Wittgenstein: Tractatus Logico Philosophicus Proposition 4.023

24 May

4.023 – A proposition must restrict to two alternatives: yes or no.  In order to do that, it must describe reality completely.                A proposition is a description of  a state of affairs……………………etc……

In Wittgenstein’s Tractatus, his statement 4.023 beings by stating that a proposition itself must restrict reality into 2 alternatives: yes or no- given that a proposition describes reality completely and that a proposition is a description of a state of affairs. It goes on in that same proposition to explain its justification further.

That statement or statements after that do no justify why/how reality is restricted to the alternatives of yes and no. I dont feel that I can write a whole paper about why this is a somewhat false statement, but I felt it needed addressing as I was reading the Tractatus.

Think about things that go on every day in your life.  Contemplate upon the problems you deal with on a daily basis and how you solve those problems. In retrospection on the previous issues you have dealt with, are those issues simple ones? Are the truths and falsities easily recognizable between each other making it easier for you to react accordingly? If you are able to understand what things are true and false and you are able to sort through them and recognize their distinctions, the issues of daily life would not really be issues. They would be momentary discrepancies that you immediately address. Wittgenstein states in statement 4.023 that propositions in reality have only 2 possible answers of yes or no. My opinion is that if this were true, life would be a lot easier.

Propositions of reality differentiate in truth and falsity in variations of time, perception, and in existence. These 3 variations are ones that I think exist. There may be more, but these 3 are what I immediately understand.

First, I think that propositions of reality are going to vary in truth and falsity (yes or no) by variations in time. What may be true one second/month/year/decade may not be true the next and vice versa. For example, ” if the economy is prosperous, then technology will advance leading to better computers”. Logically read:

E –> ( T –> C)



Reiterated, if all of the economy gets prosperous then some technology will advance leading to better computers.

Thinking about time itself, do you think that in any time in the whole existence of the universe that a better economy will lead to a technology advance and better computers? No. In most of the existence of the world and the universe, computers did not even exist. Yes technology can advance, for example, human precursor Olduvan tools get more advanced leading to Acheulian tools. If the proposition was just that better economies lead to better technology, that would lead to a truth without exceptions, but what Wittgenstein says in 4.023 is that all propositions of reality lead to a yes or no (truth/falsity) answer. In E–> (T–>C) a full truth or full falsity cannot be inferred due to the inconsistency of time.

I think also that 4.023 is wrong because of the inconsistency of perception. First, looking at it from Spinoza’s modes of substance, different interpretations and perceptions of the same existence can be inferred. A substance of any kind has infinite macrocosmic and microcosmic modes that modify and perceive the same substance. If each mode perceived the substance in the same fashion, only one mode would exist, but many inferences and interpretations of the same existence can be concluded. Looking at it in another way, a radical conservative would view a senate bill and its effects way differently than a left liberal would. Conservatives and liberals have beliefs and values that govern and even possibly distort their perception of the surrounding world. Their beliefs and ideas are going to cause them to have their own take on a bill or anything else in discussion.

For example, a senate bill is proposed and is going to be voted on soon. It involves creating a new income tax category that would take  money out of your pay check that would go to governmental environment agencies.  Before I even lay this out logically, think about the controversy this would spark and how each political side would react to something like this. Proposition: If we create a new income tax category to give money to governmental environment agencies, the world will be a cleaner better place for us to live. Logically:

I –> (C & B)

I represents the environmental agency income tax category and C and B meaning cleaner and better world.


∀xIx –>∀x(Cx & Bx)

When I use the examples of liberals and conservatives having different perceptions, this is not the only way modes or people could have different perceptions of the same thing. Liberals and conservatives are just a good example because they are 2 opposite sides of the political spectrum. Perceptions of the same existence are infinite in manner and fashion.

Thinking about the perspective of the liberals, this proposition would be true. Liberals think that the environment should get more money to improve and this would be a good solution to environmental problems. Thinking about the perspective of the conservatives, this proposition would be false because conservatives do not think that the environment is important and they also do not think  that the government would distribute that income tax money to the environment and its purposes. Two existences/people are interpreting the same proposition/thought and infinite variations of conclusions are inferred. A moderate view of this might look at this proposition and think it to be true in some ways and false in others: government would take some of that environmental income tax, but the money that would go to environmental agencies would make the world a tiny bit cleaner and better. These are just 3 examples to an infinite number of inferences to the truth of this proposition. Most inferences do not lead to full truth or full falsity.

The variation of existence relates fully to the time variation because at the time of existence of a being, a proposition of reality may be true and then the next moment that certain existence may vanish from existence making that entire proposition half true or totally false.

Gray Areas

If you have a proposition that says one thing is another or any other proposition, do you really think that every inference will fall either into the category of truth or falsity? In any proposition, is every answer going to be true or false and not sometimes true/sometimes false   and not  some true/some false?

Here is a good example to determine if you can eliminate all possibilities of half/some truths or falsities. “All Libertarians are potheads”. A very simple proposition. Logically:

∀x(Lx –> Px)

All L’s are P’s.

Looking at this logically and keeping in mind 4.023, do you think this is an all true or all false statement. Here are the conclusions I think cannot be left out when contemplating upon the truth of this proposition:

C1:  True, they are only in politics to get pot legalized

C2: False, they just feel that pot should not be a substance that the government should control use of.

C3: Some true/false,  some are potheads and the rest just feel that pot should not be illegal

C4: Sometimes true/false, they were potheads back in the seventies, eighties and early nineties, but not anymore.

Conclusions 1 and 2 fall into place with 4.023 because they condone all truth or all falsity to that proposition. But when looking at this proposition, can C1 and C2 be the only possible conclusions to this argument? If you want to correctly use critical reasoning and logic, you cannot blatantly state that all truth or all falsity are the only inferences of all propositions of reality.

C3 and C4 are gray areas. In my opinion, opposing Wittgenstein’s 4.023, all propositions of reality have gray areas in time, perception and existence. If you agree with 4.o23’s beginning statement, you need to study logic and critical reasoning further. Reality is way too complex to restrict its propositions to two possible answers.

So in opposition to Wittgenstein, there are gray areas and other inferences than true and false (yes or no).

Comment below your thoughts and opinions.


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