256 Syllogisms - Fourth Figure

                                            

AAA-4 

All philosophers (P) are Greeks (M).
All Greeks (M) are wise men (S).
Therefore all wise men (S) are philosophers (P).

 EAA-4 

No philosophers (P) are Greeks (M).
All Greeks (M) are wise men (S).
Therefore all wise men (S) are philosophers (P).

IAA-4 

Some philosophers (P) are Greeks (M).
All Greeks (M) are wise men (S).
Therefore all wise men (S) are philosophers (P).
 

OAA-4 

Some philosophers (P) are not Greeks (M).
All Greeks (M) are wise men (S).
Therefore all wise men (S) are philosophers (P).
 

AAE-4                   

All philosophers (P) are Greeks (M).
All Greeks (M) are wise men (S).
Therefore no wise men (S) are philosophers (P). 

EAE-4 

No philosophers (P) are Greeks (M).
All Greeks (M) are wise men (S).
Therefore no wise men (S) are philosophers (P). 

IAE-4 

Some philosophers (P) are Greeks (M). 
All Greeks (M) are wise men (S).
Therefore no wise men (S) are philosophers (P).

OAE-4 

Some philosophers (P) are not Greeks (M).
All Greeks (M) are wise men (S).
Therefore no wise men (S) are philosophers (P).

AAI-4 

All philosophers (P) are Greeks (M).
All Greeks (M) are wise men (S).
Therefore some wise men (S) are philosophers (P). 

EAI-4 

No philosophers (P) are Greeks (M).
All Greeks (M) are wise men (S).
Therefore some wise men (S) are philosophers (P).

IAI-4                      VALID 

Some philosophers (P) are Greeks (M).
All Greeks (M) are wise men (S).
Therefore some wise men (S) are philosophers (P). 

OAI-4 

Some philosophers (P) are not Greeks (M).
All Greeks (M) are wise men (S).
Therefore some wise men (S) are philosophers (P). 

AAO-4  

All philosophers (P) are Greeks (M).
All Greeks (M) are wise men (S).
Therefore some wise men (S) are not philosophers (P). 

EAO-4       

No philosophers (P) are Greeks (M).
All Greeks (M) are wise men (S).
Therefore some wise men (S) are not philosophers (P). 

IAO-4  

Some philosophers (P) are Greeks (M).
All Greeks (M) are wise men (S).
Therefore some wise men (S) are not philosophers (P).   

OAO-4 

Some philosophers (P) are not Greeks (M).
All Greeks (M) are wise men (S).
Therefore some wise men (S) are not philosophers (P). 

AEA -4 

All philosophers (P) are Greeks (M).
No Greeks (M) are wise men (S).
Therefore all wise men (S) are philosophers (P).     

EEA-4    

No philosophers (P) are Greeks (M).
No Greeks (M) are wise men (S).
Therefore all wise men (S) are philosophers (P). 

IEA-4  

Some philosophers (P) are Greeks (M).
No Greeks (M) are wise men (S).
Therefore all wise men (S) are philosophers (P). 

OEA-4 

Some philosophers (P) are not Greeks (M).
No Greeks (M) are wise men (S).
Therefore all wise men (S) are philosophers (P). 

AEE-4                  VALID  

All philosophers (P) are Greeks (M).
No Greeks (M) are wise men (S).
Therefore no wise men (S) are philosophers (P).
     

EEE-4

No philosophers (P) are Greeks (M).
No Greeks (M) are wise men (S).
Therefore no wise men (S) are philosophers (P).
     

IEE -4        

Some philosophers (P) are Greeks (M).
No Greeks (M) are wise men (S).
Therefore no wise men (S) are philosophers (P). 

OEE-4 

Some philosophers (P) are not Greeks (M).
No Greeks (M) are wise men (S).
Therefore no wise men (S) are philosophers (P).
 

AEI -4 

All philosophers (P) are Greeks (M).
No Greeks (M) are wise men (S).
Therefore some wise men (S) are philosophers (P).     

EEI -4        

No philosophers (P) are Greeks (M).
No Greeks (M) are wise men (S).
Therefore some wise men (S) are philosophers (P). 

IEI -4       

Some philosophers (P) are Greeks (M).
No Greeks (M) are wise men (S).
Therefore some wise men (S) are philosophers (P). 

OEI-4 

Some philosophers (P) are not Greeks (M).
No Greeks (M) are wise men (S).
Therefore some wise men (S) are philosophers (P). 

AEO-4 

All philosophers (P) are Greeks (M).
No Greeks (M) are wise men (S).
Therefore some wise men (S) are not philosophers (P).     

EEO-4       

No philosophers (P) are Greeks (M).
No Greeks (M) are wise men (S).
Therefore some wise men (S) are not philosophers (P). 

IEO-4         

Some philosophers (P) are Greeks (M).
No Greeks (M) are wise men (S).
Therefore some wise men (S) are not philosophers (P).

OEO-4 

Some philosophers (P) are not Greeks (M).
No Greeks (M) are wise men (S).
Therefore some wise men (S) are not philosophers (P). 

AIA-4 

All philosophers (P) are Greeks (M).
Some Greeks (M) are wise men (S).
Therefore all wise men (S) are philosophers (P). 

EIA-4         

No philosophers (P) are Greeks (M).
Some Greeks (M) are wise men (S).
Therefore all wise men (S) are philosophers (P). 

IIA-4  

Some philosophers (P) are Greeks (M).
Some Greeks (M) are wise men (S).
Therefore all wise men (S) are philosophers (P).     

OIA-4 

Some philosophers (P) are not Greeks (M).
Some Greeks (M) are wise men (S).
Therefore all wise men (S) are philosophers (P). 

AIE-4         

All philosophers (P) are Greeks (M).
Some Greeks (M) are wise men (S).
Therefore no wise men (S) are philosophers (P). 

EIE-4         

No philosophers (P) are Greeks (M).
Some Greeks (M) are wise men (S).
Therefore no wise men (S) are philosophers (P). 

IIE-4       

Some philosophers (P) are Greeks (M).
Some Greeks (M) are wise men (S).
Therefore no wise men (S) are philosophers (P).

OIE-4 

Some philosophers (P) are not Greeks (M).
Some Greeks (M) are wise men (S).
Therefore no wise men (S) are philosophers (P). 

AII-4                   

 All philosophers (P) are Greeks (M).
Some Greeks (M) are wise men (S).
Therefore some wise men (S) are philosophers (P).
 

EII-4  

No philosophers (P). are Greeks (M).
Some Greeks (M) are wise men (S).
Therefore some wise men (S) are philosophers (P).
     

III-4  

Some philosophers (P) are Greeks (M).
Some Greeks (M) are wise men (S).
Therefore some wise men (S) are philosophers (P).
     

OII-4 

Some philosophers (P) are not Greeks (M).
Some Greeks (M) are wise men (S).
Therefore some wise men (S) are philosophers (P).
 

AIO-4         

All philosophers (P) are Greeks (M).
Some Greeks (M) are wise men (S).
Therefore some wise men (S) are not philosophers (P). 

EIO-4                    VALID             

No philosophers (P) are Greeks (M).
Some Greeks (M) are wise men (S).
Therefore some wise men (S) are not philosophers (P). 

IIO-4  

Some philosophers (P) are Greeks (M).
Some Greeks (M) are wise men (S).
Therefore some wise men (S) are not philosophers (P).    

OIO-4 

Some philosophers (P) are not Greeks (M).
Some Greeks (M) are wise men (S).
Therefore some wise men (S) are not philosophers (P). 

AOA-4   

 All philosophers (P) are Greeks (M).
Some Greeks (M) are not wise men (S).
Therefore all wise men (S) are philosophers (P). 

EOA-4 

No philosophers (P) are Greeks (M).
Some Greeks (M) are not wise men (S)
Therefore all wise men (S) are philosophers (P).     

IOA-4  

Some philosophers (P) are Greeks (M).
Some Greeks (M) are not wise men (S)
Therefore all wise men (S) are philosophers (P).     

OOA-4 

Some philosophers (P) are not Greeks (M).
Some Greeks (M) are not wise men (S)
Therefore all wise men (S) are philosophers (P). 

AOE-4       

All philosophers (P) are Greeks (M).
Some Greeks (M) are not wise men (S)
Therefore no wise men (S) are philosophers (P). 

EOE-4  

No philosophers (P) are Greeks (M).
Some Greeks (M) are not wise men (S)
Therefore no wise men (S) are philosophers (P).     

IOE-4  

Some philosophers (P) are Greeks (M).
Some Greeks (M) are not wise men (S)
Therefore no wise men (S) are philosophers (P).

 

OOE-4 

Some philosophers (P) are not Greeks (M).
Some Greeks (M) are not wise men (S)
Therefore no wise men (S) are philosophers (P).  

 AOI-4         

All philosophers (P) are Greeks (M).
Some Greeks (M) are not wise men (S)
Therefore some wise men (S) are philosophers (P). 

EOI-4  

No philosophers (P) are Greeks (M).
Some Greeks (M) are not wise men (S)
Therefore some wise men (S) are philosophers (P).

 IOI -4          

Some philosophers (P) are Greeks (M).
Some Greeks (M) are not wise men (S).
Therefore some wise men (S) are philosophers (P). 

OOI-4

Some philosophers (P) are not Greeks (M).
Some Greeks (M) are not wise men (S).
Therefore some wise men (S) are philosophers (P). 

AOO-4  

All philosophers (P) are Greeks (M).
Some Greeks (M) are not wise men (S).
Therefore some wise men (S) are not philosophers (P).
     

EOO-4       

No philosophers (P) are Greeks (M).
Some Greeks (M) are not wise men (S).
Therefore some wise men (S) are not philosophers (P).

IOO-4         

Some philosophers (P) are Greeks (M).
Some Greeks (M) are not wise men (S).
Therefore some wise men (S) are not philosophers (P).

OOO-4 

Some philosophers (P) are not Greeks (M).
Some Greeks (M) are not wise men (S).
Therefore some wise men (S) are not philosophers (P).