.   

Wittgenstein, as can be seen from the examples illustrated, has provided us with a logical scaffolding of immense power which can be used to advance the cause of logic and of  reason employed  in specific  arguments.  

See Also:

Is the Religious Brain Capable of Reason?