What Is Truth Tables – Definition, Meaning And Concept

The truth is something very relative. According to Sergio Matos, when a court asks witnesses to swear to tell the whole truth and nothing but the truth and the whole truth and they do so, they are lying. Truth is a relationship between reality and the knowledge one has of it. These knowledge may be more or less close to reality but never fully coincide with it.

Since the existence of philosophy, legal sciences and social networks, the truth has always been an object of debate. How can we get to know the truth if we all have different points of view? Different knowledge of reality? Different life experiences?

Between the end of the 19th century and the beginning of the 20th century, the search for an answer to this question led to the development of an objective logical method: the semantic method and its main tool: truth tables, with which statements are analyzed.

Basic concepts

According to the Encyclopedic Dictionary Océano Uno Color (1997: 595), a statement can be defined in two ways:

1. As a sentence or sequence of grammatical sentences and
2. Like the set of words with which the theorem to be proved is stated, the problem to be solved, etc.

The truth tables of the semantic method were used in the logical-algebraic tradition by authors such as Peirce (in unpublished notes prior to 1910) or Post (1920). However, it was authors such as Bertrand Russell (1918) and Ludwig Wittgenstein (1921) who made it known as an instrument for analyzing the meaning of statements in terms of truth conditions.

According to Wittgenstein (2005), truth tables serve to determine the truth conditions of a statement, that is, its meaning, based on the truth conditions of its atomic elements. In other words, the truth table tells us in which situations the statement is true and in which it is false.

Let’s take a sentence as an example:

There was a fight in the bar last night and several patrons were injured.

The first part of the sentence before the connector “and” is atomic sentence 1 (PA1), while the one after the connector is atomic sentence 2 (PA2). They are considered to be atomic propositions because nothing can be deduced from them, (they state a fact and that’s all) separately. When these two atomic propositions are joined we get a logical proposition.

This logical proposition, in particular, results in a logical conjunction, since two conditions are met simultaneously or nearly simultaneously that allow us to infer the truth. And that we can represent like this:

Truth table 1

However, it may be the case that there is no way to verify a fact because it has not yet happened but could happen.

For example:

If they finish repairing my bike today, tomorrow I’m going to get to work early.

Truth table 2

PA1
In this second example there are four possibilities. There can be: a) a logical conjunction in which both atomic propositions are true. b) a disjunction in the case that both atomic propositions are false. c) that the first atomic statement is true but the second is false, or that the first statement is false and the second true, in which case we are dealing with a conditional statement, that is to say that an atomic statement can be true or false if given certain conditions.

There is also the case that there are propositions that do not fit into these categories.

For example:

There are trees growing among the clouds, are they going to throw their fruits to us when the moon rises?

Truth table 4

This case may seem like a disjunction, but it is not because the disjunction occurs when the event it narrates is probable. This is a denial and there are no aerial trees and therefore we will never see their fruits fall when the moon rises.

So far everything is going very well, now the difficult part begins. How to use this table to analyze a speech.

What do you need

• Have a basic command of how Word works to design a custom table.
• Know how to use Excel in case you want to work with numerical values.
•  Do a lot of research when you see irregularities in your logical analysis.

Instructions

To analyze a speech we must:

1. Select a speech that can be a text in the newspaper, a text from a book, a statement by a politician on television and even the dialogue of a character in a television or streaming series.
2. Transcribe or cut and paste the speech on a blank Word page. I selected a dialogue between two characters from a TV series I’m watching: We had a simulation (…) of terror. What to do when a shooter comes to the office and starts killing people? Do you run, look for a hole in the stairs or barricade yourself in your office? (Source: Tell me a story Temp. 1. Ch.1)
3. You make a table where you divide the text into atomic propositions that you identify.

Then you make a truth table with the propositions of the dialogue, which depending on the size of the text you have chosen to analyze can give you something more or less like this:

1. As we can see in this short dialogue, the first proposition is true because there is nothing to tell us otherwise. The second and third core statements are either a logical statement with a conjunction(if both events hold), a disjunction (if the shooter never enters the office and shoots no one), or a conditional statement (in which the shooter enters the office). the office but decide not to shoot anyone). Nuclear propositions 4, 5, 6 are exclusive and conditional, if he decides to do one thing, you exclude the others because in such a situation you don’t have time to choose more than one option.
2. There are also those who add the condition of indeterminate (represented by I) when they do not know if the statement is true (V) or false (F). And even two columns are added to evaluate if we can establish with certainty if even being false one of the statements or atomic propositions that constitute the logical proposition (LP) can still be considered predominantly true.

In mathematics, this same table can be replaced by numbers, where 1 is true and 0 is false.

Tips

When you make a truth table you should take into account:

• The extension of the dialogue or the text that you want to analyze, since texts that are too long tend to present greater variability when analyzing atomic propositions.
• You must also be observant when choosing texts, since not all of them are suitable to be represented in a truth table, such as poetry or certain types of stories.
• And you need to practice a lot to master it well.
• It is also necessary to differentiate between language, language and speech.