VS.

# Therefore vs. Thus

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• Therefore

Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically follows from one or more statements. A valid logical argument is one in which the conclusion is entailed by the premises, because the conclusion is the consequence of the premises. The philosophical analysis of logical consequence involves the questions: In what sense does a conclusion follow from its premises? and What does it mean for a conclusion to be a consequence of premises? All of philosophical logic is meant to provide accounts of the nature of logical consequence and the nature of logical truth.Logical consequence is necessary and formal, by way of examples that explain with formal proof and models of interpretation. A sentence is said to be a logical consequence of a set of sentences, for a given language, if and only if, using only logic (i.e. without regard to any personal interpretations of the sentences) the sentence must be true if every sentence in the set is true.Logicians make precise accounts of logical consequence regarding a given language

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. The Polish logician Alfred Tarski identified three features of an adequate characterization of entailment: (1) The logical consequence relation relies on the logical form of the sentences, (2) The relation is a priori, i.e. it can be determined with or without regard to empirical evidence (sense experience), and (3) The logical consequence relation has a modal component.

Wikipedia

For that or this purpose, referring to something previously stated.

Consequently, by or in consequence of that or this cause; referring to something previously stated.

"Traditional values will always have a place, therefore they will never lose relevance."

In this way or manner.

"If you throw the ball thus, as I’m showing you, you’ll have better luck hitting the target."

As a result.

"I have all the tools I need; thus, I will be able to fix the car without having to call a mechanic."

Wiktionary
• Therefore (conjunction)

For that or this reason, referring to something previously stated; for that.

• Therefore (conjunction)

Consequently; by consequence.

• Thus (noun)

The commoner kind of frankincense, or that obtained from the Norway spruce, the long-leaved pine, and other conifers.

In this or that manner; on this wise.

To this degree or extent; so far; so; as, thus wise; thus peaceble; thus bold.

Webster Dictionary

(used to introduce a logical conclusion) from that fact or reason or as a result;

"therefore X must be true"

"the eggs were fresh and hence satisfactory"

"we were young and thence optimistic"

"it is late and thus we must go"

"the witness is biased and so cannot be trusted"

as a consequence;

"he had good reason to be grateful for the opportunities which they had made available to him and which consequently led to the good position he now held"

• Thus (noun)

an aromatic gum resin obtained from various Arabian or East African trees; formerly valued for worship and for embalming and fumigation

(used to introduce a logical conclusion) from that fact or reason or as a result;

"therefore X must be true"

"the eggs were fresh and hence satisfactory"

"we were young and thence optimistic"

"it is late and thus we must go"

"the witness is biased and so cannot be trusted"

in the way indicated;

"hold the brush so"

"set up the pieces thus"

Princeton's WordNet