Math as language

[shahar]

Can I define axiom as Fact and as it is that, it will be in tense of Present Simple only?

Can one refute my way of thinking?

 

[JeffM]

This is really not a math question, but rather a question of English grammar.

It is false that English requires that a fact must be stated in the present tense. We do not say

Israel declares its independence way back in 1948.

It is true that mathematical axioms are almost invariably stated in the present tense. The reason is not because they are considered true. The reason is that they are considered true at the time of utterance.

 

[shahar]

This is really not a math question, but rather a question of English grammar.

It is false that English requires that a fact must be stated in the present tense. We do not say

Israel declares its independence way back in 1948.

It is true that mathematical axioms are almost invariably stated in the present tense. The reason is not because they are considered true. The reason is that they are considered true at the time of utterance.

I don't under the underline text.

Can you elaborate the meaning of "Axioms is considered true at the time of utterance"?
1. If I were try to translate it to Hebrew it is mean when I said it or We said it (The utterance) is considered true,
Maybe I guess you mean that " the utterance is always" but I don't really find it the dictionary and i need to guess.
So what does you mean?

2. .I don't understand the grammatical example you give, it has't have a sense also in Hebrew.
You said Israel "coming back" by declaring (?) its independent... (????)
(?!)

 

[JeffM]

I don't under the underline text.

Can you elaborate the meaning of "Axioms is considered true at the time of utterance"?
1. If I were try to translate it to Hebrew it is mean when I said it or We said it (The utterance) is considered true,
Maybe I guess you mean that " the utterance is always" but I don't really find it the dictionary and i need to guess.
So what does you mean?

2. .I don't understand the grammatical example you give, it has't have a sense also in Hebrew.
You said Israel "coming back" by declaring (?) its independent... (????)
(?!)

If we ignore the numerous complications involving the present perfect and oddities like the historical present, English tenses simply indicate time relative to when a statement is made rather than to truth. (Other Indo-European languages use mode to indicate belief, but English has only residual aspects of mode and uses different means to indicate counter-factual statements.)

"Israel declares independence in 1948" is not idiomatic because it happened in the past. Consequently, we should use the past tense. "Israel declared independence in 1948." It is a true statement even though it is in the past tense. Tense relates to time rather than belief in the truth.

We state axioms in the present because we mean they are true now. "I am married" means that I am married at the present time. Of course it does not deny that I was also married yesterday and last week and last year (although there was a time when I was not married).

"Two things that are equal to a third thing are themselves equal" is true at this very instant.

I shall not bother to explain the temporal idiom "way back" in distinction to the spatial meaning of "the way back" as being completely off topic for a math site. If you want to discuss the complexities of English grammar and usage, I recommend English Learners Stack Exchange, where I frequently post.

 

[Dr.Peterson]

Can I define axiom as Fact and as it is that, it will be in tense of Present Simple only?

Can one refute my way of thinking?

The simple present tense in English has several uses, as stated for example here:

• USE 1 Repeated Actions
  
  
  
  
  
  Use the simple present to express the idea that an action is repeated or usual. The action can be a habit, a hobby, a daily event, a scheduled event or something that often happens. It can also be something a person often forgets or usually does not do.
• USE 2 Facts or Generalizations
  
  
  
  
  
  The simple present can also indicate the speaker believes that a fact was true before, is true now, and will be true in the future. It is not important if the speaker is correct about the fact. It is also used to make generalizations about people or things.
• USE 3 Scheduled Events in the Near Future
  
  
  
  
  
  Speakers occasionally use simple present to talk about scheduled events in the near future. This is most commonly done when talking about public transportation, but it can be used with other scheduled events as well.
• USE 4 Now (Non-Continuous Verbs)
  
  
  
  
  
  Speakers sometimes use the simple present to express the idea that an action is happening or is not happening now. This can only be done with non-continuous verbs and certain mixed verbs.

The second is its meaning in stating an axiom, which is true for all time (including right now).

I'm not sure what alternative you have in mind, or why you are asking.